research article multiobjective route planning model...

Research ArticleMultiobjective Route Planning Model andAlgorithm for Emergency Management

Wen-mei Gai12 Zhong-an Jiang1 Yun-feng Deng2 Jing Li3 and Yan Du1

1School of Civil and Environmental Engineering University of Science and Technology Beijing Beijing 100083 China2Chinese Academy of Governance Beijing 100089 China3Institute of Public Safety China Academy of Safety Science and Technology Beijing 100012 China

Correspondence should be addressed to Zhong-an Jiang jza1963263net

Received 4 October 2014 Revised 5 December 2014 Accepted 8 December 2014

Academic Editor Erik Cuevas

Copyright copy 2015 Wen-mei Gai et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In order tomodel route planning problem for emergency logisticsmanagement taking both route timeliness and safety into accounta multiobjective mathematical model is proposed based on the theories of bounded rationality The route safety is modeled as theproduct of safety through arcs included in the path For solving thismodel we convert themultiobjective optimization problem intoits equivalent deterministic form We take uncertainty of the weight coefficient for each objective function in actual multiobjectiveoptimization into account Finally we develop an easy-to-implement heuristic in order to gain an efficient and feasible solution andits corresponding appropriate vector of weight coefficients quickly Simulation results show the effectiveness and feasibility of themodels and algorithms presented in this paper

1 Introduction

In recent years a number of frequent natural disasters andman-made catastrophic events happen occasionally [1ndash3] Asan emerging research area emergency logistics managementis attracting more and more attention of researchers [4ndash8] Disaster relief requires efforts on many fronts providingrescue health and medical assistance water food shelterand long-term recovery efforts Much of successful and rapidrelief relies on the logistical operations of supply delivery[9 10] Furthermore important or hazardous materials mustbe transferred from the affected areas to safety areas eventhose people at risk in some disasters like gas leak and fire alsoshould be evacuated from the affected areas to safety areasMany of successful and rapid evacuation and transfer tasksrely on the effective emergency logistics operations

Route planning is one of the fundamental problemsin emergency logistics management Among the existingresearches of emergency logistics management [11ndash14] sev-eral complicated models have been built considering thedisaster conditions But most of the existing research worksof emergency logistics management took time as the most

important factor in route planning to be considered Theobjective of the existing route planning model was to mini-mize the time needed to complete the logistics transmissionprocess However the route safety should also be taken intoaccount as an objective of the route planningmodel for emer-gency logistics management considering the vulnerability ofhumans during disaster time

On the other hand most of them consider the parameterson each arc of the logistics network as constants In fact thetravel conditions on the arcswill be greatly affected by disasterextension especially under some disasters like hurricaneflood and gas leak that will extend gradually in time andspace [15 16] For example the degree of congestion on eacharc will be dynamic under disaster conditions which willmake the travel speed on each arc change correspondinglyand the safety through each arc may also change underdisaster conditions Furthermore the change extentwill differwith the positions of the arcs and the severity of the disaster

Yuan and Wang [15] constructed a model to express theeffect that the disaster extension influenced the travel speedMoreover they built a multiobjective model taking moreactual factors into account To the best of our knowledge it is

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 565403 17 pageshttpdxdoiorg1011552015565403

2 Mathematical Problems in Engineering

necessary for us to go on the research towards this directionZhang et al [16] proposed a novel bioinspiredmethod to solvethe selection model for emergency logistics managementunder real-time effect of disaster extension Both of themfirst convert two objective functions into a single-objectivefunction by using the weighted-sum method and assume theweighting coefficients as fixed real numbers However dueto the complexity of actual problems and subjectivity as wellas limitations of decision-makersrsquo cognition decision-makersoften encounter a lot of uncertainties so that they can onlyget variation ranges of the weighting coefficients [17 18]Thisuncertainty will give decision-makers a great deal of difficultyin emergency decision-making

In this paper we focus on the route planning problemin emergency logistics management and build a mathemat-ical model to select the optimal route The motivation ofthis research is to consider more actual factors in time ofdisaster and decision-making when building models anddesigning algorithms The factors we take into accountinclude travel time and the safety of the route as wellas uncertainty of the weight coefficient for each objectivefunction in actual multiobjective optimization The safetyof the path is modeled as the product of safety througharcs included in the path A multiobjective mathematicalmodel is built in our study and algorithms are developedto solve the model Our method for studying path selectionproblem in emergency logistics management is presented inFigure 1

As described in Figure 1 firstly a multiobjective mathe-matical model based on the theories of bounded rationality isbuilt for route planning in emergency logistics managementconsidering route timeliness and safetyThe two objectives ofthe model are to minimize total travel time along the routeand to maximize the safety of the route respectively Weproposed an easy-to-implement heuristic method in orderto gain an efficient and feasible solution quickly In ourmethod we first translate (6) into (9) and then the proposedmodel can be converted into a conditional multiobjectiveshortest path model which is different from classical shortestpath problem To solve this problem the weighted-summethod is used to convert the conditional multiobjectiveshortest path problem into a single-objective shortest pathproblem and two constraints where we take uncertaintyof the weight coefficient for each objective function inactual multiobjective optimization into account Based onthe single-objective shortest path model we can constructtwo auxiliary functions Finally the main-objective methodis used to define the optimal solution of the multiobjectiveroute planning model By this way two different heuristicalgorithms are designed to solve the proposed model In thestatic heuristic algorithm an efficient and feasible solutionand its corresponding appropriate vector of weight coeffi-cients for the multiobjective route planning model can beobtained quickly by using the classical Dijkstra algorithm and119860lowast algorithm based on the established auxiliary functions if

not considering real-time effect of disaster extension andin the dynamic heuristic algorithm an efficient and feasiblesolution and its corresponding appropriate vector of weightcoefficients for the multiobjective route planning model can

be acquired by using the modified Dijkstra algorithm and119863lowast algorithm based on the established auxiliary functions if

considering real-time effect of disaster extension Simulationresults show the effectiveness and feasibility of the model andalgorithm

This short communication is organized as followsSection 2 gives the multiobjective route planning modelfor emergency logistics management Section 3 introducespreliminaries briefly Section 4 details the proposed methodto solve route planning problem in static and dynamicenvironments respectively Section 5 shows the simulationresults in different cases to illustrate the efficiency of theproposed method Section 6 ends the communication withconclusion

2 Route Planning Model for EmergencyLogistics Management

21 Definition of Variables and Parameters (1) Let arcsdenote the ground roads and nodes denote road intersec-tions An emergency logistics network is defined by a graph119866 = (119881 119864) where 119881 = V

1 V2 V

119899 is the set of nodes and

119864 sube 119881 times 119881 is the set of arcs V1 V2 V

119899denote the nodes in

the network(2) 119897119894119895denotes the length of the arcs between nodes V

119894and

V119895 where (V

119894 V119895) isin 119864

(3) 119905119894119895 119904119894119895denote the travel time and route safety from

node V119894to V119895 respectively Let 119905

119894denote the time when the

logistics reach node V119894and 119905


logistics reach node V119895along arc (V

119894 V119895) It is obvious that

119905119894119895= 119905119895minus 119905119894

(4) 1199060119894119895

is the travel speed on arc (V119894 V119895) under free

travelling conditions Define 119906119894119895(119905) as the travel speed on arc

(V119894 V119895) in the affected area at time 119905 under disaster conditions

Observing the extension processes of some disasters suchas flood and hurricane we can find that the travel speedon each arc of the network will differ with the extension ofdisasters [15] Hence we use a congestion coefficient 120585

119894119895to

denote the change extent of the travel speed which is affectedby the position of the arc the type of the disaster and so forthThen 119906

119894119895(119905) = 120585

119894119895sdot 1199060119894119895 Based on the above definitions it can

be acquired that

int

119905119895

119905119894

119906119894119895(119905) 119889119905 = 119897

119894119895 0 lt 119894 le 119895 lt 119899 (1)

The congestion coefficient on each arc of the logisticsnetwork 120585

119894119895can be considered as a fixed valuewhen the period

of logistics operation is short namely in a static environmentBut when the period of logistics operation is long 120585

119894119895may

dynamically change with the extension of disasters in timeand the route planning problem we focus on is actually ashortest path problem in a dynamic environment

(5) 119909119894119895is the decision variable in the model 119909

119894119895= 0 when

arc (V119894 V119895) is not included in the fixed route and 119909

119894119895= 1 when

arc (V119894 V119895) is included in the fixed route

Mathematical Problems in Engineering 3

Multiobjective route planning model

Conditional multiobjective shortest path model

Constraints based onsatisfaction levels of the

Consider the timeliness of the path

Consider the safety of the path

Single-objective shortest path model

Consider real-time effect of disaster extension

No

Yes

Multiobjectivetime-varied routeplanning model

Dynamic heuristic algorithm

Static heuristic algorithm

Multiobjective route planning model in static

environments

Translate (6) into (9)

Construct two auxiliary functions

Weighted-sum method to deal with

the model

Theories of bounded rationality

Main-objective method

Prob

lem

st

atem

ent a

nd

form

ulat

ion

Prel

imin

arie

sPr

opos

ed h

euris

tic

algo

rithm

and

simul

atio

n re

sults

policymaker T(P) le lt S(P) ge ls

Figure 1 Method for studying multiobjective route planning problem in emergency logistics management

(6) Suppose that 119875 denotes a feasible route from thesource node to the destination node which is constitutedbased on the constraints as follows

119899

sum

119895=1119895 =119894

119909119894119895minus

119899

sum

119895=1119895 =119894

119909119895119894=

1 119894 = 1

minus1 119894 = 119899

0 otherwise(2)

119899

sum

119895=1119895 =119894

119909119894119895=

le 1 119894 = 119899

0 119894 = 119899(3)

119909119894119895= 0 1 119894 119895 isin 1 2 119899 (4)

Constraint (2) restricts the value of 119909119894119895to constitute route

119875 and Constraint (3) ensures that there are no circles in theroute 119875 Constraint (4) is the 0-1 integer constraint of thedecision variable 119909

119894119895

22 Bounded Rationality inDecision-Making After the 1950sit was recognized that the entire rationality model based onthe hypothesis of ldquoeconomic manrdquo is actually an ideal modelso it is impossible to guide decision-making in practice Tosolve this problem Herbert Simon proposed the boundedrationality model where the ldquosocial manrdquo was used instead

of ldquoeconomic manrdquo [19] Simonrsquos bounded rationality modelis a relatively realistic model and it considered that humanrationality is a bounded rationality between entire rationalityand entire irrationality The main points of this theory areissued as follows

(1) There are some contradictions in the connotations ofmeans-ends chain so single analysis of means-endschain would lead to inaccurate results

(2) Decision-makers seek something that is boundedrational rather than entirely rational

(3) Decision-makers seek something that is ldquogoodenoughrdquo that is something that is satisfactory ratherthan something that is best

Above all decision-makers tend to seek a route that isldquogood enoughrdquo but not the best for the practical problems

23Multiobjective Route PlanningModel for Emergency Logis-ticsManagement First of all time is one of themost preciousresources under disaster conditions We are able to grabthe initiative to save lives and fight for victory if we gainthe resource of time Therefore time is a decision-makingobjective that cannot be ignored under any emergencysituation


Furthermore observing the extension processes of somedisasters such as flood hurricane and gas leak we canfind that the vulnerability of humans on each arc of thenetwork will differ with the extension of disasters The probitapproach is usually used to determine the vulnerability ofhumans during disaster time based on which lethality ofhumans under disaster conditions can be estimated [20] Let119902119894119895denote the lethality of humans from node V

119894to V119895 then the

safety of arc (V119894 V119895) can be acquired as follows 119904

119894119895= 1 minus 119902

119894119895

where 0 le 119902119894119895le 1

Hence amultiobjective route planningmodel can be builttaking into account both time factor and route safety factorThe objectives of the model are to minimize total travel timealong the route and to maximize the safety through the routerespectively where the route safety is modeled as the productof safety through arcs included in the pathThemodel can beformulated as follows

Model I

min119879 (119875) = sum

(V119894 V119895)isin119875119905119894119895 (5)

max 119878 (119875) = prod

(V119894 V119895)isin119875119904119894119895 (6)

st

119879 (119875) le 119897119905 (7)

119878 (119875) ge 119897119904 (8)

Here 119897119905 119897119904denote the satisfaction level of travel time and route

safety through the selected route given by the emergencymakers respectively Constraints (7) and (8) are conditionsbased on the theories of bounded rationality

3 Preliminaries

31 Classical Algorithms to Solve Single-Objective ShortestPath Problem Classical algorithms to solve single-objectiveshortest path problem include static algorithms and dynamicalgorithms Dijkstra algorithm is one of the classical algo-rithms to solve shortest path problem in static environmentseffectively [21] The basic idea of the algorithm is to findshortest route from the source node step by step Dijkstraalgorithm maintains labels 119875 and 119879 with each node V

119894 which

are the total weight of the shortest path and an upper boundof the total weight on the shortest path from the source nodeto each node V

119894 respectively At any intermediate step the

algorithmmodifies the119879 labels of nodes and sets 119875 label for acertain node then it adds the node to the set of nodes with 119875

labels Thus the number of nodes with 119875 labels will increaseby one after each step and the shortest paths from the sourcenode to all the other nodes in the network will be found afterat most (119899 minus 1) steps

119860lowast algorithm [22] is another classical algorithm to solve

shortest path problem in static environments effectively 119860lowastalgorithm uses heuristic information to narrow the searchspace in the search so we can get the optimal solution fasterand more effectively than Dijkstra algorithm

Dijkstra algorithm and119860lowast algorithm are efficient in static

networks but they are not suitable for solving shortest pathproblems in dynamic networks such as dynamic environ-ments with weight on each road section changing constantly119863lowast algorithm [23 24] that is dynamic 119860lowast algorithm is one

of the classical algorithms to solve shortest path problem indynamic environments effectively which is mainly used inroute planning for robots The basic idea of the algorithm isto check the changes of the next node or the adjacent node onthe shortest route to update the shortest route when movingto the target point

32 Construction of Auxiliary Functions First we constructa new network 119866

1= (119881 119864

1) where 119864

1= 119890 119890 = (V

119894 V119895)

and 119904119894119895gt 0 It is necessary to translate it into a minimization

problem by using max 119878(119875) = minusmin 119878(119875) since (6) is amaximization problem In addition (6) is in the form ofproduct with respect to the weight of arc (V

119894 V119895) In order to

use the shortest path algorithm to solve (6) it is necessaryto translate (6) into a form of summation with respect to theweight of arc (V

119894 V119895) by using 119878(119875) = exp[ln 119878(119875)] By this

way we can obtain an equivalent form of (6) in network 1198661

as follows

min sum

(V119894 V119895)isin119875

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816 (9)

By this way the multiobjective route planning modelproposed in Section 23 can be translated into a conditionalmultiobjective shortest path model based on the theories ofbounded rationality as follows

Model II (5) and (9) st (7) and (8)Suppose that 119879min 119878min denote the optimal value of (5)

and (6) respectively And 119879max 119878max denote the value of (5)and (6) corresponding to the longest route between the sourcenode and destination node respectively Then we use theweighted-sum method to deal with (5) and (9) and convertthem into a single-objective model as follows

Model III

min119865 (120579) = 120579|ln 119878 (119875)| minus 1003816100381610038161003816ln 119878max

10038161003816100381610038161003816100381610038161003816ln 119878min

1003816100381610038161003816 minus1003816100381610038161003816ln 119878max

1003816100381610038161003816

+ 120578119879 (119875) minus 119879min119879max minus 119879min

119878min gt 0

(10)

Here (120579 120578) isin R = (120579 120578) | 120579 120578 ge 0 120579 + 120578 = 1 is thevector of weighting coefficients According to the theoremabout weighted-sum method [25ndash27] the minimizer of thiscombined function is Pareto optimal and the solution is anoninferior solution of multiobjective optimization problemwith respect to (5) and (9) Suppose that 119875

120579is the best path

obtained by Model III corresponding to an already knownweighting coefficient 120579 Based on Model III we can obtaintwo auxiliary functions as follows

119891119905(120579) = 119879 (119875

120579) = sum

(V119894 V119895)isin119875120579

119905119894119895 (11)

119891119904(120579) = 119878 (119875

120579) = prod

(V119894 V119895)isin119875120579

119904119894119895 (12)


In order to propose a feasible algorithm to solve ModelIII first we construct a new factor 119908

119894119895= 120579 sdot | ln 119904

119894119895|| ln 119878max minus

ln 119878min| +120578 sdot 119905119894119895(119879max minus119879min) for arc (V119894 V119895) where 0 lt 119904

119894119895le 1

then we have Lemmas 1 and 2 as follows

Lemma 1 Model III can be solved through single-objectiveshortest path algorithms and the optimum solution119875

120579 namely

is the shortest route with respect to the new factor 119908119894119895

Proof Consider the following

119865 (120579) = 120579|ln 119878 (119875)| minus 1003816100381610038161003816ln 119878max

10038161003816100381610038161003816100381610038161003816ln 119878min

1003816100381610038161003816 minus1003816100381610038161003816ln 119878max

1003816100381610038161003816


= 120579 sdot|ln 119878 (119875)|

1003816100381610038161003816ln 119878max minus ln 119878min1003816100381610038161003816

+ 120578 sdot119879 (119875)

(119879max minus 119879min)

minus 1198871minus 1198872

(13)

where 1198871= 120579sdot| ln 119878min(ln 119878maxminus ln 119878min)| 1198872 = 120578sdot119879min(119879maxminus

119879min) and 1198871 1198872are constants for a known network graph

1198661 Then 119865(120579) = sum

(V119894 V119895)isin119875((120579(| ln 119878min| minus | ln 119878max|))| ln 119904119894119895| +(120578119879max minus 119879min))119905119894119895) minus 119887

1minus 1198872 Then min119865(120579) = minsum

(V119894 V119895)isin119875119908119894119895minus 1198871minus 1198872 Therefore the shortest route with respect to the

new factor119908119894119895can be obtained by applying an existing single-

objective shortest path algorithm such as119860lowast algorithmor119863lowastalgorithm and the obtained route namely is the optimumsolution of Model III with respect to the vector of weightingcoefficients (120579 120578)

Lemma 2 Equations (11) and (12) are increasing functions of120579 respectively and (11) can obtain the minimum value of 119879(119875)when 120579 = 0 while (12) can obtain the maximum value of 119878(119875)when 120579 = 1

Proof Let 1198751205791 1198751205792be the optimum solution of Model III with

respect to 1205791and 120579

2 respectively where 0 le 120579

1lt 1205792le 1

Based on Model III and Lemma 1 we can obtain that

sum

(V119894 V119895)isin1198751205791

(1205791

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816+

1 minus 1205791

119879max minus 119879min119905119894119895)

le sum

(V119894 V119895)isin1198751205792

(1205791

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816

+1 minus 1205791

119879max minus 119879min119905119894119895)

sum

(V119894 V119895)isin1198751205791

(1205792

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816+

1 minus 1205792

119879max minus 119879min119905119894119895)

ge sum

(V119894 V119895)isin1198751205792

(1205792

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816

+1 minus 1205792

119879max minus 119879min119905119894119895)

(14)

Therefore 1205791(sum(V119894 V119895)isin1198751205791 | ln 119904119894119895| minus sum

(V119894 V119895)isin1198751205792 | ln 119904119894119895|)(| ln 119878min| minus | ln 119878max|) + (1minus120579

1)(sum(V119894 V119895)isin1198751205791 119905119894119895 minus sum

(V119894 V119895)isin1198751205792 119905119894119895)

(119879max minus 119879min) le 0 1205792(sum(V119894 V119895)isin1198751205791 | ln 119904119894119895| minus sum

(V119894 V119895)isin1198751205792 | ln 119904119894119895|)(| ln 119878min|minus | ln 119878max|)+ (1minus120579

2) (sum(V119894 V119895)isin1198751205791 119905119894119895minus sum

(V119894 V119895)isin1198751205792 119905119894119895)

(119879max minus 119879min) ge 0 Then we can get sum(V119894 V119895)isin1198751205791 | ln 119904119894119895| minus

sum(V119894 V119895)isin1198751205792 | ln 119904119894119895| ge 0 sum

(V119894 V119895)isin1198751205791 119905119894119895 minus sum(V119894 V119895)isin1198751205792 119905119894119895 le 0 that

is 119891119904(1205791) le 119891

119904(1205792) and 119891

119905(1205791) le 119891

119905(1205792) So we can conclude

that (11) and (12) are increasing functions of 120579 respectivelyLet 1198750 1198751denote the optimum solution of Model III with

respect to the vector of weighting coefficients (0 1) and (1 0)respectively According to Model III and Lemma 1 we canobtain that min119865(0) = minsum

(V119894 V119895)isin119875 119905119894119895(119879max minus 119879min) andmin119865(0) = sum

(V119894 V119895)isin1198750(1(119879max minus 119879min))119905119894119895 = sum(V119894 V119895)isin1198750 119905119894119895

(119879max minus 119879min) = 119891119905(0)(119879max minus 119879min) so we can conclude that

119891119905(0) = minsum

(V119894 V119895)isin119875 119905119894119895 = min119879(119875) Similarly we can get119891119904(1) = minsum

(V119894 V119895)isin119875 | ln 119904119894119895| = maxprod(V119894 V119895)isin119875119904119894119895 = max 119878(119875)

The conclusion is obtained

33 Main-Objective Method to Deal with Multiobjective Opti-mization Problems If a feasible route from the source nodeV1to the destination node V

119899is the best path obtained by

Model III and satisfies Constraints (7) and (8) we can easilyobtain that the route is a noninferior solution ofModel II thatis a noninferior solution of Model I According to Lemmas1 and 2 and Constraints (7) and (8) the set of noninferiorsolutions can be generated by using single-objective shortestpath algorithms to solve Model III when 120591 varies within theinterval [0 1]

According to Lemma 2 the optimization objectives ofroute timeliness and safety conflict each other in the processof multiobjective route planning within the set of noninferiorsolutions To solve this problem we use the main-objectivemethod to deal with the multiobjective route planningmodel The main-objective method is a method of solvingmultiobjective optimization problems The basic idea ofthis method is to seize the main objective and take intoaccount other requirements that is to select a target fromthe multiobjectives as the main target other objectives onlyneed to meet certain requirements The selection of mainobjective in multiobjective optimization problems dependson the needs of decision-makersTherefore the optimizationobjectives of the multiobjective route planning model inactual emergency logistics management can be divided intomajor and secondary optimal objectives In order to facilitatethe description we assume the optimization objective basedon (6) as the main target of the multiobjective route planningmodel Accordingly the optimal solution of the multiobjec-tive route planning model can be defined as follows

Definition 3 119877lowast is the optimal solution of the multiobjectiveroute planning model if 119879(119877lowast) = min119879(119877) 119877 isin 119876 where119876 is the set of all the noninferior solutions to Model I

According to Lemma 2 and Definition 3 we have adeduction of Lemma 2 as follows


Deduction 1 Let 120579 120577 isin [1205791 1205792] sube [0 1] and 119875

120577denote

the shortest path obtained by Model III with respect to theweighting coefficient 120577 then we can obtain that

(1) for forall120577 isin [1205791 120579]119879(119875

120577) lt 119897119905and 119878(119875

120577) le 119878(119875

120579) if 119891119905(120579) lt

119897119905

(2) for forall120577 isin [120579 1205792]119879(119875120577) gt 119897119905and 119878(119875

120577) ge 119878(119875

120579) if 119891119905(120579) gt

119897119905

(3) 119875lowast = 119875120579if 119891119905(120579) = 119897

119905and 119878(119875

120579) ge 119897119904

The optimal solution of themultiobjective route planningmodel can be acquired based on Definition 3 if119876 is obtainedBut the algorithm based on this idea is of high complexitywhich cannot meet the demand of emergency decision-making Therefore according to the auxiliary functionsconstructed in Section 32 and their properties we propose aheuristic method to generate the set of noninferior solutionsand find the optimal solution in the generated set Theproposed algorithm is a fast approximate algorithm

4 The Proposed Heuristic Algorithm

In general the approach of solving a multiobjective shortestpath problem is to convert the multiobjective shortest pathproblem into a single-objective shortest path problem basedon the weighted-sum method [15 25 28] However thedifficulty of using weighted-sum method is how to findthe reasonable weight coefficients to reflect the importanceof each single objective in the multiobjective optimizationproblem To solve this problem we proposed a heuristicmethod In our method different single-objective shortestpath algorithms are used to generate the set of noninfe-rior solutions by solving Model III when 120591 varies withinthe interval [0 1] and the satisfaction levels of secondaryoptimization objectives were converted into constraints andthe optimal route will be obtained finally by searching bestsolution of Model III in the direction of satisfaction ofthe main optimization objective in the multiobjective routeplanningmodel increasing In order to improve the efficiencyof the algorithm it is not finding the optimal solution atan even pace but quickly searching the optimal solution byreducing the current interval [120579

2 1205791] according to Deduction

1

41 Static Heuristic Algorithm to Solve Model I Based on 119860lowast

Algorithm In our approach first we remove the arcs thatdo not meet the safety conditions in the network and thenthe Dijkstra algorithm is applied to find the shortest route toobtain 119879min and 119878min What is more it is used to obtain 119879maxand 119878max based on Lemma 2 respectively so as to constructthe new factor 119908

119894119895for arc (V

119894 V119895) On the other hand the

119860lowast algorithm is used to find the optimum solution 119875

120579of

Model III corresponding to the weight vector (120579 120578) in thenetwork based on Lemma 1 Finally according to satisfactorylevels given by the decision-maker the optimal route of themultiobjective route planning model in static environmentscan be found

Pseudocode 1 presents the pseudocode of the heuristicalgorithm to solve the multiobjective route planning model

in static environments considering the sets parameters andvariables as defined in Section 21

42 Dynamic Heuristic Algorithm to Solve Model I Based on119863lowast Algorithm In many cases the travel conditions on the

arcs may be greatly affected by disaster extension especiallyunder some disasters like hurricane flood rainstorm andgas leak which will extend gradually in time and space Theroute safety and congestion of each arc will change dynam-ically under disaster extension and the changing extent willdiffer with the positions of the arcs and the severity of thedisaster In static environments 119875

0and 119875

1can be obtained

through the classical Dijkstra algorithm and Model III canbe obtained through the 119860

lowast algorithm and after severalcycles to solve Model III Model II can be finally solved whenobtaining the appropriate vector of weighting coefficients(120579lowast

120578lowast

) But in dynamic environments the three single-objective models based on (5) (6) and (8) cannot be solvedthrough either of the above two algorithms To solve thisproblem as presented in Pseudocode 2 the classical Dijkstraalgorithm is replaced by themodifiedDijkstra algorithm [15]and the 119860lowast algorithm is replaced by the 119863lowast algorithm othersteps of the algorithm to solve the route planning model indynamic environments are the same as those of the algorithmin Section 41 Pseudocode 2 presents the pseudocode of theheuristic algorithm to solve themultiobjective route planningmodel in dynamic environments

43 Algorithm Advantage The proposed algorithm not onlyis conducive to solving problems for the emergency decision-makers but also can help the decision-makers to raiseproblems When the satisfaction levels of decision-makersare known the proposed algorithm can be used to find theoptimal solution of multiobjective route planning model foremergency logistics management that is problem solutionIn addition the variations of 119878(119875) and 119879(119875) with the valueof 120579 can be acquired by using the proposed algorithm whenthe satisfaction levels of decision-makers are unknown andaccording to the above two curves the decision-maker canset different satisfaction levels for the optimization objectivefunctions in the multiobjective route planning model to putforward different optimization problems that is problempresentation

Thus the proposed algorithm in Section 4 can be used asan auxiliary tool for emergency decisions which can be usedto find the optimal route of multiobjective route planningmodel and get reasonable weighting coefficients

5 Computational Experiments

In order to show the effectiveness and feasibility of themodel and algorithm in this communication numericalexperiments are carried out to verify Lemma 2 in Section 51and test the algorithm advantages in Sections 52 to 53

51 Results of Model III When 120591 Varies within the Interval[0 1] We carry out our computational experiments ona logistics network with 36 nodes and the structure of


(1) Initialization (cycles counter NC = 0) Let 119866 = (119881 119864) 1205791= 0 120579

2= 1 set the value of fundamental parameters of

the heuristic algorithm including the maximum number of cycles NCmax the satisfaction level of travel time and safetyprobability through the selected route 119897

119905 119897119904 growth rate of weighting coefficient 120582 where 119897

119905gt 0 119897119904gt 0 120582 isin (0 1)

(2) Construct a new network 1198661= (119881 119864) where 119864

1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904

(3) 120579 = 0 120578 = 1 minus 120579 let 119908119894119895be the weight on arc (V

119894 V119895) 119908119894119895= 119905119894119895 use Dijkstra algorithm to obtain the shortest route 119875

120579

with respect to 119908119894119895and obtain the corresponding optimal value 119879min According to Lemma 2 119878min = 119878(119875

120579)

(31) If 119879min gt 119897119905 119875lowast has no solution the algorithm terminates

(32) Else if 119879min = 119897119905 119875lowast = 119875

120579 120579lowast = 120579 120578lowast = 1 minus 120579

lowast go to step 5(4) 120579 = 1 120578 = 1 minus 120579 let 119908

119894119895be the weight on arc (V

119894 V119895) 119908119894119895= | ln 119904

119894119895| use Dijkstra algorithm to obtain the shortest route 119875

120579

with respect to 119908119894119895and obtain the corresponding optimal value 119878max According to Lemma 2 119879max = 119879(119875

120579)

(41) Else if 119879max le 119897119905 119875lowast = 119875


lowast go to step 5(42) Else 120579 = 0 120578 = 1 minus 120579 119875lowast = 119875


lowast(421) If NC le NCmax 120579 larr 120579

1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904

119894119895|| ln 119878max minus ln 119878min| + 120578 sdot 119905

119894119895(119879max minus 119879min) use

the 119860lowast algorithm to obtain the shortest route 119875120579with respect to 119908

119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875


lowast go to step 5(4213) Else 120579

1= 120579 NC = NC + 1 119875lowast = 119875


lowast go to step 421(5) If 119878(119875lowast) ge 119897

119904 119875lowast is the optimal solution selected and (120579lowast 120578lowast) is the corresponding vector of weighting coefficients

the algorithm terminates(6) Else 119875lowast has no solution the algorithm terminates

Pseudocode 1 Pseudocode for the static heuristic algorithm



the heuristic algorithm including the maximum number of cycles NCmax the satisfaction level of travel time andsafety probability through the selected route 119897


119905gt 0 119897119904gt 0 120582 isin (0 1)


1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904


119894 V119895) 119908119894119895= 119905119894119895 use the modified Dijkstra algorithm to obtain the shortest

route 119875120579with respect to 119908

119894119895and obtain the corresponding optimal value 119879min According to Lemma 2 119878min = 119878(119875

120579)






119894 V119895) 119908119894119895= | ln 119904

119894119895| use the modified Dijkstra algorithm to obtain the shortest


119894119895and obtain the corresponding optimal value 119878max According to Lemma 2 119879max = 119879(119875

120579)






1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904


119894119895(119879max minus 119879min) use

the119863lowast algorithm to obtain the shortest route 119875120579with respect to 119908

119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875



1= 120579 NC = NC + 1 119875lowast = 119875





Pseudocode 2 Pseudocode for the dynamic heuristic algorithm

an emergency logistics network is shown in Figure 2 Supposethe disaster happens at node (0 0) that is the source nodeand node (5 5) denotes the position of exit that is the desti-nation node Suppose that the period of logistics operation isshort namely in a static environment The parameters of theemergency logistics network such as the length of each arc119897119894119895 route safety of arc (V

119894 V119895)119904119894119895 the initial travel speed 119906

0

119894119895 and

the congestion coefficient 120585119894119895 are shown in Table 1

In order to verify Lemma 2 in Section 32 first we con-struct a new network 119866

1= (119881 119864) where 119864

1= 119890 119890 =

(V119894 V119895) and 119904

119894119895gt 0 Let 120579 vary within the interval [0 1] let

the interval of each two adjacent values be 002 and let theconstructed parameter 119908

119894119895= 120579 sdot | ln 119904

119894119895|| ln 119878max minus ln 119878min| +

120578 sdot 119905119894119895(119879max minus 119879min) be assigned to weight on arc (V

119894 V119895)

and then based on Lemma 1 we can obtain the shortestpath 119875

120579from node (0 0) to node (5 5) of Model III with

respect to weighting coefficient 120579 by using the 119860lowast algorithmFrom the parameters shown in Table 1 we can obtain thetravel time and route safety of these paths Figures 3 and 4show the variation of 119891

119905and 119891

119904with the value of 120579 From

Figures 3 and 4 we can see that 119891119905and 119891

119904are increasing

functions with respect to 120579 respectively The computational


Table 1 Parameters of the emergency logistics network

(V119894 V119895) (119897

119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)

(m mmin mdash mdash) (V119894 V119895) (119897

119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)

(m mmin mdash mdash)

((0 0) (0 1)) (93 107 0705800397) ((1 0) (2 0)) (116 95 07105

00435) ((1 0) (1 1)) (86 117 0773100377)

((0 0) (1 0)) (57 119 0786600453) ((0 1) (1 1)) (110 117 07742

00511) ((1 1) (1 2)) (90 100 0745800379)

((0 1) (0 2)) (43 113 0777900354) ((1 1) (2 1)) (107 115 07663

00458)

((1 2) (1 3)) (120 116 0837200114) ((2 0) (3 0)) (42 83 08797 00251) ((3 0) (3 1)) (100 101 08429

00186)

((0 3) (1 3)) (95 93 08387 00211) ((2 1) (3 1)) (37 120 0894100114) ((3 0) (4 0)) (32 103 08985

00133)

((2 0) (2 1)) (32 79 08105 00147) ((0 2) (1 2)) (31 115 0807800175) ((2 1) (2 2)) (87 115 08665

00181)

((0 2) (0 3)) (107 93 0835100212) ((1 2) (2 2)) (68 84 08996

00140)

((2 2) (2 3)) (44 85 0877600145) ((2 2) (3 2)) (57 85 08290 00171)

((0 3) (0 4)) (63 87 0950300099) ((5 1) (5 2)) (117 108 09245

00004) ((4 2) (5 2)) (117 97 0996300020)

((0 4) (0 5)) (77 84 0936300085) ((4 0) (4 1)) (68 100 09168

00019) ((1 3) (2 3)) (58 82 0992200045)

((1 4) (1 5)) (64 99 0936700033) ((4 1) (4 2)) (99 117 09364

00062) ((2 3) (3 3)) (120 92 0917600051)

((1 3) (1 4)) (65 81 0994100025) ((4 2) (4 3)) (51 106 09268

00079) ((3 3) (4 3)) (84 93 0984200039)

((2 3) (2 4)) (105 90 0919900027) ((4 0) (5 0)) (111 118 09425

00030)((0 4) (1 4)) (38 98 09397

00037)

((2 4) (2 5)) (30 85 09167 00075) ((3 1) (4 1)) (52 112 0924600080) ((1 4) (2 4)) (91 108 09657

00006)

((3 1) (3 2)) (70 120 0969700036) ((4 1) (5 1)) (42 76 09967

00094) ((2 4) (3 4)) (78 85 09247 00001)

((3 2) (3 3)) (82 91 0929500034) ((3 2) (4 2)) (59 110 09329

00014) ((0 5) (1 5)) (85 102 0932000025)

((3 3) (3 4)) (116 91 0978600040) ((5 2) (5 3)) (33 110 09247

00041) ((1 5) (2 5)) (80 102 0986800034)

((3 4) (3 5)) (48 92 0930300088) ((5 3) (5 4)) (36 81 09652

00040) ((4 4) (5 4)) (102 114 0981000010)

((4 3) (4 4)) (62 108 0964500074) ((4 3) (5 3)) (39 79 09971

00020) ((2 5) (3 5)) (116 96 0986200097)

((4 4) (4 5)) (52 96 0920500044) ((5 4) (5 5)) (36 93 09901

00032) ((3 5) (4 5)) (31 113 0979900007)

((5 0) (5 1)) (46 78 0930600093) ((3 4) (4 4)) (39 101 09891

00042) ((4 5) (5 5)) (31 110 0927000004)

experiments results are consistent with Lemma 2 proposed inSection 32

52 Results of Model I in Static Environments

521 Optimal Route from Single Source Node to the Desti-nation Node Here we use different set of satisfaction levelsof the secondary optimization objective 119897

119905to reflect different

requirements for timeliness objective in decision-makingThe optimal route 119875

lowast and its corresponding appropriate

vector of weighting coefficients (120579lowast 120578lowast) can be obtained byapplying the static heuristic algorithm in Section 41 FromTable 2 we can see that 119875lowast is the shortest path of the safetyobjective inModel I when 119897

119905ge 72291 and the corresponding

appropriate vector of weighting coefficients is (1 0) 119875lowast is theshortest path of the timeliness objective in Model I when119897119905

= 61392 and the corresponding appropriate vector ofweighting coefficients is (0 1) Model I has no solution when119897119905lt 61392min So we can conclude that the results of the

multiobjective route planning model will differ when 119897119905is set

differently


Table 2 Parameters and route planning result under satisfaction level of travel time along the route

Optimal route 119875lowast (120579lowast 120578lowast) Travel time (min) Route safety () 119897119905(min) 119897

119904()

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (4 4) (4 5)(5 5)]

(1 0) 72291 890278 ge72291

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (3 5) (4 5)(5 5)]

(074 026) 70850 889501 72000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 700

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 68000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 66000 85

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 64000

[(0 0) (0 1) (0 2) (1 2) (2 2)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(006 094) 61845 867396 62000

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(004 096) 61392 850263 61800

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(0 1) 61392 850263 61392

No solution mdash mdash mdash lt61392

(0 0)(1 0)

(2 0)

(3 0)

(4 0)(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)

(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)

(3 4)

(2 4)

(1 4)

Figure 2 Structure of the emergency logistics network

Figures 5 and 6 show the variations of route safety of 119875lowastand its corresponding appropriate weighting coefficients withthe value of 119897

119905 respectively From Figure 5 we can see that

the value of route safety along 119875lowast tends to decrease when

119897119905becomes lower This shows that the value of route safety

through 119875lowast tends to decrease when we were more pressed for

85

855

86

865

87

875

88

885

89

895

0 02 04 06 08 1

ft

()

120579

Feasible interval of lt

Figure 3 Variation of 119891119905with the value of 120579

time in finishing the emergency logistics tasks From Figure 6we can see that 120579lowast tends to increase and 120578

lowast tends to decreasewhen the satisfaction level of the secondary optimizationobjective 119897

119905increases We can see that appropriate weighting

coefficients of timeliness optimization objective and safetyoptimization objective in the model tend to increase and


6

62

64

66

68

7

72

74

0 02 04 06 08 1

fs

(min

)

120579

Feasible interval of ls


89589

88588

87587

86586

85585

845

Safe

ty o

fPlowast

()

lt (min)6 62 64 66 68 7 72 74

Figure 5 Variation of route safety of 119875lowast with the value of 119897119905

decrease respectively when we were more pressed for timein finishing the emergency logistics tasksThis shows that theappropriate vector of weighting coefficients will be affected bythe satisfaction level of policymakers

Thus the proposed static heuristic algorithm inSection 41 can be used as an auxiliary tool for emergencydecisions which can be used to assist emergency decision-makers in finding the optimal route and reasonable weightingcoefficients quickly

522 Optimal Route from Multiple Source Nodes to theDestination Node Different position of source nodes willaffect the results of the multiobjective route planning modelHere we choose six different source nodes in the logisticsnetwork Then let 119897

119905= 614 and keep it unchanged Table 3

shows the optimal solutions to themultiobjectivemodel fromsix different source nodes to the destination node From theresults shown in Table 3 we can see that route safety through119875lowast differs with the position of the source nodeFigure 7 shows the contrast of the route safety through

119875lowast obtained by the multiobjective model from six different

source nodes to the destination node From Figure 7 we cansee that the route safety through the optimal route decreaseswith the travel time along the optimal route that is with

1

08

06

04

02

06 62 64 66 68 7 72 74

lt (min)

120579lowast120578lowast

Figure 6 Variation of the corresponding appropriate weightingcoefficients with the value of 119897

119905

80

85

90

95

100

05 1 15 2 25 3 35 4 45 5 55 6 65

S(Plowast)

() Satisfactory

interval

T(Plowast) (min)

ls = 86

(0 0) (1 1)(2 0)

(2 2)

(3 3)

(4 4)

Figure 7 Variation of route safety along the optimal route with119879(119875lowast

)

the distance from the source node to the destination nodeSuppose 119897

119904= 86 according to Figure 7 we can see that

there will be no optimal solution to the multiobjective modelin compliance with the satisfactory level of policymakers ifthe source node is at the position of node (4 4) The riskmitigation measures should be taken in the affected area ofnode (4 4) to raise the safety of emergency logisticsThus theproposed algorithm in Section 41 can be used as an auxiliarytool for emergency decisions

523 Results of the Route Planning Model under DifferentExtent of Disasters Different extent of disasters will affect thetravel condition on the arcs of the logistics network differ-ently Here we use different set of the congestion coefficient120585119894119895and route safety of arc (V

119894 V119895)119904119894119895to reflect the extent of

disasters 120585119894119895and 119904119894119895can reflect the instantaneous influence

of disasters on the travel conditions of the arcs littler 120585119894119895

and 119904119894119895

mean greater influence of disasters respectivelyFurthermore different set of 120585

119894119895and 119904119894119895can also reflect the

influence of disasters on arcs in different positionsIn order to carry out our computational experiments

under different extent of disasters first we divide the logisticsnetwork with 36 nodes into three areas the division of thenetwork is shown in Figure 8 and arcs travelled through theboundary of two areas are treated as arcs in the former areaIn each area values of 120585

119894119895and 119904119894119895are generated randomly in


Table 3 Parameters and route planning result with different set of source nodes

Source node Destination node Optimal route 119875lowast Travel timemin Route safety 119897119905(min)

(0 0) (5 5)[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)

(5 5)]61392 850263

61400

(1 1) (5 5) [(1 1) (2 1) (3 1) (3 2) (4 2)(4 3) (5 3) (5 4) (5 5)] 45894 923785

(2 0) (5 5) [(2 0) (2 1) (3 1) (3 2) (4 2)(5 2) (5 3) (5 4) (5 5)] 43956 956501

(2 2) (5 5) [(2 2) (2 3) (2 4) (3 4) (4 4)(4 5) (5 5)] 41354 974097

(3 3) (5 5) [(3 3) (3 4) (4 4) (4 5) (5 5)] 25987 987117(4 4) (5 5) [(4 4) (4 5) (5 5)] 08963 995248

Table 4 Interval of route safety and travel speed decrease parameters under different disaster grades

Disaster grade Area I Area II Area III l119905(min)

0 120585 = 1 119902 = 1 120585 = 1 119902 = 1 120585 = 1 119902 = 1

86

1 120585 isin (09 10) 119902 isin (095 10) 120585 = 1 119902 isin (09 10) 120585 = 1 119902 = 1

2 120585 isin (08 09) 119902 isin (090 095) 120585 isin (09 10) 119902 isin (095 10) 120585 = 1 119902 isin (09 10)3 120585 isin (07 08) 119902 isin (085 090) 120585 isin (08 09) 119902 isin (090 095) 120585 isin (09 10) 119902 isin (095 10)4 120585 isin (06 07) 119902 isin (080 085) 120585 isin (07 08) 119902 isin (085 090) 120585 isin (08 09) 119902 isin (090 095)5 120585 isin (05 06) 119902 isin (075 080) 120585 isin (06 07) 119902 isin (080 085) 120585 isin (07 08) 119902 isin (085 090)

Table 5 Parameters and route planning result under disaster grade 1

Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (09648 00052) ((1 0) (2 0)) (09361 00046) ((1 0) (1 1)) (09286 000002)((0 0) (1 0)) (09862 00037) ((0 1) (1 1)) (09351 00077) ((1 1) (1 2)) (09432 00002)((0 1) (0 2)) (09029 00013) ((1 1) (2 1)) (09514 00099)

II

((1 2) (1 3)) (1 0) ((2 0) (3 0)) (1 0) ((3 0) (3 1)) (1 0)((0 3) (1 3)) (1 0) ((2 1) (3 1)) (1 0) ((3 0) (4 0)) (1 0)((2 0) (2 1)) (1 0) ((0 2) (1 2)) (1 0) ((2 1) (2 2)) (1 0)((0 2) (0 3)) (1 0) ((1 2) (2 2)) (1 0)((2 2) (2 3)) (1 0) ((2 2) (3 2)) (1 0)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((4 2) (5 2)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((1 3) (2 3)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((2 3) (3 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((3 3) (4 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((0 4) (1 4)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((1 4) (2 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((2 4) (3 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((0 5) (1 5)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((1 5) (2 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((4 4) (5 4)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) (1 0) ((2 5) (3 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((3 5) (4 5)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) (1 0) ((4 5) (5 5)) (1 0)

120579lowast 096

Optimum route [(0 0) (1 0) (1 1) (1 2) (2 2) (3 2) (4 2) (4 3) (5 3) (5 4) (5 5)] Travel time 60358656minRoute safety 996117325


(0 0)(1 0)

(2 0)

(3 0)(4 0)

(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)(3 4)

(2 4)

(1 4)

Area I

Area II

Area III

Figure 8 Structure of the emergency logistics network and its division


Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (08606 00194) ((1 0) (2 0)) (08811 00226) ((1 0) (1 1)) (08735 00160)((0 0) (1 0)) (08652 00235) ((0 1) (1 1)) (08428 00250) ((1 1) (1 2)) (08332 00211)((0 1) (0 2)) (08306 00116) ((1 1) (2 1)) (08898 00141)

II

((2 0) (3 0)) (09091 00002) ((0 2) (0 3)) (09144 00097) ((3 0) (3 1)) (09110 00023)((2 1) (3 1)) (09381 00065) ((2 2) (2 3)) (09865 00043) ((3 0) (4 0)) (09302 00030)((0 2) (1 2)) (09985 00043) ((1 2) (1 3)) (09317 00099) ((2 1) (2 2)) (09572 00080)((1 2) (2 2)) (09024 00077) ((0 3) (1 3)) (09205 00089)((2 2) (3 2)) (1 0) ((2 0) (2 1)) (09352 00062)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((3 5) (4 5)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((4 2) (5 2)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((1 3) (2 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((2 3) (3 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((3 3) (4 3)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((0 4) (1 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((1 4) (2 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((2 4) (3 4)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((0 5) (1 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((1 5) (2 5)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) () ((4 5) (5 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((4 4) (5 4)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) () ((2 5) (3 5)) (1 0)

120579 1Optimum route [(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] Travel time 77491759min

Route safety 960087401

different intervals Suppose the source node and destinationnode are (0 0) and (5 5) respectively Let 119897

119905= 86min and

keep it unchanged So we can get five grades of disastersseverity as shown in Table 4 In the data of Table 4 120585

119894119895

and 119904119894119895are set litter in higher disaster grade than in lower

disaster grade in corresponding areas respectively Disastergrade 0 stands for the situation when there no disaster hap-pened and then the multiobjective route planning model is

a single-objective model with respect to the travel time thatis an ordinary shortest path problem

In Tables 5ndash9 the values of 120585119894119895and 119904119894119895and the optimal

route obtained by the proposed algorithm in Section 41 arepresented From Tables 5ndash9 we can see that the result of routeplanning differs with the disaster grade that is with the setof 120585119894119895and 119904119894119895 Figures 9 and 10 show the variations of 119891

119905and

119891119904with the value of 120579 under all the disaster grades and the



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00435) ((1 0) (1 1)) (07731 00377)((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) (07458 00379)((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((1 2) (1 3)) (08372 00114) ((2 0) (3 0)) (08797 00251) ((3 0) (3 1)) (08429 00186)((0 3) (1 3)) (08387 00211) ((2 1) (3 1)) (08941 00114) ((3 0) (4 0)) (08985 00133)((2 0) (2 1)) (08105 00147) ((0 2) (1 2)) (08078 00175) ((2 1) (2 2)) (08665 00181)((0 2) (0 3)) (08351 00212) ((1 2) (2 2)) (08996 00140)((2 2) (2 3)) (08776 00145) ((2 2) (3 2)) (08290 00171)

III

((0 3) (0 4)) (09503 00099) ((5 1) (5 2)) (09245 00004) ((4 2) (5 2)) (09963 00020)((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((1 3) (2 3)) (09922 00045)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((2 3) (3 3)) (09176 00051)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00027) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((3 2) (4 2)) (09329 00014) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((5 2) (5 3)) (09247 00041) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 3) (5 4)) (09652 00040) ((4 4) (5 4)) (09810 00010)((4 3) (4 4)) (09645 00074) ((4 3) (5 3)) (09971 00020) ((2 5) (3 5)) (09862 00097)((4 4) (4 5)) (09205 00044) ((5 4) (5 5)) (09901 00032) ((3 5) (4 5)) (09799 00007)((5 0) (5 1)) (09306 00093) ((3 4) (4 4)) (09891 00042) ((4 5) (5 5)) (09270 00004)

120579lowast 1


4

5

6

7

8

9

10

11

12

0 02 04 06 08 1

Grade 0Grade 1Grade 2


ft

(min

)

120579

Figure 9 Variation of 119891119905with the value of 120579 under different disaster

grades

interval of each two adjacent sets of 120579 is 002 From Figures 9and 10 we can see that the maximum andminimum values of119878(119875lowast

) differ with the disaster gradeFigure 11 shows values of route safety through the optimal

route under all the disaster grades From Figure 11 we can

40

50

60

70

80

90

100

0 02 04 06 08 1

fs

()

120579



Figure 10 Variation of119891119904with the value of 120579 under different disaster

grades

see that the route safety through the optimal route decreaseswith the disaster grade If we suppose 119897

119904= 86 according

to Figure 11 the emergency logistics activities on the groundare not safe and feasible if the disaster grade is higher thangrade 3 and therefore other logistics plans should be taken



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade

Satisfactoryinterval

ls = 86

S(Plowast) ()

Emergency logisticsactivities on the ground are

not safe and feasible

activities on the ground aresafe and feasible

Emergency logistics

Figure 11 Route safety through the optimum route 119875lowast under

different disaster grades

in the emergency response activities Thus the proposedalgorithm in Section 41 can be used as an auxiliary tool foremergency decisions

53 Results of Model I in Dynamic Environments When theperiod of logistics operation is long the congestion coeffi-cient 120585

119894119895and route safety of arc (V

119894 V119895)119904119894119895will be dynamically

changed in route planning problem for emergency logisticsmanagement under real-time effect of disaster extension sothe travel time 119905

119894119895on arc (V

119894 V119895) is determined not only by the

length of the arc 119897119894119895and the travel speed function 119906

119894119895(119905) but

also by the time when the logistics reach the origin node V119894of

arc (V119894 V119895) since the travel speed on each arc is dynamic with

time For the same reason route safety of arc (V119894 V119895)119904119894119895is also

determined by the time when the logistics reach the originnode V

119894of arc (V

119894 V119895)

Here the source node is (0 0) and the destination nodeis (5 5) Meanwhile let 119897

119905= 10 and keep it unchanged

Then we use different set of the values of time 1199050when the

logistics reach the source node V0to reflect the response time

of emergency logistics In Table 10 the optimal route 119875lowast in

dynamic environments obtained by the proposed algorithmin Section 42 is presented

From Table 10 we can see that the result of route planningdiffers with different set of values of 119905

0 Figure 12 shows values

of route safety through the optimal route correspondingto different set of values of 119905

0 From Figure 12 we can see

that the route safety through the optimal route decreaseswith 119905

0 that is with the response time of emergency

logisticsSuppose 119897

119904= 86 according to Figure 12 there will be no

optimal solution to the multiobjective model in compliancewith the satisfactory level of policymakers if 119905

0ge 12 So it

is necessary to respond timely so that certain tasks can beexecuted before the disaster becomes more serious

Based on Figure 12 the policymakers can easily decide areasonable response time for the emergency logistics activi-ties Thus the proposed algorithm in Section 42 can be usedas an auxiliary tool for emergency decisions



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076


Table 10 Interval of congestion coefficient and route safety at different times and route planning result with different starting time

(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)

See Table 5 See Table 6 See Table 7 See Table 8 See Table 91199050min Route id Optimal route Travel time (min) Route safety (mdash) 119897

119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions

Route planning problem is an important issue in emergencymanagement A route planning model based on multiob-jective optimization is presented in this paper The safetyof the path is modeled as the product of safety througharcs included in the path Based on bounded rationalitytheory a conditional multiobjective shortest path model was

proposed Finally a numerical example has been presentedto illustrate the effectiveness of the model There still remainquite a lot of complex factors in route selection for emergencylogisticsmanagement to be consideredHerewe just take timeand safety as the main factors in route section for emergencylogisticsmanagement Building route selectionmodels takingmore actual factors into account will be one of our futurework directions


0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()

Time of the logisticsreaching the source node


0 is reasonable

0 is not reasonable

Figure 12 Route safety of 119875lowast under different set of values of 1199050

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work described in this paper is partially supported bythe National Natural Science Foundation of China Grantnos 71173198 91324017 and 71103162 the National Scienceand Technology Support Program of China Grant nos2012BAK03B05 and 2012BAK20B02 and the FundamentalScience Research Project of China Academy of Safety Scienceand Technology Grant no 2014JBKY02

References

[1] H Toya and M Skidmore ldquoEconomic development and theimpacts of natural disastersrdquo Economics Letters vol 94 no 1pp 20ndash25 2007

[2] M-S Chang Y-L Tseng and J-W Chen ldquoA scenario planningapproach for the flood emergency logistics preparation problemunder uncertaintyrdquo Transportation Research Part E Logisticsand Transportation Review vol 43 no 6 pp 737ndash754 2007

[3] M Skidmore and H Toya ldquoNatural disaster impacts and fiscaldecentralizationrdquo Land Economics vol 89 no 1 pp 101ndash1172013

[4] Y Deng and F T S Chan ldquoA new fuzzy dempster MCDMmethod and its application in supplier selectionrdquoExpert Systemswith Applications vol 38 no 8 pp 9854ndash9861 2011

[5] MGorge ldquoCrisismanagement best practicemdashwhere dowe startfromrdquoComputer Fraud and Security vol 2006 no 6 pp 10ndash132006

[6] B Barlas ldquoOccupational fatalities in shipyards an analysis inTurkeyrdquo Brodogradnja vol 63 no 1 pp 35ndash41 2012

[7] A M Caunhye X Nie and S Pokharel ldquoOptimization modelsin emergency logistics a literature reviewrdquo Socio-EconomicPlanning Sciences vol 46 no 1 pp 4ndash13 2012

[8] M A G Bastos V B G Campos and R A de MelloBandeira ldquoLogistic processes in a post-disaster relief operationrdquoProcediamdashSocial and Behavioral Sciences vol 111 pp 1175ndash11842014

[9] W Yi and L Ozdamar ldquoA dynamic logistics coordinationmodelfor evacuation and support in disaster response activitiesrdquo

European Journal of Operational Research vol 179 no 3 pp1177ndash1193 2007

[10] L Ozdamar and O Demir ldquoA hierarchical clustering and rout-ing procedure for large scale disaster relief logistics planningrdquoTransportation Research Part E Logistics and TransportationReview vol 48 no 3 pp 591ndash602 2012

[11] J-B Sheu ldquoAn emergency logistics distribution approach forquick response to urgent relief demand in disastersrdquo Trans-portation Research Part E Logistics and Transportation Reviewvol 43 no 6 pp 687ndash709 2007

[12] Z-H Hu ldquoA container multimodal transportation schedulingapproach based on immune affinitymodel for emergency reliefrdquoExpert Systems with Applications vol 38 no 3 pp 2632ndash26392011

[13] D Berkoune J Renaud M Rekik and A Ruiz ldquoTransporta-tion in disaster response operationsrdquo Socio-Economic PlanningSciences vol 46 no 1 pp 23ndash32 2012

[14] S J Rennemo K F Roslash L M Hvattum and G TiradoldquoA three-stage stochastic facility routing model for disasterresponse planningrdquo Transportation Research Part E Logisticsand Transportation Review vol 62 pp 116ndash135 2014

[15] Y Yuan and D Wang ldquoPath selection model and algorithmfor emergency logistics managementrdquo Computers amp IndustrialEngineering vol 56 no 3 pp 1081ndash1094 2009

[16] X Zhang Z Zhang Y Zhang D Wei and Y Deng ldquoRouteselection for emergency logistics management a bio-inspiredalgorithmrdquo Safety Science vol 54 pp 87ndash91 2013

[17] H Yue Research on Method to Solve Uncertain OptimizationProblem Based on Interval Number North China Electric PowerUniversity 2013

[18] Z XWang Y GDang andC P Song ldquoMultiobjective decisionmodel of the grey situation based on interval numberrdquo Controland Decision vol 24 no 3 pp 388ndash392 2009

[19] B D Jones ldquoBounded rationality and public policy Herbert ASimon and the decisional foundation of collective choicerdquoPolicySciences vol 35 no 3 pp 269ndash284 2002

[20] International Association of Oil amp Gas Producers ldquoRisk assess-ment data directory vulnerability of humansrdquo Tech Rep 434-141 2010

[21] R K Ahuja T L Magnanti and J B Orlin Network FlowsTheory Algorithms and Application Pearson Education NewYork NY USA 1993

[22] B-C Seet G Liu B-S Lee C-H Foh K-J Wong and K-KLee ldquoA-STAR a mobile ad hoc routing strategy for metropolisvehicular communicationsrdquo in Networking 2004 vol 3042 ofLecture Notes in Computer Science pp 989ndash999 SpringerBerlin Germany 2004

[23] A Stentz ldquoOptimal and efficient path planning for partially-known environmentsrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 3310ndash3317 May1994

[24] A Stentz ldquoThe focussed Dlowast algorithm for real-time replan-ningrdquo in Proceedings of the 14th International Joint Conferenceon Artificial Intelligence (IJCAI rsquo95) vol 2 pp 1652ndash1659 1995

[25] R T Marler and J S Arora ldquoThe weighted sum methodfor multi-objective optimization new insightsrdquo Structural andMultidisciplinary Optimization vol 41 no 6 pp 853ndash862 2010

[26] R T Marler and J S Arora ldquoSurvey of multi-objective opti-mization methods for engineeringrdquo Structural and Multidisci-plinary Optimization vol 26 no 6 pp 369ndash395 2004


[27] L Zadeh ldquoOptimality and non-scalar-valued performancecriteriardquo IEEE Transactions on Automatic Control vol 8 no 1pp 59ndash60 1963

[28] K Ghoseiri and B Nadjari ldquoAn ant colony optimizationalgorithm for the bi-objective shortest path problemrdquo AppliedSoft Computing Journal vol 10 no 4 pp 1237ndash1246 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


necessary for us to go on the research towards this directionZhang et al [16] proposed a novel bioinspiredmethod to solvethe selection model for emergency logistics managementunder real-time effect of disaster extension Both of themfirst convert two objective functions into a single-objectivefunction by using the weighted-sum method and assume theweighting coefficients as fixed real numbers However dueto the complexity of actual problems and subjectivity as wellas limitations of decision-makersrsquo cognition decision-makersoften encounter a lot of uncertainties so that they can onlyget variation ranges of the weighting coefficients [17 18]Thisuncertainty will give decision-makers a great deal of difficultyin emergency decision-making

In this paper we focus on the route planning problemin emergency logistics management and build a mathemat-ical model to select the optimal route The motivation ofthis research is to consider more actual factors in time ofdisaster and decision-making when building models anddesigning algorithms The factors we take into accountinclude travel time and the safety of the route as wellas uncertainty of the weight coefficient for each objectivefunction in actual multiobjective optimization The safetyof the path is modeled as the product of safety througharcs included in the path A multiobjective mathematicalmodel is built in our study and algorithms are developedto solve the model Our method for studying path selectionproblem in emergency logistics management is presented inFigure 1

As described in Figure 1 firstly a multiobjective mathe-matical model based on the theories of bounded rationality isbuilt for route planning in emergency logistics managementconsidering route timeliness and safetyThe two objectives ofthe model are to minimize total travel time along the routeand to maximize the safety of the route respectively Weproposed an easy-to-implement heuristic method in orderto gain an efficient and feasible solution quickly In ourmethod we first translate (6) into (9) and then the proposedmodel can be converted into a conditional multiobjectiveshortest path model which is different from classical shortestpath problem To solve this problem the weighted-summethod is used to convert the conditional multiobjectiveshortest path problem into a single-objective shortest pathproblem and two constraints where we take uncertaintyof the weight coefficient for each objective function inactual multiobjective optimization into account Based onthe single-objective shortest path model we can constructtwo auxiliary functions Finally the main-objective methodis used to define the optimal solution of the multiobjectiveroute planning model By this way two different heuristicalgorithms are designed to solve the proposed model In thestatic heuristic algorithm an efficient and feasible solutionand its corresponding appropriate vector of weight coeffi-cients for the multiobjective route planning model can beobtained quickly by using the classical Dijkstra algorithm and119860lowast algorithm based on the established auxiliary functions if

not considering real-time effect of disaster extension andin the dynamic heuristic algorithm an efficient and feasiblesolution and its corresponding appropriate vector of weightcoefficients for the multiobjective route planning model can

be acquired by using the modified Dijkstra algorithm and119863lowast algorithm based on the established auxiliary functions if

considering real-time effect of disaster extension Simulationresults show the effectiveness and feasibility of the model andalgorithm

This short communication is organized as followsSection 2 gives the multiobjective route planning modelfor emergency logistics management Section 3 introducespreliminaries briefly Section 4 details the proposed methodto solve route planning problem in static and dynamicenvironments respectively Section 5 shows the simulationresults in different cases to illustrate the efficiency of theproposed method Section 6 ends the communication withconclusion

2 Route Planning Model for EmergencyLogistics Management

21 Definition of Variables and Parameters (1) Let arcsdenote the ground roads and nodes denote road intersec-tions An emergency logistics network is defined by a graph119866 = (119881 119864) where 119881 = V

1 V2 V

119899 is the set of nodes and

119864 sube 119881 times 119881 is the set of arcs V1 V2 V

119899denote the nodes in

the network(2) 119897119894119895denotes the length of the arcs between nodes V

119894and

V119895 where (V

119894 V119895) isin 119864

(3) 119905119894119895 119904119894119895denote the travel time and route safety from

node V119894to V119895 respectively Let 119905


logistics reach node V119894and 119905


logistics reach node V119895along arc (V

119894 V119895) It is obvious that

119905119894119895= 119905119895minus 119905119894

(4) 1199060119894119895

is the travel speed on arc (V119894 V119895) under free

travelling conditions Define 119906119894119895(119905) as the travel speed on arc

(V119894 V119895) in the affected area at time 119905 under disaster conditions

Observing the extension processes of some disasters suchas flood and hurricane we can find that the travel speedon each arc of the network will differ with the extension ofdisasters [15] Hence we use a congestion coefficient 120585

119894119895to

denote the change extent of the travel speed which is affectedby the position of the arc the type of the disaster and so forthThen 119906

119894119895(119905) = 120585

119894119895sdot 1199060119894119895 Based on the above definitions it can

be acquired that

int

119905119895

119905119894

119906119894119895(119905) 119889119905 = 119897

119894119895 0 lt 119894 le 119895 lt 119899 (1)

The congestion coefficient on each arc of the logisticsnetwork 120585

119894119895can be considered as a fixed valuewhen the period

of logistics operation is short namely in a static environmentBut when the period of logistics operation is long 120585

119894119895may

dynamically change with the extension of disasters in timeand the route planning problem we focus on is actually ashortest path problem in a dynamic environment

(5) 119909119894119895is the decision variable in the model 119909

119894119895= 0 when

arc (V119894 V119895) is not included in the fixed route and 119909

119894119895= 1 when

arc (V119894 V119895) is included in the fixed route









No

Yes





environments




the model



Prob

lem

st

atem

ent a

nd

form

ulat

ion

Prel

imin

arie

sPr

opos

ed h

euris

tic

algo

rithm

and

simul

atio

n re

sults




119899

sum

119895=1119895 =119894

119909119894119895minus

119899

sum

119895=1119895 =119894

119909119895119894=

1 119894 = 1

minus1 119894 = 119899

0 otherwise(2)

119899

sum

119895=1119895 =119894

119909119894119895=

le 1 119894 = 119899

0 119894 = 119899(3)

119909119894119895= 0 1 119894 119895 isin 1 2 119899 (4)



119894119895












119894119895= 1 minus 119902

119894119895

where 0 le 119902119894119895le 1


Model I

min119879 (119875) = sum

(V119894 V119895)isin119875119905119894119895 (5)

max 119878 (119875) = prod

(V119894 V119895)isin119875119904119894119895 (6)

st

119879 (119875) le 119897119905 (7)

119878 (119875) ge 119897119904 (8)



3 Preliminaries


119894 which











1= (119881 119864

1) where 119864

1= 119890 119890 = (V

119894 V119895)



119894 V119895) In order to




as follows

min sum

(V119894 V119895)isin119875

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816 (9)




Model III


10038161003816100381610038161003816100381610038161003816ln 119878min

1003816100381610038161003816 minus1003816100381610038161003816ln 119878max

1003816100381610038161003816


119878min gt 0

(10)




119891119905(120579) = 119879 (119875

120579) = sum

(V119894 V119895)isin119875120579

119905119894119895 (11)

119891119904(120579) = 119878 (119875

120579) = prod

(V119894 V119895)isin119875120579

119904119894119895 (12)



119894119895= 120579 sdot | ln 119904

119894119895|| ln 119878max minus


119894119895le 1



120579 namely



119865 (120579) = 120579|ln 119878 (119875)| minus 1003816100381610038161003816ln 119878max

10038161003816100381610038161003816100381610038161003816ln 119878min

1003816100381610038161003816 minus1003816100381610038161003816ln 119878max

1003816100381610038161003816


= 120579 sdot|ln 119878 (119875)|


+ 120578 sdot119879 (119875)


minus 1198871minus 1198872

(13)



1198661 Then 119865(120579) = sum










1lt 1205792le 1


sum

(V119894 V119895)isin1198751205791

(1205791

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816+

1 minus 1205791

119879max minus 119879min119905119894119895)

le sum

(V119894 V119895)isin1198751205792

(1205791

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816

+1 minus 1205791

119879max minus 119879min119905119894119895)

sum

(V119894 V119895)isin1198751205791

(1205792

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816+

1 minus 1205792

119879max minus 119879min119905119894119895)

ge sum

(V119894 V119895)isin1198751205792

(1205792

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816

+1 minus 1205792

119879max minus 119879min119905119894119895)

(14)




(V119894 V119895)isin1198751205792 119905119894119895)




(V119894 V119895)isin1198751205792 119905119894119895)




is 119891119904(1205791) le 119891

119904(1205792) and 119891

119905(1205791) le 119891







119891119905(0) = minsum












120577denote


(1) for forall120577 isin [1205791 120579]119879(119875

120577) lt 119897119905and 119878(119875

120577) le 119878(119875

120579) if 119891119905(120579) lt

119897119905


120577) ge 119878(119875

120579) if 119891119905(120579) gt

119897119905

(3) 119875lowast = 119875120579if 119891119905(120579) = 119897

119905and 119878(119875

120579) ge 119897119904





1



119894119895for arc (V



120579of






0and 119875

1can be obtained



120578lowast












119905gt 0 119897119904gt 0 120582 isin (0 1)


1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904



120579


120579)






119894 V119895) 119908119894119895= | ln 119904


120579


120579)






1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904


119894119895(119879max minus 119879min) use


119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875



1= 120579 NC = NC + 1 119875lowast = 119875










119905gt 0 119897119904gt 0 120582 isin (0 1)


1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904





120579)






119894 V119895) 119908119894119895= | ln 119904




120579)






1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904


119894119895(119879max minus 119879min) use


119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875



1= 120579 NC = NC + 1 119875lowast = 119875








0

119894119895 and



1= (119881 119864) where 119864

1= 119890 119890 =

(V119894 V119895) and 119904



119894119895= 120579 sdot | ln 119904



119894 V119895)




119905and 119891







(V119894 V119895) (119897

119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


((0 0) (0 1)) (93 107 0705800397) ((1 0) (2 0)) (116 95 07105

00435) ((1 0) (1 1)) (86 117 0773100377)

((0 0) (1 0)) (57 119 0786600453) ((0 1) (1 1)) (110 117 07742

00511) ((1 1) (1 2)) (90 100 0745800379)

((0 1) (0 2)) (43 113 0777900354) ((1 1) (2 1)) (107 115 07663

00458)

((1 2) (1 3)) (120 116 0837200114) ((2 0) (3 0)) (42 83 08797 00251) ((3 0) (3 1)) (100 101 08429

00186)

((0 3) (1 3)) (95 93 08387 00211) ((2 1) (3 1)) (37 120 0894100114) ((3 0) (4 0)) (32 103 08985

00133)

((2 0) (2 1)) (32 79 08105 00147) ((0 2) (1 2)) (31 115 0807800175) ((2 1) (2 2)) (87 115 08665

00181)

((0 2) (0 3)) (107 93 0835100212) ((1 2) (2 2)) (68 84 08996

00140)

((2 2) (2 3)) (44 85 0877600145) ((2 2) (3 2)) (57 85 08290 00171)

((0 3) (0 4)) (63 87 0950300099) ((5 1) (5 2)) (117 108 09245

00004) ((4 2) (5 2)) (117 97 0996300020)

((0 4) (0 5)) (77 84 0936300085) ((4 0) (4 1)) (68 100 09168

00019) ((1 3) (2 3)) (58 82 0992200045)

((1 4) (1 5)) (64 99 0936700033) ((4 1) (4 2)) (99 117 09364

00062) ((2 3) (3 3)) (120 92 0917600051)

((1 3) (1 4)) (65 81 0994100025) ((4 2) (4 3)) (51 106 09268

00079) ((3 3) (4 3)) (84 93 0984200039)

((2 3) (2 4)) (105 90 0919900027) ((4 0) (5 0)) (111 118 09425

00030)((0 4) (1 4)) (38 98 09397

00037)

((2 4) (2 5)) (30 85 09167 00075) ((3 1) (4 1)) (52 112 0924600080) ((1 4) (2 4)) (91 108 09657

00006)

((3 1) (3 2)) (70 120 0969700036) ((4 1) (5 1)) (42 76 09967

00094) ((2 4) (3 4)) (78 85 09247 00001)

((3 2) (3 3)) (82 91 0929500034) ((3 2) (4 2)) (59 110 09329

00014) ((0 5) (1 5)) (85 102 0932000025)

((3 3) (3 4)) (116 91 0978600040) ((5 2) (5 3)) (33 110 09247

00041) ((1 5) (2 5)) (80 102 0986800034)

((3 4) (3 5)) (48 92 0930300088) ((5 3) (5 4)) (36 81 09652

00040) ((4 4) (5 4)) (102 114 0981000010)

((4 3) (4 4)) (62 108 0964500074) ((4 3) (5 3)) (39 79 09971

00020) ((2 5) (3 5)) (116 96 0986200097)

((4 4) (4 5)) (52 96 0920500044) ((5 4) (5 5)) (36 93 09901

00032) ((3 5) (4 5)) (31 113 0979900007)

((5 0) (5 1)) (46 78 0930600093) ((3 4) (4 4)) (39 101 09891

00042) ((4 5) (5 5)) (31 110 0927000004)












differently




119904()

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (4 4) (4 5)(5 5)]

(1 0) 72291 890278 ge72291

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (3 5) (4 5)(5 5)]

(074 026) 70850 889501 72000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 700

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 68000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 66000 85

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 64000

[(0 0) (0 1) (0 2) (1 2) (2 2)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(006 094) 61845 867396 62000

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(004 096) 61392 850263 61800

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(0 1) 61392 850263 61392


(0 0)(1 0)

(2 0)

(3 0)

(4 0)(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)

(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)

(3 4)

(2 4)

(1 4)







85

855

86

865

87

875

88

885

89

895

0 02 04 06 08 1

ft

()

120579








6

62

64

66

68

7

72

74

0 02 04 06 08 1

fs

(min

)

120579



89589

88588

87587

86586

85585

845

Safe

ty o

fPlowast

()

lt (min)6 62 64 66 68 7 72 74









1

08

06

04

02

06 62 64 66 68 7 72 74

lt (min)



119905

80

85

90

95

100

05 1 15 2 25 3 35 4 45 5 55 6 65

S(Plowast)

() Satisfactory

interval

T(Plowast) (min)

ls = 86

(0 0) (1 1)(2 0)

(2 2)

(3 3)

(4 4)


)








and 119904119894119895









(0 0) (5 5)[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)

(5 5)]61392 850263

61400

(1 1) (5 5) [(1 1) (2 1) (3 1) (3 2) (4 2)(4 3) (5 3) (5 4) (5 5)] 45894 923785

(2 0) (5 5) [(2 0) (2 1) (3 1) (3 2) (4 2)(5 2) (5 3) (5 4) (5 5)] 43956 956501

(2 2) (5 5) [(2 2) (2 3) (2 4) (3 4) (4 4)(4 5) (5 5)] 41354 974097

(3 3) (5 5) [(3 3) (3 4) (4 4) (4 5) (5 5)] 25987 987117(4 4) (5 5) [(4 4) (4 5) (5 5)] 08963 995248



0 120585 = 1 119902 = 1 120585 = 1 119902 = 1 120585 = 1 119902 = 1

86

1 120585 isin (09 10) 119902 isin (095 10) 120585 = 1 119902 isin (09 10) 120585 = 1 119902 = 1



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (09648 00052) ((1 0) (2 0)) (09361 00046) ((1 0) (1 1)) (09286 000002)((0 0) (1 0)) (09862 00037) ((0 1) (1 1)) (09351 00077) ((1 1) (1 2)) (09432 00002)((0 1) (0 2)) (09029 00013) ((1 1) (2 1)) (09514 00099)

II

((1 2) (1 3)) (1 0) ((2 0) (3 0)) (1 0) ((3 0) (3 1)) (1 0)((0 3) (1 3)) (1 0) ((2 1) (3 1)) (1 0) ((3 0) (4 0)) (1 0)((2 0) (2 1)) (1 0) ((0 2) (1 2)) (1 0) ((2 1) (2 2)) (1 0)((0 2) (0 3)) (1 0) ((1 2) (2 2)) (1 0)((2 2) (2 3)) (1 0) ((2 2) (3 2)) (1 0)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((4 2) (5 2)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((1 3) (2 3)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((2 3) (3 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((3 3) (4 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((0 4) (1 4)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((1 4) (2 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((2 4) (3 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((0 5) (1 5)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((1 5) (2 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((4 4) (5 4)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) (1 0) ((2 5) (3 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((3 5) (4 5)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) (1 0) ((4 5) (5 5)) (1 0)

120579lowast 096



(0 0)(1 0)

(2 0)

(3 0)(4 0)

(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)(3 4)

(2 4)

(1 4)

Area I

Area II

Area III



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (08606 00194) ((1 0) (2 0)) (08811 00226) ((1 0) (1 1)) (08735 00160)((0 0) (1 0)) (08652 00235) ((0 1) (1 1)) (08428 00250) ((1 1) (1 2)) (08332 00211)((0 1) (0 2)) (08306 00116) ((1 1) (2 1)) (08898 00141)

II

((2 0) (3 0)) (09091 00002) ((0 2) (0 3)) (09144 00097) ((3 0) (3 1)) (09110 00023)((2 1) (3 1)) (09381 00065) ((2 2) (2 3)) (09865 00043) ((3 0) (4 0)) (09302 00030)((0 2) (1 2)) (09985 00043) ((1 2) (1 3)) (09317 00099) ((2 1) (2 2)) (09572 00080)((1 2) (2 2)) (09024 00077) ((0 3) (1 3)) (09205 00089)((2 2) (3 2)) (1 0) ((2 0) (2 1)) (09352 00062)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((3 5) (4 5)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((4 2) (5 2)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((1 3) (2 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((2 3) (3 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((3 3) (4 3)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((0 4) (1 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((1 4) (2 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((2 4) (3 4)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((0 5) (1 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((1 5) (2 5)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) () ((4 5) (5 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((4 4) (5 4)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) () ((2 5) (3 5)) (1 0)




119905= 86min and


119894119895






119905and




Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00435) ((1 0) (1 1)) (07731 00377)((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) (07458 00379)((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((1 2) (1 3)) (08372 00114) ((2 0) (3 0)) (08797 00251) ((3 0) (3 1)) (08429 00186)((0 3) (1 3)) (08387 00211) ((2 1) (3 1)) (08941 00114) ((3 0) (4 0)) (08985 00133)((2 0) (2 1)) (08105 00147) ((0 2) (1 2)) (08078 00175) ((2 1) (2 2)) (08665 00181)((0 2) (0 3)) (08351 00212) ((1 2) (2 2)) (08996 00140)((2 2) (2 3)) (08776 00145) ((2 2) (3 2)) (08290 00171)

III

((0 3) (0 4)) (09503 00099) ((5 1) (5 2)) (09245 00004) ((4 2) (5 2)) (09963 00020)((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((1 3) (2 3)) (09922 00045)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((2 3) (3 3)) (09176 00051)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00027) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((3 2) (4 2)) (09329 00014) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((5 2) (5 3)) (09247 00041) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 3) (5 4)) (09652 00040) ((4 4) (5 4)) (09810 00010)((4 3) (4 4)) (09645 00074) ((4 3) (5 3)) (09971 00020) ((2 5) (3 5)) (09862 00097)((4 4) (4 5)) (09205 00044) ((5 4) (5 5)) (09901 00032) ((3 5) (4 5)) (09799 00007)((5 0) (5 1)) (09306 00093) ((3 4) (4 4)) (09891 00042) ((4 5) (5 5)) (09270 00004)

120579lowast 1


4

5

6

7

8

9

10

11

12

0 02 04 06 08 1



ft

(min

)

120579


grades




40

50

60

70

80

90

100

0 02 04 06 08 1

fs

()

120579




grades






Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade


ls = 86

S(Plowast) ()




Emergency logistics








119894119895on arc (V



119894119895(119905) but





119894of arc (V

119894 V119895)
















0ge 12 So it





Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















No

Yes





environments




the model



Prob

lem

st

atem

ent a

nd

form

ulat

ion

Prel

imin

arie

sPr

opos

ed h

euris

tic

algo

rithm

and

simul

atio

n re

sults




119899

sum

119895=1119895 =119894

119909119894119895minus

119899

sum

119895=1119895 =119894

119909119895119894=

1 119894 = 1

minus1 119894 = 119899

0 otherwise(2)

119899

sum

119895=1119895 =119894

119909119894119895=

le 1 119894 = 119899

0 119894 = 119899(3)

119909119894119895= 0 1 119894 119895 isin 1 2 119899 (4)



119894119895












119894119895= 1 minus 119902

119894119895

where 0 le 119902119894119895le 1


Model I

min119879 (119875) = sum

(V119894 V119895)isin119875119905119894119895 (5)

max 119878 (119875) = prod

(V119894 V119895)isin119875119904119894119895 (6)

st

119879 (119875) le 119897119905 (7)

119878 (119875) ge 119897119904 (8)



3 Preliminaries


119894 which











1= (119881 119864

1) where 119864

1= 119890 119890 = (V

119894 V119895)



119894 V119895) In order to




as follows

min sum

(V119894 V119895)isin119875

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816 (9)




Model III


10038161003816100381610038161003816100381610038161003816ln 119878min

1003816100381610038161003816 minus1003816100381610038161003816ln 119878max

1003816100381610038161003816


119878min gt 0

(10)




119891119905(120579) = 119879 (119875

120579) = sum

(V119894 V119895)isin119875120579

119905119894119895 (11)

119891119904(120579) = 119878 (119875

120579) = prod

(V119894 V119895)isin119875120579

119904119894119895 (12)



119894119895= 120579 sdot | ln 119904

119894119895|| ln 119878max minus


119894119895le 1



120579 namely



119865 (120579) = 120579|ln 119878 (119875)| minus 1003816100381610038161003816ln 119878max

10038161003816100381610038161003816100381610038161003816ln 119878min

1003816100381610038161003816 minus1003816100381610038161003816ln 119878max

1003816100381610038161003816


= 120579 sdot|ln 119878 (119875)|


+ 120578 sdot119879 (119875)


minus 1198871minus 1198872

(13)



1198661 Then 119865(120579) = sum










1lt 1205792le 1


sum

(V119894 V119895)isin1198751205791

(1205791

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816+

1 minus 1205791

119879max minus 119879min119905119894119895)

le sum

(V119894 V119895)isin1198751205792

(1205791

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816

+1 minus 1205791

119879max minus 119879min119905119894119895)

sum

(V119894 V119895)isin1198751205791

(1205792

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816+

1 minus 1205792

119879max minus 119879min119905119894119895)

ge sum

(V119894 V119895)isin1198751205792

(1205792

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816

+1 minus 1205792

119879max minus 119879min119905119894119895)

(14)




(V119894 V119895)isin1198751205792 119905119894119895)




(V119894 V119895)isin1198751205792 119905119894119895)




is 119891119904(1205791) le 119891

119904(1205792) and 119891

119905(1205791) le 119891







119891119905(0) = minsum












120577denote


(1) for forall120577 isin [1205791 120579]119879(119875

120577) lt 119897119905and 119878(119875

120577) le 119878(119875

120579) if 119891119905(120579) lt

119897119905


120577) ge 119878(119875

120579) if 119891119905(120579) gt

119897119905

(3) 119875lowast = 119875120579if 119891119905(120579) = 119897

119905and 119878(119875

120579) ge 119897119904





1



119894119895for arc (V



120579of






0and 119875

1can be obtained



120578lowast












119905gt 0 119897119904gt 0 120582 isin (0 1)


1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904



120579


120579)






119894 V119895) 119908119894119895= | ln 119904


120579


120579)






1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904


119894119895(119879max minus 119879min) use


119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875



1= 120579 NC = NC + 1 119875lowast = 119875










119905gt 0 119897119904gt 0 120582 isin (0 1)


1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904





120579)






119894 V119895) 119908119894119895= | ln 119904




120579)






1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904


119894119895(119879max minus 119879min) use


119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875



1= 120579 NC = NC + 1 119875lowast = 119875








0

119894119895 and



1= (119881 119864) where 119864

1= 119890 119890 =

(V119894 V119895) and 119904



119894119895= 120579 sdot | ln 119904



119894 V119895)




119905and 119891







(V119894 V119895) (119897

119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


((0 0) (0 1)) (93 107 0705800397) ((1 0) (2 0)) (116 95 07105

00435) ((1 0) (1 1)) (86 117 0773100377)

((0 0) (1 0)) (57 119 0786600453) ((0 1) (1 1)) (110 117 07742

00511) ((1 1) (1 2)) (90 100 0745800379)

((0 1) (0 2)) (43 113 0777900354) ((1 1) (2 1)) (107 115 07663

00458)

((1 2) (1 3)) (120 116 0837200114) ((2 0) (3 0)) (42 83 08797 00251) ((3 0) (3 1)) (100 101 08429

00186)

((0 3) (1 3)) (95 93 08387 00211) ((2 1) (3 1)) (37 120 0894100114) ((3 0) (4 0)) (32 103 08985

00133)

((2 0) (2 1)) (32 79 08105 00147) ((0 2) (1 2)) (31 115 0807800175) ((2 1) (2 2)) (87 115 08665

00181)

((0 2) (0 3)) (107 93 0835100212) ((1 2) (2 2)) (68 84 08996

00140)

((2 2) (2 3)) (44 85 0877600145) ((2 2) (3 2)) (57 85 08290 00171)

((0 3) (0 4)) (63 87 0950300099) ((5 1) (5 2)) (117 108 09245

00004) ((4 2) (5 2)) (117 97 0996300020)

((0 4) (0 5)) (77 84 0936300085) ((4 0) (4 1)) (68 100 09168

00019) ((1 3) (2 3)) (58 82 0992200045)

((1 4) (1 5)) (64 99 0936700033) ((4 1) (4 2)) (99 117 09364

00062) ((2 3) (3 3)) (120 92 0917600051)

((1 3) (1 4)) (65 81 0994100025) ((4 2) (4 3)) (51 106 09268

00079) ((3 3) (4 3)) (84 93 0984200039)

((2 3) (2 4)) (105 90 0919900027) ((4 0) (5 0)) (111 118 09425

00030)((0 4) (1 4)) (38 98 09397

00037)

((2 4) (2 5)) (30 85 09167 00075) ((3 1) (4 1)) (52 112 0924600080) ((1 4) (2 4)) (91 108 09657

00006)

((3 1) (3 2)) (70 120 0969700036) ((4 1) (5 1)) (42 76 09967

00094) ((2 4) (3 4)) (78 85 09247 00001)

((3 2) (3 3)) (82 91 0929500034) ((3 2) (4 2)) (59 110 09329

00014) ((0 5) (1 5)) (85 102 0932000025)

((3 3) (3 4)) (116 91 0978600040) ((5 2) (5 3)) (33 110 09247

00041) ((1 5) (2 5)) (80 102 0986800034)

((3 4) (3 5)) (48 92 0930300088) ((5 3) (5 4)) (36 81 09652

00040) ((4 4) (5 4)) (102 114 0981000010)

((4 3) (4 4)) (62 108 0964500074) ((4 3) (5 3)) (39 79 09971

00020) ((2 5) (3 5)) (116 96 0986200097)

((4 4) (4 5)) (52 96 0920500044) ((5 4) (5 5)) (36 93 09901

00032) ((3 5) (4 5)) (31 113 0979900007)

((5 0) (5 1)) (46 78 0930600093) ((3 4) (4 4)) (39 101 09891

00042) ((4 5) (5 5)) (31 110 0927000004)












differently




119904()

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (4 4) (4 5)(5 5)]

(1 0) 72291 890278 ge72291

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (3 5) (4 5)(5 5)]

(074 026) 70850 889501 72000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 700

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 68000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 66000 85

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 64000

[(0 0) (0 1) (0 2) (1 2) (2 2)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(006 094) 61845 867396 62000

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(004 096) 61392 850263 61800

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(0 1) 61392 850263 61392


(0 0)(1 0)

(2 0)

(3 0)

(4 0)(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)

(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)

(3 4)

(2 4)

(1 4)







85

855

86

865

87

875

88

885

89

895

0 02 04 06 08 1

ft

()

120579








6

62

64

66

68

7

72

74

0 02 04 06 08 1

fs

(min

)

120579



89589

88588

87587

86586

85585

845

Safe

ty o

fPlowast

()

lt (min)6 62 64 66 68 7 72 74









1

08

06

04

02

06 62 64 66 68 7 72 74

lt (min)



119905

80

85

90

95

100

05 1 15 2 25 3 35 4 45 5 55 6 65

S(Plowast)

() Satisfactory

interval

T(Plowast) (min)

ls = 86

(0 0) (1 1)(2 0)

(2 2)

(3 3)

(4 4)


)








and 119904119894119895









(0 0) (5 5)[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)

(5 5)]61392 850263

61400

(1 1) (5 5) [(1 1) (2 1) (3 1) (3 2) (4 2)(4 3) (5 3) (5 4) (5 5)] 45894 923785

(2 0) (5 5) [(2 0) (2 1) (3 1) (3 2) (4 2)(5 2) (5 3) (5 4) (5 5)] 43956 956501

(2 2) (5 5) [(2 2) (2 3) (2 4) (3 4) (4 4)(4 5) (5 5)] 41354 974097

(3 3) (5 5) [(3 3) (3 4) (4 4) (4 5) (5 5)] 25987 987117(4 4) (5 5) [(4 4) (4 5) (5 5)] 08963 995248



0 120585 = 1 119902 = 1 120585 = 1 119902 = 1 120585 = 1 119902 = 1

86

1 120585 isin (09 10) 119902 isin (095 10) 120585 = 1 119902 isin (09 10) 120585 = 1 119902 = 1



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (09648 00052) ((1 0) (2 0)) (09361 00046) ((1 0) (1 1)) (09286 000002)((0 0) (1 0)) (09862 00037) ((0 1) (1 1)) (09351 00077) ((1 1) (1 2)) (09432 00002)((0 1) (0 2)) (09029 00013) ((1 1) (2 1)) (09514 00099)

II

((1 2) (1 3)) (1 0) ((2 0) (3 0)) (1 0) ((3 0) (3 1)) (1 0)((0 3) (1 3)) (1 0) ((2 1) (3 1)) (1 0) ((3 0) (4 0)) (1 0)((2 0) (2 1)) (1 0) ((0 2) (1 2)) (1 0) ((2 1) (2 2)) (1 0)((0 2) (0 3)) (1 0) ((1 2) (2 2)) (1 0)((2 2) (2 3)) (1 0) ((2 2) (3 2)) (1 0)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((4 2) (5 2)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((1 3) (2 3)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((2 3) (3 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((3 3) (4 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((0 4) (1 4)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((1 4) (2 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((2 4) (3 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((0 5) (1 5)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((1 5) (2 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((4 4) (5 4)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) (1 0) ((2 5) (3 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((3 5) (4 5)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) (1 0) ((4 5) (5 5)) (1 0)

120579lowast 096



(0 0)(1 0)

(2 0)

(3 0)(4 0)

(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)(3 4)

(2 4)

(1 4)

Area I

Area II

Area III



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (08606 00194) ((1 0) (2 0)) (08811 00226) ((1 0) (1 1)) (08735 00160)((0 0) (1 0)) (08652 00235) ((0 1) (1 1)) (08428 00250) ((1 1) (1 2)) (08332 00211)((0 1) (0 2)) (08306 00116) ((1 1) (2 1)) (08898 00141)

II

((2 0) (3 0)) (09091 00002) ((0 2) (0 3)) (09144 00097) ((3 0) (3 1)) (09110 00023)((2 1) (3 1)) (09381 00065) ((2 2) (2 3)) (09865 00043) ((3 0) (4 0)) (09302 00030)((0 2) (1 2)) (09985 00043) ((1 2) (1 3)) (09317 00099) ((2 1) (2 2)) (09572 00080)((1 2) (2 2)) (09024 00077) ((0 3) (1 3)) (09205 00089)((2 2) (3 2)) (1 0) ((2 0) (2 1)) (09352 00062)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((3 5) (4 5)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((4 2) (5 2)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((1 3) (2 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((2 3) (3 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((3 3) (4 3)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((0 4) (1 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((1 4) (2 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((2 4) (3 4)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((0 5) (1 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((1 5) (2 5)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) () ((4 5) (5 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((4 4) (5 4)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) () ((2 5) (3 5)) (1 0)




119905= 86min and


119894119895






119905and




Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00435) ((1 0) (1 1)) (07731 00377)((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) (07458 00379)((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((1 2) (1 3)) (08372 00114) ((2 0) (3 0)) (08797 00251) ((3 0) (3 1)) (08429 00186)((0 3) (1 3)) (08387 00211) ((2 1) (3 1)) (08941 00114) ((3 0) (4 0)) (08985 00133)((2 0) (2 1)) (08105 00147) ((0 2) (1 2)) (08078 00175) ((2 1) (2 2)) (08665 00181)((0 2) (0 3)) (08351 00212) ((1 2) (2 2)) (08996 00140)((2 2) (2 3)) (08776 00145) ((2 2) (3 2)) (08290 00171)

III

((0 3) (0 4)) (09503 00099) ((5 1) (5 2)) (09245 00004) ((4 2) (5 2)) (09963 00020)((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((1 3) (2 3)) (09922 00045)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((2 3) (3 3)) (09176 00051)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00027) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((3 2) (4 2)) (09329 00014) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((5 2) (5 3)) (09247 00041) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 3) (5 4)) (09652 00040) ((4 4) (5 4)) (09810 00010)((4 3) (4 4)) (09645 00074) ((4 3) (5 3)) (09971 00020) ((2 5) (3 5)) (09862 00097)((4 4) (4 5)) (09205 00044) ((5 4) (5 5)) (09901 00032) ((3 5) (4 5)) (09799 00007)((5 0) (5 1)) (09306 00093) ((3 4) (4 4)) (09891 00042) ((4 5) (5 5)) (09270 00004)

120579lowast 1


4

5

6

7

8

9

10

11

12

0 02 04 06 08 1



ft

(min

)

120579


grades




40

50

60

70

80

90

100

0 02 04 06 08 1

fs

()

120579




grades






Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade


ls = 86

S(Plowast) ()




Emergency logistics








119894119895on arc (V



119894119895(119905) but





119894of arc (V

119894 V119895)
















0ge 12 So it





Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













119894119895= 1 minus 119902

119894119895

where 0 le 119902119894119895le 1


Model I

min119879 (119875) = sum

(V119894 V119895)isin119875119905119894119895 (5)

max 119878 (119875) = prod

(V119894 V119895)isin119875119904119894119895 (6)

st

119879 (119875) le 119897119905 (7)

119878 (119875) ge 119897119904 (8)



3 Preliminaries


119894 which











1= (119881 119864

1) where 119864

1= 119890 119890 = (V

119894 V119895)



119894 V119895) In order to




as follows

min sum

(V119894 V119895)isin119875

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816 (9)




Model III


10038161003816100381610038161003816100381610038161003816ln 119878min

1003816100381610038161003816 minus1003816100381610038161003816ln 119878max

1003816100381610038161003816


119878min gt 0

(10)




119891119905(120579) = 119879 (119875

120579) = sum

(V119894 V119895)isin119875120579

119905119894119895 (11)

119891119904(120579) = 119878 (119875

120579) = prod

(V119894 V119895)isin119875120579

119904119894119895 (12)



119894119895= 120579 sdot | ln 119904

119894119895|| ln 119878max minus


119894119895le 1



120579 namely



119865 (120579) = 120579|ln 119878 (119875)| minus 1003816100381610038161003816ln 119878max

10038161003816100381610038161003816100381610038161003816ln 119878min

1003816100381610038161003816 minus1003816100381610038161003816ln 119878max

1003816100381610038161003816


= 120579 sdot|ln 119878 (119875)|


+ 120578 sdot119879 (119875)


minus 1198871minus 1198872

(13)



1198661 Then 119865(120579) = sum










1lt 1205792le 1


sum

(V119894 V119895)isin1198751205791

(1205791

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816+

1 minus 1205791

119879max minus 119879min119905119894119895)

le sum

(V119894 V119895)isin1198751205792

(1205791

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816

+1 minus 1205791

119879max minus 119879min119905119894119895)

sum

(V119894 V119895)isin1198751205791

(1205792

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816+

1 minus 1205792

119879max minus 119879min119905119894119895)

ge sum

(V119894 V119895)isin1198751205792

(1205792

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816

+1 minus 1205792

119879max minus 119879min119905119894119895)

(14)




(V119894 V119895)isin1198751205792 119905119894119895)




(V119894 V119895)isin1198751205792 119905119894119895)




is 119891119904(1205791) le 119891

119904(1205792) and 119891

119905(1205791) le 119891







119891119905(0) = minsum












120577denote


(1) for forall120577 isin [1205791 120579]119879(119875

120577) lt 119897119905and 119878(119875

120577) le 119878(119875

120579) if 119891119905(120579) lt

119897119905


120577) ge 119878(119875

120579) if 119891119905(120579) gt

119897119905

(3) 119875lowast = 119875120579if 119891119905(120579) = 119897

119905and 119878(119875

120579) ge 119897119904





1



119894119895for arc (V



120579of






0and 119875

1can be obtained



120578lowast












119905gt 0 119897119904gt 0 120582 isin (0 1)


1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904



120579


120579)






119894 V119895) 119908119894119895= | ln 119904


120579


120579)






1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904


119894119895(119879max minus 119879min) use


119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875



1= 120579 NC = NC + 1 119875lowast = 119875










119905gt 0 119897119904gt 0 120582 isin (0 1)


1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904





120579)






119894 V119895) 119908119894119895= | ln 119904




120579)






1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904


119894119895(119879max minus 119879min) use


119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875



1= 120579 NC = NC + 1 119875lowast = 119875








0

119894119895 and



1= (119881 119864) where 119864

1= 119890 119890 =

(V119894 V119895) and 119904



119894119895= 120579 sdot | ln 119904



119894 V119895)




119905and 119891







(V119894 V119895) (119897

119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


((0 0) (0 1)) (93 107 0705800397) ((1 0) (2 0)) (116 95 07105

00435) ((1 0) (1 1)) (86 117 0773100377)

((0 0) (1 0)) (57 119 0786600453) ((0 1) (1 1)) (110 117 07742

00511) ((1 1) (1 2)) (90 100 0745800379)

((0 1) (0 2)) (43 113 0777900354) ((1 1) (2 1)) (107 115 07663

00458)

((1 2) (1 3)) (120 116 0837200114) ((2 0) (3 0)) (42 83 08797 00251) ((3 0) (3 1)) (100 101 08429

00186)

((0 3) (1 3)) (95 93 08387 00211) ((2 1) (3 1)) (37 120 0894100114) ((3 0) (4 0)) (32 103 08985

00133)

((2 0) (2 1)) (32 79 08105 00147) ((0 2) (1 2)) (31 115 0807800175) ((2 1) (2 2)) (87 115 08665

00181)

((0 2) (0 3)) (107 93 0835100212) ((1 2) (2 2)) (68 84 08996

00140)

((2 2) (2 3)) (44 85 0877600145) ((2 2) (3 2)) (57 85 08290 00171)

((0 3) (0 4)) (63 87 0950300099) ((5 1) (5 2)) (117 108 09245

00004) ((4 2) (5 2)) (117 97 0996300020)

((0 4) (0 5)) (77 84 0936300085) ((4 0) (4 1)) (68 100 09168

00019) ((1 3) (2 3)) (58 82 0992200045)

((1 4) (1 5)) (64 99 0936700033) ((4 1) (4 2)) (99 117 09364

00062) ((2 3) (3 3)) (120 92 0917600051)

((1 3) (1 4)) (65 81 0994100025) ((4 2) (4 3)) (51 106 09268

00079) ((3 3) (4 3)) (84 93 0984200039)

((2 3) (2 4)) (105 90 0919900027) ((4 0) (5 0)) (111 118 09425

00030)((0 4) (1 4)) (38 98 09397

00037)

((2 4) (2 5)) (30 85 09167 00075) ((3 1) (4 1)) (52 112 0924600080) ((1 4) (2 4)) (91 108 09657

00006)

((3 1) (3 2)) (70 120 0969700036) ((4 1) (5 1)) (42 76 09967

00094) ((2 4) (3 4)) (78 85 09247 00001)

((3 2) (3 3)) (82 91 0929500034) ((3 2) (4 2)) (59 110 09329

00014) ((0 5) (1 5)) (85 102 0932000025)

((3 3) (3 4)) (116 91 0978600040) ((5 2) (5 3)) (33 110 09247

00041) ((1 5) (2 5)) (80 102 0986800034)

((3 4) (3 5)) (48 92 0930300088) ((5 3) (5 4)) (36 81 09652

00040) ((4 4) (5 4)) (102 114 0981000010)

((4 3) (4 4)) (62 108 0964500074) ((4 3) (5 3)) (39 79 09971

00020) ((2 5) (3 5)) (116 96 0986200097)

((4 4) (4 5)) (52 96 0920500044) ((5 4) (5 5)) (36 93 09901

00032) ((3 5) (4 5)) (31 113 0979900007)

((5 0) (5 1)) (46 78 0930600093) ((3 4) (4 4)) (39 101 09891

00042) ((4 5) (5 5)) (31 110 0927000004)












differently




119904()

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (4 4) (4 5)(5 5)]

(1 0) 72291 890278 ge72291

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (3 5) (4 5)(5 5)]

(074 026) 70850 889501 72000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 700

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 68000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 66000 85

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 64000

[(0 0) (0 1) (0 2) (1 2) (2 2)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(006 094) 61845 867396 62000

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(004 096) 61392 850263 61800

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(0 1) 61392 850263 61392


(0 0)(1 0)

(2 0)

(3 0)

(4 0)(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)

(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)

(3 4)

(2 4)

(1 4)







85

855

86

865

87

875

88

885

89

895

0 02 04 06 08 1

ft

()

120579








6

62

64

66

68

7

72

74

0 02 04 06 08 1

fs

(min

)

120579



89589

88588

87587

86586

85585

845

Safe

ty o

fPlowast

()

lt (min)6 62 64 66 68 7 72 74









1

08

06

04

02

06 62 64 66 68 7 72 74

lt (min)



119905

80

85

90

95

100

05 1 15 2 25 3 35 4 45 5 55 6 65

S(Plowast)

() Satisfactory

interval

T(Plowast) (min)

ls = 86

(0 0) (1 1)(2 0)

(2 2)

(3 3)

(4 4)


)








and 119904119894119895









(0 0) (5 5)[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)

(5 5)]61392 850263

61400

(1 1) (5 5) [(1 1) (2 1) (3 1) (3 2) (4 2)(4 3) (5 3) (5 4) (5 5)] 45894 923785

(2 0) (5 5) [(2 0) (2 1) (3 1) (3 2) (4 2)(5 2) (5 3) (5 4) (5 5)] 43956 956501

(2 2) (5 5) [(2 2) (2 3) (2 4) (3 4) (4 4)(4 5) (5 5)] 41354 974097

(3 3) (5 5) [(3 3) (3 4) (4 4) (4 5) (5 5)] 25987 987117(4 4) (5 5) [(4 4) (4 5) (5 5)] 08963 995248



0 120585 = 1 119902 = 1 120585 = 1 119902 = 1 120585 = 1 119902 = 1

86

1 120585 isin (09 10) 119902 isin (095 10) 120585 = 1 119902 isin (09 10) 120585 = 1 119902 = 1



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (09648 00052) ((1 0) (2 0)) (09361 00046) ((1 0) (1 1)) (09286 000002)((0 0) (1 0)) (09862 00037) ((0 1) (1 1)) (09351 00077) ((1 1) (1 2)) (09432 00002)((0 1) (0 2)) (09029 00013) ((1 1) (2 1)) (09514 00099)

II

((1 2) (1 3)) (1 0) ((2 0) (3 0)) (1 0) ((3 0) (3 1)) (1 0)((0 3) (1 3)) (1 0) ((2 1) (3 1)) (1 0) ((3 0) (4 0)) (1 0)((2 0) (2 1)) (1 0) ((0 2) (1 2)) (1 0) ((2 1) (2 2)) (1 0)((0 2) (0 3)) (1 0) ((1 2) (2 2)) (1 0)((2 2) (2 3)) (1 0) ((2 2) (3 2)) (1 0)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((4 2) (5 2)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((1 3) (2 3)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((2 3) (3 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((3 3) (4 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((0 4) (1 4)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((1 4) (2 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((2 4) (3 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((0 5) (1 5)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((1 5) (2 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((4 4) (5 4)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) (1 0) ((2 5) (3 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((3 5) (4 5)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) (1 0) ((4 5) (5 5)) (1 0)

120579lowast 096



(0 0)(1 0)

(2 0)

(3 0)(4 0)

(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)(3 4)

(2 4)

(1 4)

Area I

Area II

Area III



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (08606 00194) ((1 0) (2 0)) (08811 00226) ((1 0) (1 1)) (08735 00160)((0 0) (1 0)) (08652 00235) ((0 1) (1 1)) (08428 00250) ((1 1) (1 2)) (08332 00211)((0 1) (0 2)) (08306 00116) ((1 1) (2 1)) (08898 00141)

II

((2 0) (3 0)) (09091 00002) ((0 2) (0 3)) (09144 00097) ((3 0) (3 1)) (09110 00023)((2 1) (3 1)) (09381 00065) ((2 2) (2 3)) (09865 00043) ((3 0) (4 0)) (09302 00030)((0 2) (1 2)) (09985 00043) ((1 2) (1 3)) (09317 00099) ((2 1) (2 2)) (09572 00080)((1 2) (2 2)) (09024 00077) ((0 3) (1 3)) (09205 00089)((2 2) (3 2)) (1 0) ((2 0) (2 1)) (09352 00062)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((3 5) (4 5)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((4 2) (5 2)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((1 3) (2 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((2 3) (3 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((3 3) (4 3)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((0 4) (1 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((1 4) (2 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((2 4) (3 4)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((0 5) (1 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((1 5) (2 5)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) () ((4 5) (5 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((4 4) (5 4)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) () ((2 5) (3 5)) (1 0)




119905= 86min and


119894119895






119905and




Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00435) ((1 0) (1 1)) (07731 00377)((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) (07458 00379)((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((1 2) (1 3)) (08372 00114) ((2 0) (3 0)) (08797 00251) ((3 0) (3 1)) (08429 00186)((0 3) (1 3)) (08387 00211) ((2 1) (3 1)) (08941 00114) ((3 0) (4 0)) (08985 00133)((2 0) (2 1)) (08105 00147) ((0 2) (1 2)) (08078 00175) ((2 1) (2 2)) (08665 00181)((0 2) (0 3)) (08351 00212) ((1 2) (2 2)) (08996 00140)((2 2) (2 3)) (08776 00145) ((2 2) (3 2)) (08290 00171)

III

((0 3) (0 4)) (09503 00099) ((5 1) (5 2)) (09245 00004) ((4 2) (5 2)) (09963 00020)((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((1 3) (2 3)) (09922 00045)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((2 3) (3 3)) (09176 00051)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00027) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((3 2) (4 2)) (09329 00014) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((5 2) (5 3)) (09247 00041) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 3) (5 4)) (09652 00040) ((4 4) (5 4)) (09810 00010)((4 3) (4 4)) (09645 00074) ((4 3) (5 3)) (09971 00020) ((2 5) (3 5)) (09862 00097)((4 4) (4 5)) (09205 00044) ((5 4) (5 5)) (09901 00032) ((3 5) (4 5)) (09799 00007)((5 0) (5 1)) (09306 00093) ((3 4) (4 4)) (09891 00042) ((4 5) (5 5)) (09270 00004)

120579lowast 1


4

5

6

7

8

9

10

11

12

0 02 04 06 08 1



ft

(min

)

120579


grades




40

50

60

70

80

90

100

0 02 04 06 08 1

fs

()

120579




grades






Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade


ls = 86

S(Plowast) ()




Emergency logistics








119894119895on arc (V



119894119895(119905) but





119894of arc (V

119894 V119895)
















0ge 12 So it





Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119894119895= 120579 sdot | ln 119904

119894119895|| ln 119878max minus


119894119895le 1



120579 namely



119865 (120579) = 120579|ln 119878 (119875)| minus 1003816100381610038161003816ln 119878max

10038161003816100381610038161003816100381610038161003816ln 119878min

1003816100381610038161003816 minus1003816100381610038161003816ln 119878max

1003816100381610038161003816


= 120579 sdot|ln 119878 (119875)|


+ 120578 sdot119879 (119875)


minus 1198871minus 1198872

(13)



1198661 Then 119865(120579) = sum










1lt 1205792le 1


sum

(V119894 V119895)isin1198751205791

(1205791

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816+

1 minus 1205791

119879max minus 119879min119905119894119895)

le sum

(V119894 V119895)isin1198751205792

(1205791

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816

+1 minus 1205791

119879max minus 119879min119905119894119895)

sum

(V119894 V119895)isin1198751205791

(1205792

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816+

1 minus 1205792

119879max minus 119879min119905119894119895)

ge sum

(V119894 V119895)isin1198751205792

(1205792

1003816100381610038161003816ln 119878min1003816100381610038161003816 minus

1003816100381610038161003816ln 119878max1003816100381610038161003816

10038161003816100381610038161003816ln 119904119894119895

10038161003816100381610038161003816

+1 minus 1205792

119879max minus 119879min119905119894119895)

(14)




(V119894 V119895)isin1198751205792 119905119894119895)




(V119894 V119895)isin1198751205792 119905119894119895)




is 119891119904(1205791) le 119891

119904(1205792) and 119891

119905(1205791) le 119891







119891119905(0) = minsum












120577denote


(1) for forall120577 isin [1205791 120579]119879(119875

120577) lt 119897119905and 119878(119875

120577) le 119878(119875

120579) if 119891119905(120579) lt

119897119905


120577) ge 119878(119875

120579) if 119891119905(120579) gt

119897119905

(3) 119875lowast = 119875120579if 119891119905(120579) = 119897

119905and 119878(119875

120579) ge 119897119904





1



119894119895for arc (V



120579of






0and 119875

1can be obtained



120578lowast












119905gt 0 119897119904gt 0 120582 isin (0 1)


1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904



120579


120579)






119894 V119895) 119908119894119895= | ln 119904


120579


120579)






1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904


119894119895(119879max minus 119879min) use


119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875



1= 120579 NC = NC + 1 119875lowast = 119875










119905gt 0 119897119904gt 0 120582 isin (0 1)


1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904





120579)






119894 V119895) 119908119894119895= | ln 119904




120579)






1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904


119894119895(119879max minus 119879min) use


119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875



1= 120579 NC = NC + 1 119875lowast = 119875








0

119894119895 and



1= (119881 119864) where 119864

1= 119890 119890 =

(V119894 V119895) and 119904



119894119895= 120579 sdot | ln 119904



119894 V119895)




119905and 119891







(V119894 V119895) (119897

119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


((0 0) (0 1)) (93 107 0705800397) ((1 0) (2 0)) (116 95 07105

00435) ((1 0) (1 1)) (86 117 0773100377)

((0 0) (1 0)) (57 119 0786600453) ((0 1) (1 1)) (110 117 07742

00511) ((1 1) (1 2)) (90 100 0745800379)

((0 1) (0 2)) (43 113 0777900354) ((1 1) (2 1)) (107 115 07663

00458)

((1 2) (1 3)) (120 116 0837200114) ((2 0) (3 0)) (42 83 08797 00251) ((3 0) (3 1)) (100 101 08429

00186)

((0 3) (1 3)) (95 93 08387 00211) ((2 1) (3 1)) (37 120 0894100114) ((3 0) (4 0)) (32 103 08985

00133)

((2 0) (2 1)) (32 79 08105 00147) ((0 2) (1 2)) (31 115 0807800175) ((2 1) (2 2)) (87 115 08665

00181)

((0 2) (0 3)) (107 93 0835100212) ((1 2) (2 2)) (68 84 08996

00140)

((2 2) (2 3)) (44 85 0877600145) ((2 2) (3 2)) (57 85 08290 00171)

((0 3) (0 4)) (63 87 0950300099) ((5 1) (5 2)) (117 108 09245

00004) ((4 2) (5 2)) (117 97 0996300020)

((0 4) (0 5)) (77 84 0936300085) ((4 0) (4 1)) (68 100 09168

00019) ((1 3) (2 3)) (58 82 0992200045)

((1 4) (1 5)) (64 99 0936700033) ((4 1) (4 2)) (99 117 09364

00062) ((2 3) (3 3)) (120 92 0917600051)

((1 3) (1 4)) (65 81 0994100025) ((4 2) (4 3)) (51 106 09268

00079) ((3 3) (4 3)) (84 93 0984200039)

((2 3) (2 4)) (105 90 0919900027) ((4 0) (5 0)) (111 118 09425

00030)((0 4) (1 4)) (38 98 09397

00037)

((2 4) (2 5)) (30 85 09167 00075) ((3 1) (4 1)) (52 112 0924600080) ((1 4) (2 4)) (91 108 09657

00006)

((3 1) (3 2)) (70 120 0969700036) ((4 1) (5 1)) (42 76 09967

00094) ((2 4) (3 4)) (78 85 09247 00001)

((3 2) (3 3)) (82 91 0929500034) ((3 2) (4 2)) (59 110 09329

00014) ((0 5) (1 5)) (85 102 0932000025)

((3 3) (3 4)) (116 91 0978600040) ((5 2) (5 3)) (33 110 09247

00041) ((1 5) (2 5)) (80 102 0986800034)

((3 4) (3 5)) (48 92 0930300088) ((5 3) (5 4)) (36 81 09652

00040) ((4 4) (5 4)) (102 114 0981000010)

((4 3) (4 4)) (62 108 0964500074) ((4 3) (5 3)) (39 79 09971

00020) ((2 5) (3 5)) (116 96 0986200097)

((4 4) (4 5)) (52 96 0920500044) ((5 4) (5 5)) (36 93 09901

00032) ((3 5) (4 5)) (31 113 0979900007)

((5 0) (5 1)) (46 78 0930600093) ((3 4) (4 4)) (39 101 09891

00042) ((4 5) (5 5)) (31 110 0927000004)












differently




119904()

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (4 4) (4 5)(5 5)]

(1 0) 72291 890278 ge72291

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (3 5) (4 5)(5 5)]

(074 026) 70850 889501 72000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 700

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 68000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 66000 85

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 64000

[(0 0) (0 1) (0 2) (1 2) (2 2)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(006 094) 61845 867396 62000

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(004 096) 61392 850263 61800

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(0 1) 61392 850263 61392


(0 0)(1 0)

(2 0)

(3 0)

(4 0)(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)

(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)

(3 4)

(2 4)

(1 4)







85

855

86

865

87

875

88

885

89

895

0 02 04 06 08 1

ft

()

120579








6

62

64

66

68

7

72

74

0 02 04 06 08 1

fs

(min

)

120579



89589

88588

87587

86586

85585

845

Safe

ty o

fPlowast

()

lt (min)6 62 64 66 68 7 72 74









1

08

06

04

02

06 62 64 66 68 7 72 74

lt (min)



119905

80

85

90

95

100

05 1 15 2 25 3 35 4 45 5 55 6 65

S(Plowast)

() Satisfactory

interval

T(Plowast) (min)

ls = 86

(0 0) (1 1)(2 0)

(2 2)

(3 3)

(4 4)


)








and 119904119894119895









(0 0) (5 5)[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)

(5 5)]61392 850263

61400

(1 1) (5 5) [(1 1) (2 1) (3 1) (3 2) (4 2)(4 3) (5 3) (5 4) (5 5)] 45894 923785

(2 0) (5 5) [(2 0) (2 1) (3 1) (3 2) (4 2)(5 2) (5 3) (5 4) (5 5)] 43956 956501

(2 2) (5 5) [(2 2) (2 3) (2 4) (3 4) (4 4)(4 5) (5 5)] 41354 974097

(3 3) (5 5) [(3 3) (3 4) (4 4) (4 5) (5 5)] 25987 987117(4 4) (5 5) [(4 4) (4 5) (5 5)] 08963 995248



0 120585 = 1 119902 = 1 120585 = 1 119902 = 1 120585 = 1 119902 = 1

86

1 120585 isin (09 10) 119902 isin (095 10) 120585 = 1 119902 isin (09 10) 120585 = 1 119902 = 1



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (09648 00052) ((1 0) (2 0)) (09361 00046) ((1 0) (1 1)) (09286 000002)((0 0) (1 0)) (09862 00037) ((0 1) (1 1)) (09351 00077) ((1 1) (1 2)) (09432 00002)((0 1) (0 2)) (09029 00013) ((1 1) (2 1)) (09514 00099)

II

((1 2) (1 3)) (1 0) ((2 0) (3 0)) (1 0) ((3 0) (3 1)) (1 0)((0 3) (1 3)) (1 0) ((2 1) (3 1)) (1 0) ((3 0) (4 0)) (1 0)((2 0) (2 1)) (1 0) ((0 2) (1 2)) (1 0) ((2 1) (2 2)) (1 0)((0 2) (0 3)) (1 0) ((1 2) (2 2)) (1 0)((2 2) (2 3)) (1 0) ((2 2) (3 2)) (1 0)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((4 2) (5 2)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((1 3) (2 3)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((2 3) (3 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((3 3) (4 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((0 4) (1 4)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((1 4) (2 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((2 4) (3 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((0 5) (1 5)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((1 5) (2 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((4 4) (5 4)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) (1 0) ((2 5) (3 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((3 5) (4 5)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) (1 0) ((4 5) (5 5)) (1 0)

120579lowast 096



(0 0)(1 0)

(2 0)

(3 0)(4 0)

(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)(3 4)

(2 4)

(1 4)

Area I

Area II

Area III



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (08606 00194) ((1 0) (2 0)) (08811 00226) ((1 0) (1 1)) (08735 00160)((0 0) (1 0)) (08652 00235) ((0 1) (1 1)) (08428 00250) ((1 1) (1 2)) (08332 00211)((0 1) (0 2)) (08306 00116) ((1 1) (2 1)) (08898 00141)

II

((2 0) (3 0)) (09091 00002) ((0 2) (0 3)) (09144 00097) ((3 0) (3 1)) (09110 00023)((2 1) (3 1)) (09381 00065) ((2 2) (2 3)) (09865 00043) ((3 0) (4 0)) (09302 00030)((0 2) (1 2)) (09985 00043) ((1 2) (1 3)) (09317 00099) ((2 1) (2 2)) (09572 00080)((1 2) (2 2)) (09024 00077) ((0 3) (1 3)) (09205 00089)((2 2) (3 2)) (1 0) ((2 0) (2 1)) (09352 00062)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((3 5) (4 5)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((4 2) (5 2)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((1 3) (2 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((2 3) (3 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((3 3) (4 3)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((0 4) (1 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((1 4) (2 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((2 4) (3 4)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((0 5) (1 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((1 5) (2 5)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) () ((4 5) (5 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((4 4) (5 4)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) () ((2 5) (3 5)) (1 0)




119905= 86min and


119894119895






119905and




Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00435) ((1 0) (1 1)) (07731 00377)((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) (07458 00379)((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((1 2) (1 3)) (08372 00114) ((2 0) (3 0)) (08797 00251) ((3 0) (3 1)) (08429 00186)((0 3) (1 3)) (08387 00211) ((2 1) (3 1)) (08941 00114) ((3 0) (4 0)) (08985 00133)((2 0) (2 1)) (08105 00147) ((0 2) (1 2)) (08078 00175) ((2 1) (2 2)) (08665 00181)((0 2) (0 3)) (08351 00212) ((1 2) (2 2)) (08996 00140)((2 2) (2 3)) (08776 00145) ((2 2) (3 2)) (08290 00171)

III

((0 3) (0 4)) (09503 00099) ((5 1) (5 2)) (09245 00004) ((4 2) (5 2)) (09963 00020)((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((1 3) (2 3)) (09922 00045)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((2 3) (3 3)) (09176 00051)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00027) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((3 2) (4 2)) (09329 00014) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((5 2) (5 3)) (09247 00041) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 3) (5 4)) (09652 00040) ((4 4) (5 4)) (09810 00010)((4 3) (4 4)) (09645 00074) ((4 3) (5 3)) (09971 00020) ((2 5) (3 5)) (09862 00097)((4 4) (4 5)) (09205 00044) ((5 4) (5 5)) (09901 00032) ((3 5) (4 5)) (09799 00007)((5 0) (5 1)) (09306 00093) ((3 4) (4 4)) (09891 00042) ((4 5) (5 5)) (09270 00004)

120579lowast 1


4

5

6

7

8

9

10

11

12

0 02 04 06 08 1



ft

(min

)

120579


grades




40

50

60

70

80

90

100

0 02 04 06 08 1

fs

()

120579




grades






Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade


ls = 86

S(Plowast) ()




Emergency logistics








119894119895on arc (V



119894119895(119905) but





119894of arc (V

119894 V119895)
















0ge 12 So it





Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











120577denote


(1) for forall120577 isin [1205791 120579]119879(119875

120577) lt 119897119905and 119878(119875

120577) le 119878(119875

120579) if 119891119905(120579) lt

119897119905


120577) ge 119878(119875

120579) if 119891119905(120579) gt

119897119905

(3) 119875lowast = 119875120579if 119891119905(120579) = 119897

119905and 119878(119875

120579) ge 119897119904





1



119894119895for arc (V



120579of






0and 119875

1can be obtained



120578lowast












119905gt 0 119897119904gt 0 120582 isin (0 1)


1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904



120579


120579)






119894 V119895) 119908119894119895= | ln 119904


120579


120579)






1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904


119894119895(119879max minus 119879min) use


119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875



1= 120579 NC = NC + 1 119875lowast = 119875










119905gt 0 119897119904gt 0 120582 isin (0 1)


1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904





120579)






119894 V119895) 119908119894119895= | ln 119904




120579)






1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904


119894119895(119879max minus 119879min) use


119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875



1= 120579 NC = NC + 1 119875lowast = 119875








0

119894119895 and



1= (119881 119864) where 119864

1= 119890 119890 =

(V119894 V119895) and 119904



119894119895= 120579 sdot | ln 119904



119894 V119895)




119905and 119891







(V119894 V119895) (119897

119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


((0 0) (0 1)) (93 107 0705800397) ((1 0) (2 0)) (116 95 07105

00435) ((1 0) (1 1)) (86 117 0773100377)

((0 0) (1 0)) (57 119 0786600453) ((0 1) (1 1)) (110 117 07742

00511) ((1 1) (1 2)) (90 100 0745800379)

((0 1) (0 2)) (43 113 0777900354) ((1 1) (2 1)) (107 115 07663

00458)

((1 2) (1 3)) (120 116 0837200114) ((2 0) (3 0)) (42 83 08797 00251) ((3 0) (3 1)) (100 101 08429

00186)

((0 3) (1 3)) (95 93 08387 00211) ((2 1) (3 1)) (37 120 0894100114) ((3 0) (4 0)) (32 103 08985

00133)

((2 0) (2 1)) (32 79 08105 00147) ((0 2) (1 2)) (31 115 0807800175) ((2 1) (2 2)) (87 115 08665

00181)

((0 2) (0 3)) (107 93 0835100212) ((1 2) (2 2)) (68 84 08996

00140)

((2 2) (2 3)) (44 85 0877600145) ((2 2) (3 2)) (57 85 08290 00171)

((0 3) (0 4)) (63 87 0950300099) ((5 1) (5 2)) (117 108 09245

00004) ((4 2) (5 2)) (117 97 0996300020)

((0 4) (0 5)) (77 84 0936300085) ((4 0) (4 1)) (68 100 09168

00019) ((1 3) (2 3)) (58 82 0992200045)

((1 4) (1 5)) (64 99 0936700033) ((4 1) (4 2)) (99 117 09364

00062) ((2 3) (3 3)) (120 92 0917600051)

((1 3) (1 4)) (65 81 0994100025) ((4 2) (4 3)) (51 106 09268

00079) ((3 3) (4 3)) (84 93 0984200039)

((2 3) (2 4)) (105 90 0919900027) ((4 0) (5 0)) (111 118 09425

00030)((0 4) (1 4)) (38 98 09397

00037)

((2 4) (2 5)) (30 85 09167 00075) ((3 1) (4 1)) (52 112 0924600080) ((1 4) (2 4)) (91 108 09657

00006)

((3 1) (3 2)) (70 120 0969700036) ((4 1) (5 1)) (42 76 09967

00094) ((2 4) (3 4)) (78 85 09247 00001)

((3 2) (3 3)) (82 91 0929500034) ((3 2) (4 2)) (59 110 09329

00014) ((0 5) (1 5)) (85 102 0932000025)

((3 3) (3 4)) (116 91 0978600040) ((5 2) (5 3)) (33 110 09247

00041) ((1 5) (2 5)) (80 102 0986800034)

((3 4) (3 5)) (48 92 0930300088) ((5 3) (5 4)) (36 81 09652

00040) ((4 4) (5 4)) (102 114 0981000010)

((4 3) (4 4)) (62 108 0964500074) ((4 3) (5 3)) (39 79 09971

00020) ((2 5) (3 5)) (116 96 0986200097)

((4 4) (4 5)) (52 96 0920500044) ((5 4) (5 5)) (36 93 09901

00032) ((3 5) (4 5)) (31 113 0979900007)

((5 0) (5 1)) (46 78 0930600093) ((3 4) (4 4)) (39 101 09891

00042) ((4 5) (5 5)) (31 110 0927000004)












differently




119904()

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (4 4) (4 5)(5 5)]

(1 0) 72291 890278 ge72291

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (3 5) (4 5)(5 5)]

(074 026) 70850 889501 72000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 700

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 68000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 66000 85

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 64000

[(0 0) (0 1) (0 2) (1 2) (2 2)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(006 094) 61845 867396 62000

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(004 096) 61392 850263 61800

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(0 1) 61392 850263 61392


(0 0)(1 0)

(2 0)

(3 0)

(4 0)(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)

(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)

(3 4)

(2 4)

(1 4)







85

855

86

865

87

875

88

885

89

895

0 02 04 06 08 1

ft

()

120579








6

62

64

66

68

7

72

74

0 02 04 06 08 1

fs

(min

)

120579



89589

88588

87587

86586

85585

845

Safe

ty o

fPlowast

()

lt (min)6 62 64 66 68 7 72 74









1

08

06

04

02

06 62 64 66 68 7 72 74

lt (min)



119905

80

85

90

95

100

05 1 15 2 25 3 35 4 45 5 55 6 65

S(Plowast)

() Satisfactory

interval

T(Plowast) (min)

ls = 86

(0 0) (1 1)(2 0)

(2 2)

(3 3)

(4 4)


)








and 119904119894119895









(0 0) (5 5)[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)

(5 5)]61392 850263

61400

(1 1) (5 5) [(1 1) (2 1) (3 1) (3 2) (4 2)(4 3) (5 3) (5 4) (5 5)] 45894 923785

(2 0) (5 5) [(2 0) (2 1) (3 1) (3 2) (4 2)(5 2) (5 3) (5 4) (5 5)] 43956 956501

(2 2) (5 5) [(2 2) (2 3) (2 4) (3 4) (4 4)(4 5) (5 5)] 41354 974097

(3 3) (5 5) [(3 3) (3 4) (4 4) (4 5) (5 5)] 25987 987117(4 4) (5 5) [(4 4) (4 5) (5 5)] 08963 995248



0 120585 = 1 119902 = 1 120585 = 1 119902 = 1 120585 = 1 119902 = 1

86

1 120585 isin (09 10) 119902 isin (095 10) 120585 = 1 119902 isin (09 10) 120585 = 1 119902 = 1



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (09648 00052) ((1 0) (2 0)) (09361 00046) ((1 0) (1 1)) (09286 000002)((0 0) (1 0)) (09862 00037) ((0 1) (1 1)) (09351 00077) ((1 1) (1 2)) (09432 00002)((0 1) (0 2)) (09029 00013) ((1 1) (2 1)) (09514 00099)

II

((1 2) (1 3)) (1 0) ((2 0) (3 0)) (1 0) ((3 0) (3 1)) (1 0)((0 3) (1 3)) (1 0) ((2 1) (3 1)) (1 0) ((3 0) (4 0)) (1 0)((2 0) (2 1)) (1 0) ((0 2) (1 2)) (1 0) ((2 1) (2 2)) (1 0)((0 2) (0 3)) (1 0) ((1 2) (2 2)) (1 0)((2 2) (2 3)) (1 0) ((2 2) (3 2)) (1 0)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((4 2) (5 2)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((1 3) (2 3)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((2 3) (3 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((3 3) (4 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((0 4) (1 4)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((1 4) (2 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((2 4) (3 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((0 5) (1 5)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((1 5) (2 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((4 4) (5 4)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) (1 0) ((2 5) (3 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((3 5) (4 5)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) (1 0) ((4 5) (5 5)) (1 0)

120579lowast 096



(0 0)(1 0)

(2 0)

(3 0)(4 0)

(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)(3 4)

(2 4)

(1 4)

Area I

Area II

Area III



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (08606 00194) ((1 0) (2 0)) (08811 00226) ((1 0) (1 1)) (08735 00160)((0 0) (1 0)) (08652 00235) ((0 1) (1 1)) (08428 00250) ((1 1) (1 2)) (08332 00211)((0 1) (0 2)) (08306 00116) ((1 1) (2 1)) (08898 00141)

II

((2 0) (3 0)) (09091 00002) ((0 2) (0 3)) (09144 00097) ((3 0) (3 1)) (09110 00023)((2 1) (3 1)) (09381 00065) ((2 2) (2 3)) (09865 00043) ((3 0) (4 0)) (09302 00030)((0 2) (1 2)) (09985 00043) ((1 2) (1 3)) (09317 00099) ((2 1) (2 2)) (09572 00080)((1 2) (2 2)) (09024 00077) ((0 3) (1 3)) (09205 00089)((2 2) (3 2)) (1 0) ((2 0) (2 1)) (09352 00062)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((3 5) (4 5)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((4 2) (5 2)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((1 3) (2 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((2 3) (3 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((3 3) (4 3)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((0 4) (1 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((1 4) (2 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((2 4) (3 4)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((0 5) (1 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((1 5) (2 5)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) () ((4 5) (5 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((4 4) (5 4)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) () ((2 5) (3 5)) (1 0)




119905= 86min and


119894119895






119905and




Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00435) ((1 0) (1 1)) (07731 00377)((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) (07458 00379)((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((1 2) (1 3)) (08372 00114) ((2 0) (3 0)) (08797 00251) ((3 0) (3 1)) (08429 00186)((0 3) (1 3)) (08387 00211) ((2 1) (3 1)) (08941 00114) ((3 0) (4 0)) (08985 00133)((2 0) (2 1)) (08105 00147) ((0 2) (1 2)) (08078 00175) ((2 1) (2 2)) (08665 00181)((0 2) (0 3)) (08351 00212) ((1 2) (2 2)) (08996 00140)((2 2) (2 3)) (08776 00145) ((2 2) (3 2)) (08290 00171)

III

((0 3) (0 4)) (09503 00099) ((5 1) (5 2)) (09245 00004) ((4 2) (5 2)) (09963 00020)((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((1 3) (2 3)) (09922 00045)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((2 3) (3 3)) (09176 00051)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00027) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((3 2) (4 2)) (09329 00014) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((5 2) (5 3)) (09247 00041) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 3) (5 4)) (09652 00040) ((4 4) (5 4)) (09810 00010)((4 3) (4 4)) (09645 00074) ((4 3) (5 3)) (09971 00020) ((2 5) (3 5)) (09862 00097)((4 4) (4 5)) (09205 00044) ((5 4) (5 5)) (09901 00032) ((3 5) (4 5)) (09799 00007)((5 0) (5 1)) (09306 00093) ((3 4) (4 4)) (09891 00042) ((4 5) (5 5)) (09270 00004)

120579lowast 1


4

5

6

7

8

9

10

11

12

0 02 04 06 08 1



ft

(min

)

120579


grades




40

50

60

70

80

90

100

0 02 04 06 08 1

fs

()

120579




grades






Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade


ls = 86

S(Plowast) ()




Emergency logistics








119894119895on arc (V



119894119895(119905) but





119894of arc (V

119894 V119895)
















0ge 12 So it





Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














119905gt 0 119897119904gt 0 120582 isin (0 1)


1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904



120579


120579)






119894 V119895) 119908119894119895= | ln 119904


120579


120579)






1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904


119894119895(119879max minus 119879min) use


119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875



1= 120579 NC = NC + 1 119875lowast = 119875










119905gt 0 119897119904gt 0 120582 isin (0 1)


1= 119890 119890 = (V

119894 V119895) and 119904

119894119895ge 119897119904





120579)






119894 V119895) 119908119894119895= | ln 119904




120579)






1+ 120582 sdot (120579

2minus 1205791) 119908119894119895= 120579 sdot | ln 119904


119894119895(119879max minus 119879min) use


119894119895

(4211) If 119891119905(120579) gt 119897

119905 1205792= 120579 NC = NC + 1 go to step 421

(4212) Else if 119891119905(120579) = 119897

119905 119875lowast = 119875



1= 120579 NC = NC + 1 119875lowast = 119875








0

119894119895 and



1= (119881 119864) where 119864

1= 119890 119890 =

(V119894 V119895) and 119904



119894119895= 120579 sdot | ln 119904



119894 V119895)




119905and 119891







(V119894 V119895) (119897

119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


((0 0) (0 1)) (93 107 0705800397) ((1 0) (2 0)) (116 95 07105

00435) ((1 0) (1 1)) (86 117 0773100377)

((0 0) (1 0)) (57 119 0786600453) ((0 1) (1 1)) (110 117 07742

00511) ((1 1) (1 2)) (90 100 0745800379)

((0 1) (0 2)) (43 113 0777900354) ((1 1) (2 1)) (107 115 07663

00458)

((1 2) (1 3)) (120 116 0837200114) ((2 0) (3 0)) (42 83 08797 00251) ((3 0) (3 1)) (100 101 08429

00186)

((0 3) (1 3)) (95 93 08387 00211) ((2 1) (3 1)) (37 120 0894100114) ((3 0) (4 0)) (32 103 08985

00133)

((2 0) (2 1)) (32 79 08105 00147) ((0 2) (1 2)) (31 115 0807800175) ((2 1) (2 2)) (87 115 08665

00181)

((0 2) (0 3)) (107 93 0835100212) ((1 2) (2 2)) (68 84 08996

00140)

((2 2) (2 3)) (44 85 0877600145) ((2 2) (3 2)) (57 85 08290 00171)

((0 3) (0 4)) (63 87 0950300099) ((5 1) (5 2)) (117 108 09245

00004) ((4 2) (5 2)) (117 97 0996300020)

((0 4) (0 5)) (77 84 0936300085) ((4 0) (4 1)) (68 100 09168

00019) ((1 3) (2 3)) (58 82 0992200045)

((1 4) (1 5)) (64 99 0936700033) ((4 1) (4 2)) (99 117 09364

00062) ((2 3) (3 3)) (120 92 0917600051)

((1 3) (1 4)) (65 81 0994100025) ((4 2) (4 3)) (51 106 09268

00079) ((3 3) (4 3)) (84 93 0984200039)

((2 3) (2 4)) (105 90 0919900027) ((4 0) (5 0)) (111 118 09425

00030)((0 4) (1 4)) (38 98 09397

00037)

((2 4) (2 5)) (30 85 09167 00075) ((3 1) (4 1)) (52 112 0924600080) ((1 4) (2 4)) (91 108 09657

00006)

((3 1) (3 2)) (70 120 0969700036) ((4 1) (5 1)) (42 76 09967

00094) ((2 4) (3 4)) (78 85 09247 00001)

((3 2) (3 3)) (82 91 0929500034) ((3 2) (4 2)) (59 110 09329

00014) ((0 5) (1 5)) (85 102 0932000025)

((3 3) (3 4)) (116 91 0978600040) ((5 2) (5 3)) (33 110 09247

00041) ((1 5) (2 5)) (80 102 0986800034)

((3 4) (3 5)) (48 92 0930300088) ((5 3) (5 4)) (36 81 09652

00040) ((4 4) (5 4)) (102 114 0981000010)

((4 3) (4 4)) (62 108 0964500074) ((4 3) (5 3)) (39 79 09971

00020) ((2 5) (3 5)) (116 96 0986200097)

((4 4) (4 5)) (52 96 0920500044) ((5 4) (5 5)) (36 93 09901

00032) ((3 5) (4 5)) (31 113 0979900007)

((5 0) (5 1)) (46 78 0930600093) ((3 4) (4 4)) (39 101 09891

00042) ((4 5) (5 5)) (31 110 0927000004)












differently




119904()

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (4 4) (4 5)(5 5)]

(1 0) 72291 890278 ge72291

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (3 5) (4 5)(5 5)]

(074 026) 70850 889501 72000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 700

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 68000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 66000 85

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 64000

[(0 0) (0 1) (0 2) (1 2) (2 2)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(006 094) 61845 867396 62000

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(004 096) 61392 850263 61800

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(0 1) 61392 850263 61392


(0 0)(1 0)

(2 0)

(3 0)

(4 0)(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)

(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)

(3 4)

(2 4)

(1 4)







85

855

86

865

87

875

88

885

89

895

0 02 04 06 08 1

ft

()

120579








6

62

64

66

68

7

72

74

0 02 04 06 08 1

fs

(min

)

120579



89589

88588

87587

86586

85585

845

Safe

ty o

fPlowast

()

lt (min)6 62 64 66 68 7 72 74









1

08

06

04

02

06 62 64 66 68 7 72 74

lt (min)



119905

80

85

90

95

100

05 1 15 2 25 3 35 4 45 5 55 6 65

S(Plowast)

() Satisfactory

interval

T(Plowast) (min)

ls = 86

(0 0) (1 1)(2 0)

(2 2)

(3 3)

(4 4)


)








and 119904119894119895









(0 0) (5 5)[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)

(5 5)]61392 850263

61400

(1 1) (5 5) [(1 1) (2 1) (3 1) (3 2) (4 2)(4 3) (5 3) (5 4) (5 5)] 45894 923785

(2 0) (5 5) [(2 0) (2 1) (3 1) (3 2) (4 2)(5 2) (5 3) (5 4) (5 5)] 43956 956501

(2 2) (5 5) [(2 2) (2 3) (2 4) (3 4) (4 4)(4 5) (5 5)] 41354 974097

(3 3) (5 5) [(3 3) (3 4) (4 4) (4 5) (5 5)] 25987 987117(4 4) (5 5) [(4 4) (4 5) (5 5)] 08963 995248



0 120585 = 1 119902 = 1 120585 = 1 119902 = 1 120585 = 1 119902 = 1

86

1 120585 isin (09 10) 119902 isin (095 10) 120585 = 1 119902 isin (09 10) 120585 = 1 119902 = 1



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (09648 00052) ((1 0) (2 0)) (09361 00046) ((1 0) (1 1)) (09286 000002)((0 0) (1 0)) (09862 00037) ((0 1) (1 1)) (09351 00077) ((1 1) (1 2)) (09432 00002)((0 1) (0 2)) (09029 00013) ((1 1) (2 1)) (09514 00099)

II

((1 2) (1 3)) (1 0) ((2 0) (3 0)) (1 0) ((3 0) (3 1)) (1 0)((0 3) (1 3)) (1 0) ((2 1) (3 1)) (1 0) ((3 0) (4 0)) (1 0)((2 0) (2 1)) (1 0) ((0 2) (1 2)) (1 0) ((2 1) (2 2)) (1 0)((0 2) (0 3)) (1 0) ((1 2) (2 2)) (1 0)((2 2) (2 3)) (1 0) ((2 2) (3 2)) (1 0)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((4 2) (5 2)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((1 3) (2 3)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((2 3) (3 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((3 3) (4 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((0 4) (1 4)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((1 4) (2 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((2 4) (3 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((0 5) (1 5)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((1 5) (2 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((4 4) (5 4)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) (1 0) ((2 5) (3 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((3 5) (4 5)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) (1 0) ((4 5) (5 5)) (1 0)

120579lowast 096



(0 0)(1 0)

(2 0)

(3 0)(4 0)

(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)(3 4)

(2 4)

(1 4)

Area I

Area II

Area III



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (08606 00194) ((1 0) (2 0)) (08811 00226) ((1 0) (1 1)) (08735 00160)((0 0) (1 0)) (08652 00235) ((0 1) (1 1)) (08428 00250) ((1 1) (1 2)) (08332 00211)((0 1) (0 2)) (08306 00116) ((1 1) (2 1)) (08898 00141)

II

((2 0) (3 0)) (09091 00002) ((0 2) (0 3)) (09144 00097) ((3 0) (3 1)) (09110 00023)((2 1) (3 1)) (09381 00065) ((2 2) (2 3)) (09865 00043) ((3 0) (4 0)) (09302 00030)((0 2) (1 2)) (09985 00043) ((1 2) (1 3)) (09317 00099) ((2 1) (2 2)) (09572 00080)((1 2) (2 2)) (09024 00077) ((0 3) (1 3)) (09205 00089)((2 2) (3 2)) (1 0) ((2 0) (2 1)) (09352 00062)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((3 5) (4 5)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((4 2) (5 2)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((1 3) (2 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((2 3) (3 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((3 3) (4 3)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((0 4) (1 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((1 4) (2 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((2 4) (3 4)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((0 5) (1 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((1 5) (2 5)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) () ((4 5) (5 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((4 4) (5 4)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) () ((2 5) (3 5)) (1 0)




119905= 86min and


119894119895






119905and




Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00435) ((1 0) (1 1)) (07731 00377)((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) (07458 00379)((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((1 2) (1 3)) (08372 00114) ((2 0) (3 0)) (08797 00251) ((3 0) (3 1)) (08429 00186)((0 3) (1 3)) (08387 00211) ((2 1) (3 1)) (08941 00114) ((3 0) (4 0)) (08985 00133)((2 0) (2 1)) (08105 00147) ((0 2) (1 2)) (08078 00175) ((2 1) (2 2)) (08665 00181)((0 2) (0 3)) (08351 00212) ((1 2) (2 2)) (08996 00140)((2 2) (2 3)) (08776 00145) ((2 2) (3 2)) (08290 00171)

III

((0 3) (0 4)) (09503 00099) ((5 1) (5 2)) (09245 00004) ((4 2) (5 2)) (09963 00020)((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((1 3) (2 3)) (09922 00045)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((2 3) (3 3)) (09176 00051)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00027) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((3 2) (4 2)) (09329 00014) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((5 2) (5 3)) (09247 00041) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 3) (5 4)) (09652 00040) ((4 4) (5 4)) (09810 00010)((4 3) (4 4)) (09645 00074) ((4 3) (5 3)) (09971 00020) ((2 5) (3 5)) (09862 00097)((4 4) (4 5)) (09205 00044) ((5 4) (5 5)) (09901 00032) ((3 5) (4 5)) (09799 00007)((5 0) (5 1)) (09306 00093) ((3 4) (4 4)) (09891 00042) ((4 5) (5 5)) (09270 00004)

120579lowast 1


4

5

6

7

8

9

10

11

12

0 02 04 06 08 1



ft

(min

)

120579


grades




40

50

60

70

80

90

100

0 02 04 06 08 1

fs

()

120579




grades






Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade


ls = 86

S(Plowast) ()




Emergency logistics








119894119895on arc (V



119894119895(119905) but





119894of arc (V

119894 V119895)
















0ge 12 So it





Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











(V119894 V119895) (119897

119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


119894119895 1199060119894119895 120585119894119895 | ln 119902

119894119895|)


((0 0) (0 1)) (93 107 0705800397) ((1 0) (2 0)) (116 95 07105

00435) ((1 0) (1 1)) (86 117 0773100377)

((0 0) (1 0)) (57 119 0786600453) ((0 1) (1 1)) (110 117 07742

00511) ((1 1) (1 2)) (90 100 0745800379)

((0 1) (0 2)) (43 113 0777900354) ((1 1) (2 1)) (107 115 07663

00458)

((1 2) (1 3)) (120 116 0837200114) ((2 0) (3 0)) (42 83 08797 00251) ((3 0) (3 1)) (100 101 08429

00186)

((0 3) (1 3)) (95 93 08387 00211) ((2 1) (3 1)) (37 120 0894100114) ((3 0) (4 0)) (32 103 08985

00133)

((2 0) (2 1)) (32 79 08105 00147) ((0 2) (1 2)) (31 115 0807800175) ((2 1) (2 2)) (87 115 08665

00181)

((0 2) (0 3)) (107 93 0835100212) ((1 2) (2 2)) (68 84 08996

00140)

((2 2) (2 3)) (44 85 0877600145) ((2 2) (3 2)) (57 85 08290 00171)

((0 3) (0 4)) (63 87 0950300099) ((5 1) (5 2)) (117 108 09245

00004) ((4 2) (5 2)) (117 97 0996300020)

((0 4) (0 5)) (77 84 0936300085) ((4 0) (4 1)) (68 100 09168

00019) ((1 3) (2 3)) (58 82 0992200045)

((1 4) (1 5)) (64 99 0936700033) ((4 1) (4 2)) (99 117 09364

00062) ((2 3) (3 3)) (120 92 0917600051)

((1 3) (1 4)) (65 81 0994100025) ((4 2) (4 3)) (51 106 09268

00079) ((3 3) (4 3)) (84 93 0984200039)

((2 3) (2 4)) (105 90 0919900027) ((4 0) (5 0)) (111 118 09425

00030)((0 4) (1 4)) (38 98 09397

00037)

((2 4) (2 5)) (30 85 09167 00075) ((3 1) (4 1)) (52 112 0924600080) ((1 4) (2 4)) (91 108 09657

00006)

((3 1) (3 2)) (70 120 0969700036) ((4 1) (5 1)) (42 76 09967

00094) ((2 4) (3 4)) (78 85 09247 00001)

((3 2) (3 3)) (82 91 0929500034) ((3 2) (4 2)) (59 110 09329

00014) ((0 5) (1 5)) (85 102 0932000025)

((3 3) (3 4)) (116 91 0978600040) ((5 2) (5 3)) (33 110 09247

00041) ((1 5) (2 5)) (80 102 0986800034)

((3 4) (3 5)) (48 92 0930300088) ((5 3) (5 4)) (36 81 09652

00040) ((4 4) (5 4)) (102 114 0981000010)

((4 3) (4 4)) (62 108 0964500074) ((4 3) (5 3)) (39 79 09971

00020) ((2 5) (3 5)) (116 96 0986200097)

((4 4) (4 5)) (52 96 0920500044) ((5 4) (5 5)) (36 93 09901

00032) ((3 5) (4 5)) (31 113 0979900007)

((5 0) (5 1)) (46 78 0930600093) ((3 4) (4 4)) (39 101 09891

00042) ((4 5) (5 5)) (31 110 0927000004)












differently




119904()

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (4 4) (4 5)(5 5)]

(1 0) 72291 890278 ge72291

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (3 5) (4 5)(5 5)]

(074 026) 70850 889501 72000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 700

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 68000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 66000 85

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 64000

[(0 0) (0 1) (0 2) (1 2) (2 2)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(006 094) 61845 867396 62000

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(004 096) 61392 850263 61800

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(0 1) 61392 850263 61392


(0 0)(1 0)

(2 0)

(3 0)

(4 0)(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)

(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)

(3 4)

(2 4)

(1 4)







85

855

86

865

87

875

88

885

89

895

0 02 04 06 08 1

ft

()

120579








6

62

64

66

68

7

72

74

0 02 04 06 08 1

fs

(min

)

120579



89589

88588

87587

86586

85585

845

Safe

ty o

fPlowast

()

lt (min)6 62 64 66 68 7 72 74









1

08

06

04

02

06 62 64 66 68 7 72 74

lt (min)



119905

80

85

90

95

100

05 1 15 2 25 3 35 4 45 5 55 6 65

S(Plowast)

() Satisfactory

interval

T(Plowast) (min)

ls = 86

(0 0) (1 1)(2 0)

(2 2)

(3 3)

(4 4)


)








and 119904119894119895









(0 0) (5 5)[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)

(5 5)]61392 850263

61400

(1 1) (5 5) [(1 1) (2 1) (3 1) (3 2) (4 2)(4 3) (5 3) (5 4) (5 5)] 45894 923785

(2 0) (5 5) [(2 0) (2 1) (3 1) (3 2) (4 2)(5 2) (5 3) (5 4) (5 5)] 43956 956501

(2 2) (5 5) [(2 2) (2 3) (2 4) (3 4) (4 4)(4 5) (5 5)] 41354 974097

(3 3) (5 5) [(3 3) (3 4) (4 4) (4 5) (5 5)] 25987 987117(4 4) (5 5) [(4 4) (4 5) (5 5)] 08963 995248



0 120585 = 1 119902 = 1 120585 = 1 119902 = 1 120585 = 1 119902 = 1

86

1 120585 isin (09 10) 119902 isin (095 10) 120585 = 1 119902 isin (09 10) 120585 = 1 119902 = 1



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (09648 00052) ((1 0) (2 0)) (09361 00046) ((1 0) (1 1)) (09286 000002)((0 0) (1 0)) (09862 00037) ((0 1) (1 1)) (09351 00077) ((1 1) (1 2)) (09432 00002)((0 1) (0 2)) (09029 00013) ((1 1) (2 1)) (09514 00099)

II

((1 2) (1 3)) (1 0) ((2 0) (3 0)) (1 0) ((3 0) (3 1)) (1 0)((0 3) (1 3)) (1 0) ((2 1) (3 1)) (1 0) ((3 0) (4 0)) (1 0)((2 0) (2 1)) (1 0) ((0 2) (1 2)) (1 0) ((2 1) (2 2)) (1 0)((0 2) (0 3)) (1 0) ((1 2) (2 2)) (1 0)((2 2) (2 3)) (1 0) ((2 2) (3 2)) (1 0)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((4 2) (5 2)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((1 3) (2 3)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((2 3) (3 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((3 3) (4 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((0 4) (1 4)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((1 4) (2 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((2 4) (3 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((0 5) (1 5)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((1 5) (2 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((4 4) (5 4)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) (1 0) ((2 5) (3 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((3 5) (4 5)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) (1 0) ((4 5) (5 5)) (1 0)

120579lowast 096



(0 0)(1 0)

(2 0)

(3 0)(4 0)

(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)(3 4)

(2 4)

(1 4)

Area I

Area II

Area III



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (08606 00194) ((1 0) (2 0)) (08811 00226) ((1 0) (1 1)) (08735 00160)((0 0) (1 0)) (08652 00235) ((0 1) (1 1)) (08428 00250) ((1 1) (1 2)) (08332 00211)((0 1) (0 2)) (08306 00116) ((1 1) (2 1)) (08898 00141)

II

((2 0) (3 0)) (09091 00002) ((0 2) (0 3)) (09144 00097) ((3 0) (3 1)) (09110 00023)((2 1) (3 1)) (09381 00065) ((2 2) (2 3)) (09865 00043) ((3 0) (4 0)) (09302 00030)((0 2) (1 2)) (09985 00043) ((1 2) (1 3)) (09317 00099) ((2 1) (2 2)) (09572 00080)((1 2) (2 2)) (09024 00077) ((0 3) (1 3)) (09205 00089)((2 2) (3 2)) (1 0) ((2 0) (2 1)) (09352 00062)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((3 5) (4 5)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((4 2) (5 2)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((1 3) (2 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((2 3) (3 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((3 3) (4 3)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((0 4) (1 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((1 4) (2 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((2 4) (3 4)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((0 5) (1 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((1 5) (2 5)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) () ((4 5) (5 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((4 4) (5 4)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) () ((2 5) (3 5)) (1 0)




119905= 86min and


119894119895






119905and




Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00435) ((1 0) (1 1)) (07731 00377)((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) (07458 00379)((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((1 2) (1 3)) (08372 00114) ((2 0) (3 0)) (08797 00251) ((3 0) (3 1)) (08429 00186)((0 3) (1 3)) (08387 00211) ((2 1) (3 1)) (08941 00114) ((3 0) (4 0)) (08985 00133)((2 0) (2 1)) (08105 00147) ((0 2) (1 2)) (08078 00175) ((2 1) (2 2)) (08665 00181)((0 2) (0 3)) (08351 00212) ((1 2) (2 2)) (08996 00140)((2 2) (2 3)) (08776 00145) ((2 2) (3 2)) (08290 00171)

III

((0 3) (0 4)) (09503 00099) ((5 1) (5 2)) (09245 00004) ((4 2) (5 2)) (09963 00020)((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((1 3) (2 3)) (09922 00045)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((2 3) (3 3)) (09176 00051)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00027) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((3 2) (4 2)) (09329 00014) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((5 2) (5 3)) (09247 00041) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 3) (5 4)) (09652 00040) ((4 4) (5 4)) (09810 00010)((4 3) (4 4)) (09645 00074) ((4 3) (5 3)) (09971 00020) ((2 5) (3 5)) (09862 00097)((4 4) (4 5)) (09205 00044) ((5 4) (5 5)) (09901 00032) ((3 5) (4 5)) (09799 00007)((5 0) (5 1)) (09306 00093) ((3 4) (4 4)) (09891 00042) ((4 5) (5 5)) (09270 00004)

120579lowast 1


4

5

6

7

8

9

10

11

12

0 02 04 06 08 1



ft

(min

)

120579


grades




40

50

60

70

80

90

100

0 02 04 06 08 1

fs

()

120579




grades






Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade


ls = 86

S(Plowast) ()




Emergency logistics








119894119895on arc (V



119894119895(119905) but





119894of arc (V

119894 V119895)
















0ge 12 So it





Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119904()

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (4 4) (4 5)(5 5)]

(1 0) 72291 890278 ge72291

[(0 0) (0 1) (0 2) (1 2) (1 3)(1 4) (2 4) (3 4) (3 5) (4 5)(5 5)]

(074 026) 70850 889501 72000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 700

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 68000

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 66000 85

[(0 0) (1 0) (2 0) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(044 056) 62042 871939 64000

[(0 0) (0 1) (0 2) (1 2) (2 2)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(006 094) 61845 867396 62000

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(004 096) 61392 850263 61800

[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)(5 5)]

(0 1) 61392 850263 61392


(0 0)(1 0)

(2 0)

(3 0)

(4 0)(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)

(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)

(3 4)

(2 4)

(1 4)







85

855

86

865

87

875

88

885

89

895

0 02 04 06 08 1

ft

()

120579








6

62

64

66

68

7

72

74

0 02 04 06 08 1

fs

(min

)

120579



89589

88588

87587

86586

85585

845

Safe

ty o

fPlowast

()

lt (min)6 62 64 66 68 7 72 74









1

08

06

04

02

06 62 64 66 68 7 72 74

lt (min)



119905

80

85

90

95

100

05 1 15 2 25 3 35 4 45 5 55 6 65

S(Plowast)

() Satisfactory

interval

T(Plowast) (min)

ls = 86

(0 0) (1 1)(2 0)

(2 2)

(3 3)

(4 4)


)








and 119904119894119895









(0 0) (5 5)[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)

(5 5)]61392 850263

61400

(1 1) (5 5) [(1 1) (2 1) (3 1) (3 2) (4 2)(4 3) (5 3) (5 4) (5 5)] 45894 923785

(2 0) (5 5) [(2 0) (2 1) (3 1) (3 2) (4 2)(5 2) (5 3) (5 4) (5 5)] 43956 956501

(2 2) (5 5) [(2 2) (2 3) (2 4) (3 4) (4 4)(4 5) (5 5)] 41354 974097

(3 3) (5 5) [(3 3) (3 4) (4 4) (4 5) (5 5)] 25987 987117(4 4) (5 5) [(4 4) (4 5) (5 5)] 08963 995248



0 120585 = 1 119902 = 1 120585 = 1 119902 = 1 120585 = 1 119902 = 1

86

1 120585 isin (09 10) 119902 isin (095 10) 120585 = 1 119902 isin (09 10) 120585 = 1 119902 = 1



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (09648 00052) ((1 0) (2 0)) (09361 00046) ((1 0) (1 1)) (09286 000002)((0 0) (1 0)) (09862 00037) ((0 1) (1 1)) (09351 00077) ((1 1) (1 2)) (09432 00002)((0 1) (0 2)) (09029 00013) ((1 1) (2 1)) (09514 00099)

II

((1 2) (1 3)) (1 0) ((2 0) (3 0)) (1 0) ((3 0) (3 1)) (1 0)((0 3) (1 3)) (1 0) ((2 1) (3 1)) (1 0) ((3 0) (4 0)) (1 0)((2 0) (2 1)) (1 0) ((0 2) (1 2)) (1 0) ((2 1) (2 2)) (1 0)((0 2) (0 3)) (1 0) ((1 2) (2 2)) (1 0)((2 2) (2 3)) (1 0) ((2 2) (3 2)) (1 0)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((4 2) (5 2)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((1 3) (2 3)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((2 3) (3 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((3 3) (4 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((0 4) (1 4)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((1 4) (2 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((2 4) (3 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((0 5) (1 5)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((1 5) (2 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((4 4) (5 4)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) (1 0) ((2 5) (3 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((3 5) (4 5)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) (1 0) ((4 5) (5 5)) (1 0)

120579lowast 096



(0 0)(1 0)

(2 0)

(3 0)(4 0)

(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)(3 4)

(2 4)

(1 4)

Area I

Area II

Area III



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (08606 00194) ((1 0) (2 0)) (08811 00226) ((1 0) (1 1)) (08735 00160)((0 0) (1 0)) (08652 00235) ((0 1) (1 1)) (08428 00250) ((1 1) (1 2)) (08332 00211)((0 1) (0 2)) (08306 00116) ((1 1) (2 1)) (08898 00141)

II

((2 0) (3 0)) (09091 00002) ((0 2) (0 3)) (09144 00097) ((3 0) (3 1)) (09110 00023)((2 1) (3 1)) (09381 00065) ((2 2) (2 3)) (09865 00043) ((3 0) (4 0)) (09302 00030)((0 2) (1 2)) (09985 00043) ((1 2) (1 3)) (09317 00099) ((2 1) (2 2)) (09572 00080)((1 2) (2 2)) (09024 00077) ((0 3) (1 3)) (09205 00089)((2 2) (3 2)) (1 0) ((2 0) (2 1)) (09352 00062)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((3 5) (4 5)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((4 2) (5 2)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((1 3) (2 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((2 3) (3 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((3 3) (4 3)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((0 4) (1 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((1 4) (2 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((2 4) (3 4)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((0 5) (1 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((1 5) (2 5)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) () ((4 5) (5 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((4 4) (5 4)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) () ((2 5) (3 5)) (1 0)




119905= 86min and


119894119895






119905and




Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00435) ((1 0) (1 1)) (07731 00377)((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) (07458 00379)((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((1 2) (1 3)) (08372 00114) ((2 0) (3 0)) (08797 00251) ((3 0) (3 1)) (08429 00186)((0 3) (1 3)) (08387 00211) ((2 1) (3 1)) (08941 00114) ((3 0) (4 0)) (08985 00133)((2 0) (2 1)) (08105 00147) ((0 2) (1 2)) (08078 00175) ((2 1) (2 2)) (08665 00181)((0 2) (0 3)) (08351 00212) ((1 2) (2 2)) (08996 00140)((2 2) (2 3)) (08776 00145) ((2 2) (3 2)) (08290 00171)

III

((0 3) (0 4)) (09503 00099) ((5 1) (5 2)) (09245 00004) ((4 2) (5 2)) (09963 00020)((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((1 3) (2 3)) (09922 00045)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((2 3) (3 3)) (09176 00051)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00027) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((3 2) (4 2)) (09329 00014) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((5 2) (5 3)) (09247 00041) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 3) (5 4)) (09652 00040) ((4 4) (5 4)) (09810 00010)((4 3) (4 4)) (09645 00074) ((4 3) (5 3)) (09971 00020) ((2 5) (3 5)) (09862 00097)((4 4) (4 5)) (09205 00044) ((5 4) (5 5)) (09901 00032) ((3 5) (4 5)) (09799 00007)((5 0) (5 1)) (09306 00093) ((3 4) (4 4)) (09891 00042) ((4 5) (5 5)) (09270 00004)

120579lowast 1


4

5

6

7

8

9

10

11

12

0 02 04 06 08 1



ft

(min

)

120579


grades




40

50

60

70

80

90

100

0 02 04 06 08 1

fs

()

120579




grades






Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade


ls = 86

S(Plowast) ()




Emergency logistics








119894119895on arc (V



119894119895(119905) but





119894of arc (V

119894 V119895)
















0ge 12 So it





Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










6

62

64

66

68

7

72

74

0 02 04 06 08 1

fs

(min

)

120579



89589

88588

87587

86586

85585

845

Safe

ty o

fPlowast

()

lt (min)6 62 64 66 68 7 72 74









1

08

06

04

02

06 62 64 66 68 7 72 74

lt (min)



119905

80

85

90

95

100

05 1 15 2 25 3 35 4 45 5 55 6 65

S(Plowast)

() Satisfactory

interval

T(Plowast) (min)

ls = 86

(0 0) (1 1)(2 0)

(2 2)

(3 3)

(4 4)


)








and 119904119894119895









(0 0) (5 5)[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)

(5 5)]61392 850263

61400

(1 1) (5 5) [(1 1) (2 1) (3 1) (3 2) (4 2)(4 3) (5 3) (5 4) (5 5)] 45894 923785

(2 0) (5 5) [(2 0) (2 1) (3 1) (3 2) (4 2)(5 2) (5 3) (5 4) (5 5)] 43956 956501

(2 2) (5 5) [(2 2) (2 3) (2 4) (3 4) (4 4)(4 5) (5 5)] 41354 974097

(3 3) (5 5) [(3 3) (3 4) (4 4) (4 5) (5 5)] 25987 987117(4 4) (5 5) [(4 4) (4 5) (5 5)] 08963 995248



0 120585 = 1 119902 = 1 120585 = 1 119902 = 1 120585 = 1 119902 = 1

86

1 120585 isin (09 10) 119902 isin (095 10) 120585 = 1 119902 isin (09 10) 120585 = 1 119902 = 1



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (09648 00052) ((1 0) (2 0)) (09361 00046) ((1 0) (1 1)) (09286 000002)((0 0) (1 0)) (09862 00037) ((0 1) (1 1)) (09351 00077) ((1 1) (1 2)) (09432 00002)((0 1) (0 2)) (09029 00013) ((1 1) (2 1)) (09514 00099)

II

((1 2) (1 3)) (1 0) ((2 0) (3 0)) (1 0) ((3 0) (3 1)) (1 0)((0 3) (1 3)) (1 0) ((2 1) (3 1)) (1 0) ((3 0) (4 0)) (1 0)((2 0) (2 1)) (1 0) ((0 2) (1 2)) (1 0) ((2 1) (2 2)) (1 0)((0 2) (0 3)) (1 0) ((1 2) (2 2)) (1 0)((2 2) (2 3)) (1 0) ((2 2) (3 2)) (1 0)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((4 2) (5 2)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((1 3) (2 3)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((2 3) (3 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((3 3) (4 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((0 4) (1 4)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((1 4) (2 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((2 4) (3 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((0 5) (1 5)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((1 5) (2 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((4 4) (5 4)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) (1 0) ((2 5) (3 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((3 5) (4 5)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) (1 0) ((4 5) (5 5)) (1 0)

120579lowast 096



(0 0)(1 0)

(2 0)

(3 0)(4 0)

(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)(3 4)

(2 4)

(1 4)

Area I

Area II

Area III



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (08606 00194) ((1 0) (2 0)) (08811 00226) ((1 0) (1 1)) (08735 00160)((0 0) (1 0)) (08652 00235) ((0 1) (1 1)) (08428 00250) ((1 1) (1 2)) (08332 00211)((0 1) (0 2)) (08306 00116) ((1 1) (2 1)) (08898 00141)

II

((2 0) (3 0)) (09091 00002) ((0 2) (0 3)) (09144 00097) ((3 0) (3 1)) (09110 00023)((2 1) (3 1)) (09381 00065) ((2 2) (2 3)) (09865 00043) ((3 0) (4 0)) (09302 00030)((0 2) (1 2)) (09985 00043) ((1 2) (1 3)) (09317 00099) ((2 1) (2 2)) (09572 00080)((1 2) (2 2)) (09024 00077) ((0 3) (1 3)) (09205 00089)((2 2) (3 2)) (1 0) ((2 0) (2 1)) (09352 00062)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((3 5) (4 5)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((4 2) (5 2)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((1 3) (2 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((2 3) (3 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((3 3) (4 3)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((0 4) (1 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((1 4) (2 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((2 4) (3 4)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((0 5) (1 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((1 5) (2 5)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) () ((4 5) (5 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((4 4) (5 4)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) () ((2 5) (3 5)) (1 0)




119905= 86min and


119894119895






119905and




Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00435) ((1 0) (1 1)) (07731 00377)((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) (07458 00379)((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((1 2) (1 3)) (08372 00114) ((2 0) (3 0)) (08797 00251) ((3 0) (3 1)) (08429 00186)((0 3) (1 3)) (08387 00211) ((2 1) (3 1)) (08941 00114) ((3 0) (4 0)) (08985 00133)((2 0) (2 1)) (08105 00147) ((0 2) (1 2)) (08078 00175) ((2 1) (2 2)) (08665 00181)((0 2) (0 3)) (08351 00212) ((1 2) (2 2)) (08996 00140)((2 2) (2 3)) (08776 00145) ((2 2) (3 2)) (08290 00171)

III

((0 3) (0 4)) (09503 00099) ((5 1) (5 2)) (09245 00004) ((4 2) (5 2)) (09963 00020)((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((1 3) (2 3)) (09922 00045)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((2 3) (3 3)) (09176 00051)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00027) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((3 2) (4 2)) (09329 00014) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((5 2) (5 3)) (09247 00041) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 3) (5 4)) (09652 00040) ((4 4) (5 4)) (09810 00010)((4 3) (4 4)) (09645 00074) ((4 3) (5 3)) (09971 00020) ((2 5) (3 5)) (09862 00097)((4 4) (4 5)) (09205 00044) ((5 4) (5 5)) (09901 00032) ((3 5) (4 5)) (09799 00007)((5 0) (5 1)) (09306 00093) ((3 4) (4 4)) (09891 00042) ((4 5) (5 5)) (09270 00004)

120579lowast 1


4

5

6

7

8

9

10

11

12

0 02 04 06 08 1



ft

(min

)

120579


grades




40

50

60

70

80

90

100

0 02 04 06 08 1

fs

()

120579




grades






Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade


ls = 86

S(Plowast) ()




Emergency logistics








119894119895on arc (V



119894119895(119905) but





119894of arc (V

119894 V119895)
















0ge 12 So it





Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












(0 0) (5 5)[(0 0) (1 0) (1 1) (2 1) (3 1)(3 2) (4 2) (4 3) (5 3) (5 4)

(5 5)]61392 850263

61400

(1 1) (5 5) [(1 1) (2 1) (3 1) (3 2) (4 2)(4 3) (5 3) (5 4) (5 5)] 45894 923785

(2 0) (5 5) [(2 0) (2 1) (3 1) (3 2) (4 2)(5 2) (5 3) (5 4) (5 5)] 43956 956501

(2 2) (5 5) [(2 2) (2 3) (2 4) (3 4) (4 4)(4 5) (5 5)] 41354 974097

(3 3) (5 5) [(3 3) (3 4) (4 4) (4 5) (5 5)] 25987 987117(4 4) (5 5) [(4 4) (4 5) (5 5)] 08963 995248



0 120585 = 1 119902 = 1 120585 = 1 119902 = 1 120585 = 1 119902 = 1

86

1 120585 isin (09 10) 119902 isin (095 10) 120585 = 1 119902 isin (09 10) 120585 = 1 119902 = 1



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (09648 00052) ((1 0) (2 0)) (09361 00046) ((1 0) (1 1)) (09286 000002)((0 0) (1 0)) (09862 00037) ((0 1) (1 1)) (09351 00077) ((1 1) (1 2)) (09432 00002)((0 1) (0 2)) (09029 00013) ((1 1) (2 1)) (09514 00099)

II

((1 2) (1 3)) (1 0) ((2 0) (3 0)) (1 0) ((3 0) (3 1)) (1 0)((0 3) (1 3)) (1 0) ((2 1) (3 1)) (1 0) ((3 0) (4 0)) (1 0)((2 0) (2 1)) (1 0) ((0 2) (1 2)) (1 0) ((2 1) (2 2)) (1 0)((0 2) (0 3)) (1 0) ((1 2) (2 2)) (1 0)((2 2) (2 3)) (1 0) ((2 2) (3 2)) (1 0)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((4 2) (5 2)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((1 3) (2 3)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((2 3) (3 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((3 3) (4 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((0 4) (1 4)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((1 4) (2 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((2 4) (3 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((0 5) (1 5)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((1 5) (2 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((4 4) (5 4)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) (1 0) ((2 5) (3 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((3 5) (4 5)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) (1 0) ((4 5) (5 5)) (1 0)

120579lowast 096



(0 0)(1 0)

(2 0)

(3 0)(4 0)

(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)(3 4)

(2 4)

(1 4)

Area I

Area II

Area III



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (08606 00194) ((1 0) (2 0)) (08811 00226) ((1 0) (1 1)) (08735 00160)((0 0) (1 0)) (08652 00235) ((0 1) (1 1)) (08428 00250) ((1 1) (1 2)) (08332 00211)((0 1) (0 2)) (08306 00116) ((1 1) (2 1)) (08898 00141)

II

((2 0) (3 0)) (09091 00002) ((0 2) (0 3)) (09144 00097) ((3 0) (3 1)) (09110 00023)((2 1) (3 1)) (09381 00065) ((2 2) (2 3)) (09865 00043) ((3 0) (4 0)) (09302 00030)((0 2) (1 2)) (09985 00043) ((1 2) (1 3)) (09317 00099) ((2 1) (2 2)) (09572 00080)((1 2) (2 2)) (09024 00077) ((0 3) (1 3)) (09205 00089)((2 2) (3 2)) (1 0) ((2 0) (2 1)) (09352 00062)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((3 5) (4 5)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((4 2) (5 2)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((1 3) (2 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((2 3) (3 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((3 3) (4 3)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((0 4) (1 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((1 4) (2 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((2 4) (3 4)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((0 5) (1 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((1 5) (2 5)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) () ((4 5) (5 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((4 4) (5 4)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) () ((2 5) (3 5)) (1 0)




119905= 86min and


119894119895






119905and




Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00435) ((1 0) (1 1)) (07731 00377)((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) (07458 00379)((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((1 2) (1 3)) (08372 00114) ((2 0) (3 0)) (08797 00251) ((3 0) (3 1)) (08429 00186)((0 3) (1 3)) (08387 00211) ((2 1) (3 1)) (08941 00114) ((3 0) (4 0)) (08985 00133)((2 0) (2 1)) (08105 00147) ((0 2) (1 2)) (08078 00175) ((2 1) (2 2)) (08665 00181)((0 2) (0 3)) (08351 00212) ((1 2) (2 2)) (08996 00140)((2 2) (2 3)) (08776 00145) ((2 2) (3 2)) (08290 00171)

III

((0 3) (0 4)) (09503 00099) ((5 1) (5 2)) (09245 00004) ((4 2) (5 2)) (09963 00020)((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((1 3) (2 3)) (09922 00045)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((2 3) (3 3)) (09176 00051)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00027) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((3 2) (4 2)) (09329 00014) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((5 2) (5 3)) (09247 00041) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 3) (5 4)) (09652 00040) ((4 4) (5 4)) (09810 00010)((4 3) (4 4)) (09645 00074) ((4 3) (5 3)) (09971 00020) ((2 5) (3 5)) (09862 00097)((4 4) (4 5)) (09205 00044) ((5 4) (5 5)) (09901 00032) ((3 5) (4 5)) (09799 00007)((5 0) (5 1)) (09306 00093) ((3 4) (4 4)) (09891 00042) ((4 5) (5 5)) (09270 00004)

120579lowast 1


4

5

6

7

8

9

10

11

12

0 02 04 06 08 1



ft

(min

)

120579


grades




40

50

60

70

80

90

100

0 02 04 06 08 1

fs

()

120579




grades






Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade


ls = 86

S(Plowast) ()




Emergency logistics








119894119895on arc (V



119894119895(119905) but





119894of arc (V

119894 V119895)
















0ge 12 So it





Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(0 0)(1 0)

(2 0)

(3 0)(4 0)

(5 0)

(5 1)

(5 2)

(5 3)

(5 4)

(5 5)(4 5)

(3 5)

(2 5)

(1 5)(0 5)

(0 4)

(0 3)

(0 2)

(0 1)(1 1)

(2 1)

(3 1)(4 1)

(4 2)

(3 2)

(2 2)

(1 2)

(1 3)

(2 3)

(3 3)(4 3)

(4 4)(3 4)

(2 4)

(1 4)

Area I

Area II

Area III



Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (08606 00194) ((1 0) (2 0)) (08811 00226) ((1 0) (1 1)) (08735 00160)((0 0) (1 0)) (08652 00235) ((0 1) (1 1)) (08428 00250) ((1 1) (1 2)) (08332 00211)((0 1) (0 2)) (08306 00116) ((1 1) (2 1)) (08898 00141)

II

((2 0) (3 0)) (09091 00002) ((0 2) (0 3)) (09144 00097) ((3 0) (3 1)) (09110 00023)((2 1) (3 1)) (09381 00065) ((2 2) (2 3)) (09865 00043) ((3 0) (4 0)) (09302 00030)((0 2) (1 2)) (09985 00043) ((1 2) (1 3)) (09317 00099) ((2 1) (2 2)) (09572 00080)((1 2) (2 2)) (09024 00077) ((0 3) (1 3)) (09205 00089)((2 2) (3 2)) (1 0) ((2 0) (2 1)) (09352 00062)

III

((0 3) (0 4)) (1 0) ((5 1) (5 2)) (1 0) ((3 5) (4 5)) (1 0)((0 4) (0 5)) (1 0) ((4 0) (4 1)) (1 0) ((4 2) (5 2)) (1 0)((1 4) (1 5)) (1 0) ((4 1) (4 2)) (1 0) ((1 3) (2 3)) (1 0)((1 3) (1 4)) (1 0) ((4 2) (4 3)) (1 0) ((2 3) (3 3)) (1 0)((2 3) (2 4)) (1 0) ((4 0) (5 0)) (1 0) ((3 3) (4 3)) (1 0)((2 4) (2 5)) (1 0) ((3 1) (4 1)) (1 0) ((0 4) (1 4)) (1 0)((3 1) (3 2)) (1 0) ((4 1) (5 1)) (1 0) ((1 4) (2 4)) (1 0)((3 2) (3 3)) (1 0) ((3 2) (4 2)) (1 0) ((2 4) (3 4)) (1 0)((3 3) (3 4)) (1 0) ((5 2) (5 3)) (1 0) ((0 5) (1 5)) (1 0)((3 4) (3 5)) (1 0) ((5 3) (5 4)) (1 0) ((1 5) (2 5)) (1 0)((4 3) (4 4)) (1 0) ((4 3) (5 3)) () ((4 5) (5 5)) (1 0)((4 4) (4 5)) (1 0) ((5 4) (5 5)) (1 0) ((4 4) (5 4)) (1 0)((5 0) (5 1)) (1 0) ((3 4) (4 4)) () ((2 5) (3 5)) (1 0)




119905= 86min and


119894119895






119905and




Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00435) ((1 0) (1 1)) (07731 00377)((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) (07458 00379)((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((1 2) (1 3)) (08372 00114) ((2 0) (3 0)) (08797 00251) ((3 0) (3 1)) (08429 00186)((0 3) (1 3)) (08387 00211) ((2 1) (3 1)) (08941 00114) ((3 0) (4 0)) (08985 00133)((2 0) (2 1)) (08105 00147) ((0 2) (1 2)) (08078 00175) ((2 1) (2 2)) (08665 00181)((0 2) (0 3)) (08351 00212) ((1 2) (2 2)) (08996 00140)((2 2) (2 3)) (08776 00145) ((2 2) (3 2)) (08290 00171)

III

((0 3) (0 4)) (09503 00099) ((5 1) (5 2)) (09245 00004) ((4 2) (5 2)) (09963 00020)((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((1 3) (2 3)) (09922 00045)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((2 3) (3 3)) (09176 00051)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00027) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((3 2) (4 2)) (09329 00014) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((5 2) (5 3)) (09247 00041) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 3) (5 4)) (09652 00040) ((4 4) (5 4)) (09810 00010)((4 3) (4 4)) (09645 00074) ((4 3) (5 3)) (09971 00020) ((2 5) (3 5)) (09862 00097)((4 4) (4 5)) (09205 00044) ((5 4) (5 5)) (09901 00032) ((3 5) (4 5)) (09799 00007)((5 0) (5 1)) (09306 00093) ((3 4) (4 4)) (09891 00042) ((4 5) (5 5)) (09270 00004)

120579lowast 1


4

5

6

7

8

9

10

11

12

0 02 04 06 08 1



ft

(min

)

120579


grades




40

50

60

70

80

90

100

0 02 04 06 08 1

fs

()

120579




grades






Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade


ls = 86

S(Plowast) ()




Emergency logistics








119894119895on arc (V



119894119895(119905) but





119894of arc (V

119894 V119895)
















0ge 12 So it





Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00435) ((1 0) (1 1)) (07731 00377)((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) (07458 00379)((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((1 2) (1 3)) (08372 00114) ((2 0) (3 0)) (08797 00251) ((3 0) (3 1)) (08429 00186)((0 3) (1 3)) (08387 00211) ((2 1) (3 1)) (08941 00114) ((3 0) (4 0)) (08985 00133)((2 0) (2 1)) (08105 00147) ((0 2) (1 2)) (08078 00175) ((2 1) (2 2)) (08665 00181)((0 2) (0 3)) (08351 00212) ((1 2) (2 2)) (08996 00140)((2 2) (2 3)) (08776 00145) ((2 2) (3 2)) (08290 00171)

III

((0 3) (0 4)) (09503 00099) ((5 1) (5 2)) (09245 00004) ((4 2) (5 2)) (09963 00020)((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((1 3) (2 3)) (09922 00045)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((2 3) (3 3)) (09176 00051)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00027) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((3 2) (4 2)) (09329 00014) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((5 2) (5 3)) (09247 00041) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 3) (5 4)) (09652 00040) ((4 4) (5 4)) (09810 00010)((4 3) (4 4)) (09645 00074) ((4 3) (5 3)) (09971 00020) ((2 5) (3 5)) (09862 00097)((4 4) (4 5)) (09205 00044) ((5 4) (5 5)) (09901 00032) ((3 5) (4 5)) (09799 00007)((5 0) (5 1)) (09306 00093) ((3 4) (4 4)) (09891 00042) ((4 5) (5 5)) (09270 00004)

120579lowast 1


4

5

6

7

8

9

10

11

12

0 02 04 06 08 1



ft

(min

)

120579


grades




40

50

60

70

80

90

100

0 02 04 06 08 1

fs

()

120579




grades






Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade


ls = 86

S(Plowast) ()




Emergency logistics








119894119895on arc (V



119894119895(119905) but





119894of arc (V

119894 V119895)
















0ge 12 So it





Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (06743 01132) ((1 0) (2 0)) (06920 01518) ((1 0) (1 1)) (06817 01610)((0 0) (1 0)) (06219 01140) ((0 1) (1 1)) (06292 00551) ((1 1) (1 2)) (06119 00866)((0 1) (0 2)) (06958 007189) ((1 1) (2 1)) (06621 01452)

II

((2 0) (3 0)) (07706 00280) ((0 2) (0 3)) (07723 00309) ((2 2) (2 3)) (07388 00420)((2 2) (3 2)) (07817 00333) ((1 2) (1 3)) (07370 00511) ((3 0) (3 1)) (07851 00282)((2 1) (3 1)) (07920 00490) ((0 3) (1 3)) (07274 00430) ((3 0) (4 0)) (07849 00411)((0 2) (1 2)) (07615 00492) ((2 0) (2 1)) (07145 00477)((1 2) (2 2)) (07252 00292) ((2 1) (2 2)) (07820 00448)

III

((0 3) (0 4)) (08396 00101) ((4 0) (4 1)) (08920 00205) ((4 2) (5 2)) (08680 00194)((0 4) (0 5)) (08414 00168) ((4 1) (4 2)) (08093 00195) ((1 3) (2 3)) (09419 00219)((1 4) (1 5)) (08128 00222) ((4 2) (4 3)) (08810 00105) ((2 3) (3 3)) (08927 00240)((1 3) (1 4)) (08397 00167) ((5 1) (5 2)) (08632 00191) ((3 3) (4 3)) (08858 00109)((2 3) (2 4)) (08786 00134) ((4 0) (5 0)) (08152 00245) ((0 4) (1 4)) (08255 00243)((2 4) (2 5)) (08341 00221) ((3 1) (4 1)) (08522 00185) ((1 4) (2 4)) (08277 00236)((3 1) (3 2)) (08784 00122) ((4 1) (5 1)) (08403 00109) ((2 4) (3 4)) (08986 00216)((3 2) (3 3)) (08285 00201761187147) ((3 2) (4 2)) (08255 00218) ((0 5) (1 5)) (08282 00117)((3 3) (3 4)) (08751 00237) ((5 2) (5 3)) (08360 00209) ((1 5) (2 5)) (08503 00103)((3 4) (3 5)) (08133 00192) ((5 3) (5 4)) (08803 00239) ((4 5) (5 5)) (08248 00247)((4 3) (4 4)) (08414 00131) ((4 3) (5 3)) (08407 00232) ((4 4) (5 4)) (08083 00168)((4 4) (4 5)) (08674 00106) ((5 4) (5 5)) (08048 00181) ((2 5) (3 5)) (08897 00162)((5 0) (5 1)) (08122 00241) ((3 4) (4 4)) (08740 00204) ((3 5) (4 5)) (08867 00146)

120579lowast 066


0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

Disa

ster g

rade


ls = 86

S(Plowast) ()




Emergency logistics








119894119895on arc (V



119894119895(119905) but





119894of arc (V

119894 V119895)
















0ge 12 So it





Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Area (V119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash) (V

119894 V119895) (120585

119894119895 | ln 119902

119894119895|) (mdash mdash)

I((0 0) (0 1)) (07058 00397) ((1 0) (2 0)) (07105 00436) ((1 0) (1 1)) ((1 0) (1 1))((0 0) (1 0)) (07866 00453) ((0 1) (1 1)) (07742 00511) ((1 1) (1 2)) ((1 1) (1 2))((0 1) (0 2)) (07779 00354) ((1 1) (2 1)) (07663 00458)

II

((0 3) (1 3)) (08387 00211) ((2 2) (2 3)) (08776 00145) ((3 0) (3 1)) (08429 00186)((2 0) (3 0)) (08797 00251) ((1 2) (1 3)) (08372 00114) ((3 0) (4 0)) (08985 00133)((2 1) (3 1)) (08941 00114) ((0 2) (0 3)) (08351 00212) ((2 2) (3 2)) (08290 00171)((0 2) (1 2)) (08078 00175) ((2 0) (2 1)) (08105 00147)((1 2) (2 2)) (08996 00140) ((2 1) (2 2)) (08665 00181)

III

((0 4) (0 5)) (09363 00085) ((4 0) (4 1)) (09168 00019) ((4 2) (5 2)) (09963 00020)((1 4) (1 5)) (09367 00033) ((4 1) (4 2)) (09364 00062) ((1 3) (2 3)) (09922 00045)((1 3) (1 4)) (09941 00025) ((4 2) (4 3)) (09268 00079) ((2 3) (3 3)) (09176 00051)((0 3) (0 4)) (09503 00099) ((3 4) (4 4)) (09891 00042) ((3 3) (4 3)) (09842 00039)((2 3) (2 4)) (09199 00026) ((4 0) (5 0)) (09425 00030) ((0 4) (1 4)) (09397 00037)((2 4) (2 5)) (09167 00075) ((3 1) (4 1)) (09246 00080) ((1 4) (2 4)) (09657 00006)((3 1) (3 2)) (09697 00036) ((4 1) (5 1)) (09967 00094) ((2 4) (3 4)) (09247 00001)((3 2) (3 3)) (09295 00034) ((5 1) (5 2)) (09245 00004) ((0 5) (1 5)) (09320 00025)((3 3) (3 4)) (09786 00040) ((3 2) (4 2)) (09329 00014) ((1 5) (2 5)) (09868 00034)((3 4) (3 5)) (09303 00088) ((5 2) (5 3)) (09247 00041) ((4 5) (5 5)) (09270 00004)((4 3) (4 4)) (09645 00074) ((5 3) (5 4)) (09652 00040) (((4 4) (5 4)) (09810 00100)((4 4) (4 5)) (09205 00044) ((5 2) (5 3)) (09247 00041) ((2 5) (3 5)) (09862 00097)((5 0) (5 1)) (09306 00093) ((4 3) (5 3)) (09971 00020) ((3 5) (4 5)) (09798 00007)

120579lowast 076



(120585119894119895 | ln 119902

119894119895|) (mdash mdash)

Time interval[0 5) [5 10) [10 15) [15 20) [20 25)


119905(min)

0 1198750

[(0 0) (1 0) (1 1) (1 2) (0 2) (0 3) (04) (0 5) (1 5) (2 5) (3 5) (4 5) (5 5)] 8670753 0986905

3 1198751

[(0 0) (1 0) (1 1) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 6619152 0981555

6 1198752

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (1 4) (2 4) (3 4) (4 4) (4 5) (5 5)] 9126793 0942204

9 1198753

[(0 0) (0 1) (0 1) (0 2) (1 2) (1 3) (14) (2 4) (3 4) (4 4) (4 5) (5 5)] 7009755 090845

10

12 1198754

[(0 0) (0 1) (0 2) (1 2) (1 3) (1 4) (15) (2 5) (3 5) (4 5) (5 5)] 7990459 0804204

15 1198755

[(0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (15) (2 5) (3 5) (4 5) (5 5)] 7842856 0632161

6 Conclusions




0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 10 20 30 40 50 60 70 80 90 100

0

3

6

9

12

15

t 0(m

in)


ls = 86

S(Plowast) ()



0 is reasonable

0 is not reasonable




Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article multiobjective route planning model...

Documents