dynamic conflict-free routing of automated guided...

int j prod res 1999 vol 37 no 9 2003 plusmn 2030

Dynamic conmacr ict-free routing of automated guided vehicles

CHRISTOPHER OBOTHsup2 RAJAN BATTA sup3 and MARK KARWANsup3

This paper presents work performed to address design and operational controlissues for an Automated Guided Vehicle (AGV) based material handling systemVarious design issues connected with macr ow path design such as tra c macr ow alongthe guide paths location and representation of intersections bu ers pickup anddropo points are outlined A network representation of the AVG system(AGVS) is presented Operational control factors such as demand selectionand assignment route planning and tra c management idle AGV positioningand AGV characteristics are addressed In particular the performance of sixdemand selection policies four demand assignment policies and two idle AGVpositioning policies are outlined A very e ective route-generation technique thatprovides conmacr ict-free routes for multiple AGVs with varying speeds is presentedA large-scale simulation of a dynamic batch type manufacturing system to test thefeasibility of the proposed scheme for real time control of AGVs and to determinethe e ect of several factors on several performance measures is presented Ourreg ndings indicate that performance is signireg cantly a ected by vehicle speednumber of vehicles demand arrival interval idle AGV positioning and thedemand selection and assignment policy in use

1 Introduction

Automated Guided Vehicles (AGVs) have for some time now been regarded asan alternative for better material handling due to their dexterity e ciency andmacr exibility They have found wide applications in many areas including warehousingmacr exible manufacturing and assembly operations The design of the AGV controlsystem involves the ability of the individual vehicle to perform its required tasks thecoordination of many vehicles in executing the system transportation requirementsand the monitoring of the material handling system This is handled through ahierarchy of computers usually consisting of the following host computer systemmanagement computer tra c controller and on board vehicle controller

The host computer directs the functions in the material handling system (AGVsAutomated Storage and Retrieval Systems robots etc) maintains inventoriesschedules production holds database records generates management reports onsystem performance and controls other functions within the plant It conveys thetasks needed to be performed by the material handling system and receives data onthe throughput achieved

The system management controller (commonly referred to as the centralcontroller) manages the macr eet of AGVs in an optimal way by coordinating vehicleschedules making assignments for pickup and delivery of loads and keeping

0020plusmn 754399 $1200 Ntilde 1999 Taylor amp Francis Ltd

Revision received March 1998sup2 Faculty of Technology Makerere University PO Box 7062 Kampala Ugandasup3 Department of Industrial Engineering State University of New York at Bu alo Bu alo

NY 14260 USA To whom correspondence should be addressed

updated on all assignments It holds unused vehicles in specireg c locations in thesystem monitors the battery charging of the vehicles monitors problems thatoccur in the system re-starts the system after it has been shut down communicateswith the host computer compiles data for the host computer performs supervisoryfunctions for the AGV system and can maintain inventory records on the materialsin the material handling system

Scheduling several AGVs in a non-conmacr icting manner is a complicated real-timeproblem This is the job of the tra c controller which coordinates all tra c to makesure there are no vehicle collisions and the AGV tra c is e ciently managed If thereare any problems the tra c controller reroutes the vehicles and establishes newpriorities This controller holds all the information concerning the path networkroute and timetable of all the AGVs in the system Some tra c controllers coordi-nate the anti-collision blocking controls This paper presents the implementation of atra c controller system that can also perform a majority of the tasks of the centralcontroller

The on-board vehicle controller controls vehicle guidance steering speedacceleration stopping routing decisions safety monitoring collision and tra cavoidance interface with pickup and delivery stations doors alarms etc commu-nications with the central computer and interface with other material handlingequipment such as conveyors ASRS and robotic work cells

In the operation of an AGV based manufacturing system demands occur con-tinuously at random An e ective means must therefore be available for selectingthese demands from the set of available ones and once selected another e ectivemeans must be available for assigning the selected demands to available vehicles Thevehicles are then routed in a conmacr ict-free manner reg rst to their respective pickuppoints and then to the dropo points After demand delivery a means must beavailable to deal with empty vehicles if they cannot be immediately re-assignedother demands This process is continuously repeated during the manufacturingsystem operating period This paper presents a simulation of a dynamic batchtype manufacturing system incorporating all the above factors The performanceof the system is measured based on job system time mean number in queues vehicleutilization and mean response time

2 Literature review

Our literature review focusses only on papers that deal with research related toimplementations of a tra c controller system A detailed review of what has beendone to address the AGV routing problem can be found in Oboth (1996) Wenow summarize these works under two main categories macr ow path design issuesand operational control issues

21 Flow path design issuesIssues connected with macr ow path design like intersections and bu ers macr eet size

estimation and location of pickup and dropo stations have been addressed byMaxwell and Muckstadt (1982) Newton (1986) Egbelu and Tanchoco (19861987) Egbelu (1987) Usher et al (1988) and Sinriech and Tanchoco (1992)

22 Operational control issuesEgbelu and Tanchoco (1984) characterized dispatching rules for AGVs by com-

paring via simulation di erent combinations of workcentre and vehicle-initiated

2004 C Oboth et al

task assignments Chen (1987) presents a simulation study of the e ects of di erentvehicle dispatching rules on the performance of a macr exible manufacturing system(FMS) Vosniakos and Davies (1988) presented a study to simulate an AGVsystem serving an FMS They considered uni-directional track layout with knownmaterial macr ow intensities and formulated the problem as a 0-1 integer programKasilingam and Gobal (1996) present a simulation model to estimate the numberof AGVs needed This paper builds on earlier work by Kaslingam (1991) whoproposed an integer programming formulation that minimizes the total cost ofoperation and transportation of all the vehicles

The concept of free-ranging AGVs is fairly recent free-ranging AGVs do nottravel on guide paths but are instead controlled by radio messages In pioneeringwork Taghaboni and Tanchoco (1988) describe a LISP-driven controller for sched-uling free-ranging AGVs The controller receives requests for moves and makes thedispatching and routing decisions in real time based on the current state of thesystem

Kim and Tanchoco (1994) developed an e cient algorithm for reg nding conmacr ict-free shortest-time routes for AGVs moving in a bi-directional network Their algor-ithm is based on Dijkstrarsquos shortest-path method and maintains a list of scheduledentry and exit times of vehicles at each node Mahaden and Narendran (1990)addressed key issues involved in the design and operation of AGV-based materialhandling systems for an FMS Issues examined were the number of vehicles requiredthe layout of the AGV tracks the tra c macr ow patterns along the tracks tra ccontrol and vehicle dispatching Hoo-Gon Choi et al (1994) evaluated twocommon types of AGVS layout a traditional `multiple vehiclesrsquo layout and atandem layout with single vehicle loops Discrete event simulation models weredeveloped in SIMAN to test various system design and operation parameters inthe two layouts

Krishnamurthy et al (1993) provide an approach which considers design issuesof the AGV layout and simultaneously develops multiple routes for the AGVs via acolumn generation based heuristic Their empirical results indicate that the pro-cedure as a whole usually generates solutions that are within a few percent of aproposed bound Narasimhan et al (1993) extended this model to generate con-macr ict-free routes for AGVs with varying speeds Other analytical works done toaddress vehicle route generation include Blair et al (1987) Fuji and Sandoh(1987) and Daniels (1988)

3 The AGV routing problem dereg ned

We start by establishing a framework in which we can develop the simulationmodel for the routing of the AGVs To accomplish this the AGV environment isdereg ned in its entirety while taking into account various design aspects We present arepresentation of an AGVS which closely resembles the actual environment Themethods developed on this representation should be applicable to real systems withminimum modireg cations We consider a bi-directional guide path layout AGVS Thistype of guide path layout allows AGVs to travel in both directions We assume thatthe AGVs themselves are unidirectional that is they have to make a U-turn in orderto travel in the opposite direction We further assume that the AGVs operate underthe following shop macr oor conditions

Dynamic conmacr ict-free routing of AGVs 2005

Demands occur at random as a set of ordered pairs [p d ] where p represents apickup station and d represents a delivery station

The AGVs are of unitload capacity After completion of service an AGV looks for other demands to satisfy by

notifying the central controller If there are no demands to satisfy then whatnext happens to the AGV depends on the idle AGV positioning policy in use atthat time

The bi-directional guide path on which the AGVs travel is divided into edgesEach edge is not necessarily of the same length We use a modireg cation of zonecontrol in that only one AGV can occupy an edge at any one time

K AGVs are available for routing The AGV speeds are variable This means that if an AGV occupies an edge at a

particular instant of time the time when it will be in an adjacent edge dependson the speed at which it is traveling A faster AGV will traverse an edge in ashorter time than a slower AGV

Blocking occurs when any two AGVs are routed in such a manner that bothhave to occupy a particular edge at the same time or if two AGVs are inadjacent edges and heading towards each other

We represent the manufacturing facility as a directed graph G= (V E AEgrave ) whereV is the set of vertices E is the set of edges and AEgrave is the set of adjacency relationshipsbetween edges Each physical edge in the layout is represented by a pair of edgesin the graph Depending on the direction of travel of the AGV one of the twoedges is used It must be noted that in the graph representation an edge is notadjacent to its complementary edge to prevent the AGV from backtracking onthe edge All edges are assumed to be of integer length Consider an edge joiningvertex i to vertex j which is of length l We split this edge into l unit length segmentslabeled s1 sl as shown in reg gure 1 In our model an AGV occupies a segmentfor a specireg ed integer length of time and makes an instantaneous movement to anadjacent segment This adjacent segment either belongs to the same edge or to anadjacent edge to the one that the AGV is currently traveling on The length oftime that an AGV occupies a segment is given by its speed the faster an AGV istraveling the shorter the duration of time for which it occupies a segment We nowdiscuss the representation of each individual element of the manufacturing facilityusing directed edges

31 Flow path designThree di erent types of bi-directional network models are possible single-lane

multiple-lane and mixed model (Egbelu 1993) We use the bi-directional single-lanedesign in modeling our guide paths

2006 C Oboth et al

Figure 1 An edge of length l is split into l segments

All intersections are assumed to be either four-way or three-way and are repre-sented by six or eight directed edges respectively with appropriate adjacency rela-tionship dereg ned between them as depicted in reg gure 2 An important assumptionwith signireg cant impact on the modeling of the system is that exactly one AGV canuse the intersection at any one time


Figure 2 Four and three way intersections

Figure 3 Example network

A workstation is an area where a pickup or a dropo is made Workstations arerepresented by a directed edge whose length corresponds to the time required by thepickup or dropo operation to be made For simplicity in presentation we assumethat a workstation lies o the main travel area and is only entered by an AGV whena pickup or dropo has to be made

A bu er is an area o the main travel space where an AGV can wait usually topermit another AGV to go by Three di erent designs have been suggested in theliterature namely loop sliding and spur designs (Egbelu and Tanchoco 1986) Abu er will be represented by a directed edge with length equal to the bu er capacityWe shall use the spur design

32 The conmacr ict-free route generation processOur strategy assumes the existence of a set of demands each consisting of a

pickup and a dropo We wish to transport all these demands in a manner thatminimizes the makespan the time when all demand dropo s have been made and atthe same time avoids AGV collisions To model collisions one has to track vehiclemovement precisely and to do this we have chosen a discretized time model byassuming that edges have integer lengths and that AGVs occupy a unit-length seg-ment for a specireg ed duration of time We start by recalling that the manufacturingfacility is represented by a graph G= (V E AEgrave ) where V is the set of vertices E is theset of directed edges and AEgrave is the set of adjacency relationships between edges Let lidenote the length of an edge i 2 E li gt 0 and integer by assumption

Krishnamurthy et al (1993) developed a static version of the AGV routing prob-lem That version dealt with the problem of routing K AGVs in a network to satisfytheir requests while avoiding conmacr icts and minimizing the performance measure ofmakespan the maximum time taken to satisfy all the demand requests We intend toimplement the solution methodologies developed for this static problem in adynamic environment while relaxing some of the limiting assumptions like equaland constant speeds

Suppose at any one instant that we have K AGVs to route Our problem is toreg nd a conmacr ict-free route for each of the AGVs such that the time at which all these Kdemands are satisreg ed is minimized For this particular route assignment we start bycomputing the earliest time necessary for each AGV to accomplish its delivery tasklet it be mk for AGV k This is the sum of the time when the AGV actually becomesavailable and the time measured by the length of the shortest path necessary for theAGV to accomplish its delivery task In computing this shortest path durationconsideration is given to the speed at which the AGV is moving The AGVs arethen sorted in decreasing order of their completion times Without loss of generalityassume that m1 m2 mk AGV 1 is routed reg rst along its minimum time pathAt this instant since it is the reg rst to be routed it will not encounter any conmacr ictsNext AGV 2 is routed in such a manner that there is no conmacr ict with the reg rst AGVThis is accomplished by associating all the path segments currently occupied by thereg rst AGV with very high costs of entering them If there is no conmacr ict with the reg rstAGV the second AGV is routed along its shortest path AGV 3 is routed in such amanner that it does not conmacr ict with the reg rst and the second AGVs We ensure thisby blocking o all the path segments currently occupied by the reg rst and the secondAGVs If there are no conmacr icts with the reg rst and the second AGVs the third AGVis routed along its shortest path This same procedure is repeated to route theremaining AGVs

2008 C Oboth et al

In the extreme case when all the AGVs do not encounter any conmacr icts the timetaken to accomplish the delivery task assignment is the length of the time taken bythe reg rst AGV This is true because each subsequent AGV to be routed takes ashorter time than its predecessors and each route assignment starts at the sametime When a conmacr ict is encountered the AGV being routed has to be delayed ifan alternate route cannot be obtained for it Depending on how much delay isencountered in routing all the AGVs the actual time taken to accomplish the deliv-ery task assignment may be extended beyond the length of time taken by the reg rstAGV Our objective whenever we have a routing assignment is to generate a routefor each delivery task such that this time is minimized

In a manufacturing setup demands continuously occur at random The aboveprocedure has therefore to be invoked continuously over time In this case eachroute being developed including the one for the reg rst AGV is generated such that noconmacr icts are encountered Some AGVs may be accomplishing previously assignedtasks which have to be completed reg rst before starting on new assignments We takeall these factors into consideration when simulating the dynamic AGV routingscenario

We call the above route generation procedure the Sequential Path Generation(SPG) heuristic The steps of the heuristic and a numerical example are given in theAppendix

33 Idle AGV positioningA key control decision that needs to be made in the operation of an AGV system

is that of positioning the idle AGVs Unless a shop is overloaded the occurrence ofvehicle idleness is an inevitable event Vehicle idleness occurs when a vehiclecompletes a delivery task and there is no immediate load pickup task to reassignthe vehicle Clearly idle AGVs should be routed to a strategically selectedempty bu er location (`home positionrsquo) so as to be `out of the wayrsquo of otherAGVs Current literature on AGV system design still lacks formal procedures toassist designers to determine the home location of idle AGVs however thefollowing rules have been used in positioning idle AGVs central zone positioningrule point of release positioning rule and circulatory loop positioning rule (Egbelu1993) We present results for the investigation of the e ectiveness of the reg rst twopositioning strategies

4 The simulation model

A discrete stochastic-terminating simulation model for an existing batch typemanufacturing system is presented in this section We note here that the scope of thepaper is limited to the application of the said methodology to one reported casestudy We did however beta test our methods on a smaller layout in the manu-facturing lab at SUNY at Bu alo Details of these tests can be found in Oboth(1996)

41 Model assumptions411 The AGV system

The system modeled here is the injection molding section of the Delphi-HarrisonPlant Four located at Bu alo New York It is the area which produces all of theplastic parts for use in the assembly lines We note here that the current method ofmaterials transfer at Delphi-Harrison is fork-lif t trucks However the facility is one


2010 C Oboth et alT

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Dynamic conmacr ict-free routing of AGVs 2011T

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(b)

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2[cl

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tl(i

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tl(i

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that is well suited for AGVs should the company in fact consider them The com-panyrsquos reasons for not implementing ADVs are labor-related but the data constitu-tes a valid case study for a AGV potential implementation

There are a total of twenty workstations in this area Each workstation has anumber of presses (between 1 and 6) which produce a certain number of parts It isassumed that each workstation utilizes all of its presses to produce each partFinished parts from the presses are stored on racks When the required number ofracks are full a demand request is initiated for an AGV Each part produced in thisarea has its own production rate therefore the demand pattern for the AGV in theinjection molding area is time-dependent For the purposes of the simulation arecord is kept of which part is being produced at each workstation at di erenttimes in order to determine the demand rate to be utilized The pickup pointsbelonging to a workstation are the same irrespective of the part being producedThe dropo points are part-dependent and the route assignment procedure takes thisinto account

Each part produced in the injection mold area has its own demand rate becauseeach part is produced at a di erent mold rate each part may be a di erent sizechanging the number of pieces which reg t in a rack and each part may require adi erent type of rack resulting in a di erent number of racks per trip Table 2summarizes the demand pattern for the di erent products in the injection moldingarea

Bi-directional paths connect the di erent stations in the system All queues in thesystem are of reg nite capacity The loading and unloading of AGVs is modeled as anactivity by a random variable from a uniform distribution Figure 4 shows theschematic layout for the injection molding plant A network representation of thesame area is shown in reg gure 5

412 AGV vehiclesrsquo characteristicsVarying speed unit-load capacity AGVs are modeled All vehicles travel at the

same constant speed in both loaded and unloaded status All vehicles are idle andactive at the beginning of the simulation The initial locations of the vehicles thenumber of vehicles in the system and their speeds are specireg ed Vehicles may travel ineither direction on the bi-directional paths All the vehicles are equally qualireg ed todispatch any load under all policies

Two idle AGV positioning policies are tested in the simulation In the reg rst casewhen a vehicle completes a delivery to a dropo point it waits at the dropo pointuntil requested for a new assignment In the second case the vehicle is routed to acentralized bu er area if there is no immediate demand to satisfy Vehicle break-downs and battery charging are not explicitly modeled however they can be impli-citly modeled as a type of job request for the AGV A vehicle is in exactly one of thefollowing states at any given time

idle traveling unloaded towards a pickup point or central bu er loading at a pickup point traveling loaded towards a dropo point unloading at a dropo point blocked

2012 C Oboth et al


From To Rate From To Rate From To Rate

Workstation 10 180 5100

186 340 9400340 475 7000475 602 7000602 729 6000729 853 11300853 885 16500885 898 7000898 904 7500904 907 4200907 910 9800910 1065 4100


392 725 5100725 886 2500886 894 5100

Workstation 3480 538 4700538 588 14500588 629 5400629 640 3100640 649 3500649 707 4700707 757 14600757 798 5400798 829 7000829 840 3100840 881 2200881 887 3500


552 805 4800805 935 3000935 1002 2900

1002 1020 7100


561 1020 7600


101 146 4900146 190 7200190 509 5400

509 511 6000511 686 4600


343 670 3700670 1053 6800

1053 1063 64001063 1116 12001116 1128 24001128 1130 2700


52 104 2600104 202 4800202 230 1600230 281 2500281 306 1500306 331 8600331 355 2400355 366 2900366 374 3000374 382 3700382 397 3300397 405 3800405 412 4500412 417 1600417 422 1000422 426 2000426 430 1400430 434 2400434 438 2800438 442 1700442 446 2700446 449 1800449 455 4800455 458 4300458 461 1400461 467 6300467 470 2400470 474 4800474 475 2000


770 1020 1600


81 1201 2700




482 708 3600

Workstation 14480 992 12800992 1142 14100

1142 1205 125001205 1260 12800




208 595 7000595 625 4700625 720 7100


434 539 8900539 604 10000604 654 15000654 718 9000718 720 10100


222 332 13500332 442 8600442 526 11300526 582 10000582 620 7300

Workstation 20480 511 11300511 529 9500529 537 11900537 540 6000

from beginning time for the intervalto ending time for the intervalrate time between demand arrivals

WS 1 2 3 4 5 6 7 8 9 10MCs 4 6 3 3 3 3 4 6 14 3

WS 11 12 13 14 15 16 17 18 19 20MCs 2 2 2 1 1 2 4 1 1 2

WS workstation numberMCs number of machines

Table 2 Demand pattern distribution

413 Demand selection and assignmentSix demand selection policies were considered and modeled These are ULSAT

MFCFS MOQS MROQS RWS STT_D Under the ULSAT policy once therequired number of racks have been released to an outgoing queue a vehicledemand is created in a general demand queue which is ranked in FIFO orderaccording to demand arrival time This implies that once a vehicle becomesavailable it is assigned to the demand with the smallest arrival time The

2014 C Oboth et al

Figure 4 Delphi-Harrison plant injection moulding macr oor plan

general demand queue is updated constantly The RWS rule selects a demandat random assuming each has an equal chance of being selected Under theSTT_D policy once a vehicle becomes available the general demand queue isscanned for the closest demand to the vehicle location Closeness is based on theconmacr ict-free distance between the vehicle and the demand The MOQS ruleassigns the available vehicle to the demand waiting in the longest outgoing queue


Figure 5 Network respresentation of Delphi-Harrison layout

in the system MROQS selects the demand located at the workstation with the leastremaining queue space Under the MFCFS policy each outgoing queue can place ademand in the general demand queue Once a vehicle becomes available it isassigned to the reg rst demand in the demand queue A new demand is generatedfrom the same workstation and placed in the demand queue The ranking order inthe demand queue is FIFO

Four demand assignment policies were adopted and modeled These are LIVLUV RV and NV Under the LIV rule an idle AGV queue is maintained in orderof the time when the AGV became idle To assign an AGV the reg rst AGV from thisqueue is selected For the LUV policy the utilization of all the unassigned AGVs iscomputed The AGV with the least current utilization is dispatched The RV ruleselects a vehicle at random from the unassigned lot assuming each vehicle has anequal chance of being selected NV policy computes the conmacr ict-free distance of eachunassigned vehicle to the demand point and dispatches the vehicle with the shortestdistance

42 The experimental design421 Run conditions

The assumed input conditions are as follows

The initial status of the AGV system is empty of job entities The initial status of all workstations and vehicles are active and idle The number of workstations in the system is 20 The number of vehicles is 3 4 5 The processing times at each workstation for di erent time intervals are

specireg ed The interval between demand arrivals is determined from this The terminating event is the end of simulation time at 1440 minutes represent-

ing three working shifts All jobs being processed in the system at this time areprocessed to completion

The number of simulation runs is 5 with each run beginning at time zero Eachrun is for 1440 minutes and the system state is re-initialized between runsPrevious observations between runs are discarded Prior to collecting statisticsa warm up period of 180 minutes was provided so that the system could reachsteady-state

The AGV unloading and loading times are modeled as random variables froma uniform distribution between 10 and 20 minutes

422 Performance measuresThe following output variables were considered as performance measures for the

systemJob related

job average time in the system average number in queue

The job average time in the system is the amount of time a job spends onaverage in the system The average time in the system includes the sum of thewaiting times in queues and the blocked times when the job is loaded on the vehicleand the vehicle is blocked Average number in queue is the time average number ofparts at a queue

2016 C Oboth et al

Workstation related

queue size requirements

AGV related

mean response time utilization of each AGV

Response time is the total time a vehicle spends traveling unloaded towards apickup point Vehicle utilization is the ratio of the sum of the total loaded travel timeand total empty travel time to the total simulation time Loaded travel time is thetotal time a vehicle is transporting a job from a pickup point to a dropo point

423 Factors under studyThere were four additional factors under consideration in this model the

number of AGVs the AGV speeds the demand arrival intervals and the idleAGV positioning policy Apart from the idle AGV positioning policy (which wasconsidered at two levels) each of the other factors were considered at three levelsspecireg ed as in table 3

A demand arrival interval level of Pr refers to the current rate levels as obtainedfrom the collected data from the plant table 2 These levels were varied as indicatedabove to study the impact of di erent rates An idle AGV positioning policy of CLrefers to the centralized location policy and DPrefers to the last dropo point policyIn the CL policy the idle AGV moves to a central location and waits there for thenext call if the next call is assigned to it while traveling back to the central location itis dispatched from this intermediate point In contrast the DP policy keeps the AGVat the last drop-o point implying that the AGV travels to the next call from thisnew location

424 Factorial designA factorial design experiment with 5 observations per factor combination was

developed Each of the 54 factor combinations was tested under each of the 24dispatching control policies outlined in section 413 The total number of 6480observations were run in a completely randomized order pre-determined beforethe experiment was actually run

5 Output statistical analysis

We present summary simulation results for the tested factors and dispatchingpolicies with respect to the performance measures stated above Only summarizedresults from Newman-Keuls tests are presented except for job system time for which


Low Medium High

No of AGVs 3 4 5AGV speeds (feets) 2 3 4Demand arrival interval 075 Pr Pr 125 PrIdle AGV positioning DP CL

Table 3

additional details are given Detailed results of the response values for each perform-ance measure are contained in Oboth (1996)

51 Results for job average time in systemFrom the analysis of variance (ANOVA) report all factors are signireg cant at the

5 level Interaction e ects are also signireg cant at the 5 levelFigure 6 displays the mean system times for the jobs Figure 7 summarizes the

mean system times for the jobs when interaction e ects are considered The trend insystem time is clearly obvious The following conclusions can be drawn

The system time drops as the number of AGVs is increased the speed of theAGVs is increased and the demand arrival interval increases This can be attributedto the fact that more AGVs mean that the jobs do not have to wait for a long time tobe transported since there is a higher chance of getting a free AGV available Thehigh AGV speeds mean that the AGVs accomplish their assigned missions quicklyand become available for re-assignment quicker and so the jobs again do not have towait for a long time A high demand arrival interval means that fewer demands aregenerated and these few demands do not have to wait long time for an empty AGV

The last dropo point idle AGV positioning policy yielded a lower system timethan the centralized location policy This is not an unexpected result since in the lastdropo point policy the AGV is positioned at `high-demandrsquo locations and thisimplies a quicker response to the next dispatch on average Similar explanationshold for why this policy does better than the centralized location policy in the otherperformance measures being studied

From the interaction plots we see that as the vehicle speed is increased to thehigh level the impact of the number of AGVs the demand arrival interval thedemand selection and assignment rules become less pronounced Also whenthe number of vehicles is at the high level varying the idle AGV positioningpolicy the demand arrival interval or the demand selection and assignment policyhas little impact

To investigate the impact of the di erent dispatching rules the Student-Newman-Keuls (SNK) range test was performed on the 24 means correspondingto the V_RULE - WS_RULE combination Table 4 summarizes performance of thedi erent rule combinations based on the SNK test results The NV rule used witheither the STT_D rule or the MFCFS rule produced the smallest system times

52 Results for AGV utilizationAs with the system time the ANOVA report showed that all factors are

signireg cant at the 5 level Interaction e ects are also signireg cant The followingconclusions can be drawn

AGV utilization drops as the number of AGVs is increased the speed of theAGVs is increased and the demand arrival interval increases A low number ofAGVs means that the demand is shared among few vehicles and so reduces thechance of a vehicle being idle Hence the vehicle utilization goes up A low vehiclespeed implies that a vehicle takes longer to accomplish a mission There is therefore ahigh chance of another demand occurring during this time period which reduces thechance of the vehicle remaining idle after accomplishing the mission Hence vehicleutilization again goes up A high demand arrival interval means fewer demands tosatisfy Since there are few demands there is a higher chance of a vehicle being idleso the vehicle utilization goes down

2018 C Oboth et al


Fig

ure

6M

ean

SYST

IME

sum

mar

y

2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts

The last dropo point idle AGV positioning policy yielded a lower vehicleutilization than the centralized location policy

The interaction plots showed that as the vehicle speed is increased to the highlevel the impact of the number of AGVs the demand arrival interval the demandselection and assignment rules become more pronounced Also when the number of

2022 C Oboth et al

Group Mean WS_RULE V_RULE Group Mean WS_RULE V_RULE

(a) SYSTIME1 877 NV STT_D

914 NV MFCFS

2 1088 LIV ULSAT1128 RV RWS1143 LUV RWS1183 RWS STT_D1183 LUV STT_D1194 NV RWS1199 LIV RWS1200 LUV ULSAT

3 1330 RV ULSAT1379 RV MFCFS

4 1530 NV MROQS1539 NV ULSAT

5 1574 NV MOQS1577 LUV MFCFS1710 LIV NV

6 2381 RV MROQS2392 LIV MROQS2424 LUV MROQS2442 LUV MOQS2447 RV MOQS2449 LIV ULSAT

(b) AGV_UTIL1 9089 RV STT_D

9086 LIV STT_D9073 LUV STT_D

2 8913 NV RWS8868 NV STT_D8868 NV MROQS8838 NV MOQS

3 8680 LUV MROQS8666 LUV MOQS8575 LUV ULSAT

4 8526 RV MOQS8524 LUV RWS8515 RV ULSAT8494 LIV MOQS

5 8393 LIV MROQS8388 NV MOQS8375 NV MFCFS8357 LIV RWS8313 LUV MFCFS

6 8255 RV RWS8206 RV MROQS

7 8106 RV RWS8094 LIV ULSAT

(c) RESPTIME1 175 LUV STT_D

175 RV STT_D176 LIV STT_D195 NV STT_D198 LUV MFCFS199 RV MFCFS200 LIV MFCFS213 NV MFCFS221 LIV RWS222 LIV ULSAT225 LUV ULSAT227 LUV RWS227 LIV MROQS228 LUV MROQS229 RV ULSAT230 LUV MOQS230 LIV MOQS230 RV MOQS230 RV MROQS233 NV RWS235 NV ULSAT238 NV MOQS241 NV RWS

(d) NUM_IN_Q1 451 NV STT_D

2 605 LUV STT_D610 LIV STT_D662 RV STT_D

3 863 NV MROQS865 NV MOQS

4 910 NV ULSAT992 NV RWS

1009 NV MFCFS1065 LUV RWS

5 1422 LUV ULSAT1473 RV MROQS1481 RV MOQS1502 LIV RWS1515 RV ULSAT1517 LUV MROQS1518 RV RWS1522 LUV MOQS1567 LUV MFCFS

6 1643 RV MFCFS1714 LIV ULSAT1751 LIV MFCFS1766 LIV MOQS1772 LIV MROQS

Table 4 Characterization of despatching rules

vehicles is at the high level varying the idle AGV positioning policy the demandarrival interval or the demand selection and assignment policy gives a bigger impact

As with system time AGV utilization depends on the di erent WS_RULE -V_RULE combination in use Table 4 summarizes performance of the di erentrule combinations based on the SNK test results

53 Results for mean response timeThe ANOVA report showed that all the factors are signireg cant at the 5 sig-

nireg cance level Except for one interaction e ect all interactions are signireg cant at the5 level The following conclusions can be drawn

The mean response time drops as the number of AGVs is increased the speed ofthe AGVs is increased and the demand arrival interval increases A high number ofAGVs gives a higher chance of locating a more favorable vehicle than a low numberHigh AGV speeds mean that the vehicles once assigned reach the demand pointsquicker and so the response time lowers A high demand arrival interval means fewerdemands to satisfy Since there are few demands there is a higher chance of locatinga more favorable vehicle

The last dropo point idle AGV positioning policy yielded a higher response timethan the centralized location policy

The interaction plots showed that as the vehicle speed is increased to the highlevel the impact of the V_RULE becomes less pronounced At the high level of thenumber of vehicles the idle AGV positioning policy and the demand arrival intervalhave a more pronounced impact but the V_RULE has a less pronounced impact

The response time also depends on the di erent WS_RULE - V_RULE combi-nation in use Table 4 summarizes the performance of the di erent rule combinationsbased on the SNK test results All the di erent rules fall into one group

54 Results for mean number in queueThe ANOVA report showed that all the factors are signireg cant at the 5

signireg cance level All interactions are signireg cant at the 5 level The followingconclusions can be drawn

The mean number in queue drops as the number of AGVs is increased the speedof the AGVs is increased and the demand arrival interval increases A high numberof AGVs gives a higher chance of getting a free vehicle available than a low numberSo the jobs do not stay at the queues for a long time leading to shorter queuelengths High AGV speeds mean that the vehicles accomplish their assigned missionsquicker and become available for re-assignment faster so again the jobs do notspend a long time at the queues A high demand arrival interval means fewerdemands to satisfy Since there are few demands there is a higher chance of locatinga free vehicle so the queues are on average shorter

The last dropo point idle AGV positioning policy yielded a smaller averagenumber in the queue than the centralized location policy

The interaction plots showed that as the vehicle speed is increased to the highlevel the impact of the number of AGVs the demand arrival interval the demandselection and assignment rules become less pronounced Also when the number ofvehicles is at the high level varying the idle AGV positioning policy the demandarrival interval or the demand selection and assignment policy gives little impactDemand selection and assignment rules have little impact at the high level of thedemand arrival interval


The average number in queue also depends on the di erent WS_RULE -V_RULE combination in use Table 4 summarizes the performance of the di erentrule combinations based on the SNK test results

6 Conclusions

This paper presents an e ective network representation of an AGVS environ-ment incorporating various design issues like tra c macr ow along guide paths locationand representation of intersections bu ers pickup and dropo points We have alsoaddressed operational control factors such as demand selection and assignment idleAGV positioning route generation and AGV characteristics This system performsreal-time demand selection and assignment dynamic conmacr ict-free routing and even-tual management of idle vehicles The scheme outlined here can therefore be madeamenable for real time implementation with slight situation-dependent modireg ca-tions In fact we have used the suggested scheme to design a factorial simulationof an existing batch type manufacturing plant the results of which were presented

During the route generation process the SPG heuristic that we utilized starts bycomputing the earliest completion times for all the vehicles to be routed It then sortsthese vehicles in decreasing order based on these completion times The vehicles arethen routed based on this sorted order We have already demonstrated how thissorting procedure is one of the features that distinguishes this technique from theother route generation procedures and makes this technique highly e ective

Turning to the issue of AGV characteristics AGV speed has been very wellcaptured in our route assignment strategy We represent vehicle speed as vik depict-ing the speed of vehicle k along edge i As it is now if we want to model vehicleslowdowns say along edges at corners or intersections we specify these edges at thebeginning and the system will automatically assign the appropriate speeds whenmotion is along these edges AGV type is another issue worth mentioning Thisarises when di erent demands occur in the system requiring special purpose vehiclesThis is easily accomplished by specifying a vehicle type identireg er to the AGVsDemand assignment is now accomplished only within the appropriate vehicle cate-gory

Route generation is done only after demand selection and assignment is overProper means are therefore necessary for selecting demands and assigning them tovehicles A number of demand selection and assignment policies were presentedCurrent distance-based policies compute vehicle distances without consideringvehicle interference What is to be noted is that all our distance-based policiesincorporate vehicle interference in the distance calculations This is a great enhance-ment to these policies

Finally we can propose the following as possible directions for future research inthis area investigation of potentials for multiple capacity vehicles research in free-ranging AGV technology extending the methodology to `sensor blockingrsquo andtesting the method on a wider range of industrial areas

Acknowledgments

The reg rst author was supported by a Fulbright Scholarship from United StatesAgency for International Development The last two authors were supported by theNational Science Foundation via Grant No DDM-9201405 Both sources of sup-port are gratefully acknowledged The authors are grateful to three anonymousreferees for their constructive criticism of an earlier version of this paper

2024 C Oboth et al

Appendix

The SPG heuristic Let f ek1 e

k2 ek

nk g be the set of edges to be visited by AGV kwhere nk = the number of edges to be visited by AGV k dij = the shortest distancepath from edge i to edge j

Algorithm SPG

Step 1 Order the AGVs such thatn1shy 1

i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)

Set T =0 and j=1Step 2 Generate conmacr ict-free route for current AGV j and save the path as Pj Let

the total time taken for this AGV to reach its destination be tnow

Step 3 If tnow gt T then Set T = tnow

Set j= j + 1If j=K then goto step 4else

Set the costs on the edges blocked by path Pj-1 to inreg nity at theappropriate times and goto step 2

end ifStep 4 Paths Pj for j = 1 2 K provide a feasible set of paths The time when

the time-dependent costs vary is updated to the reg nal value of T

To accomplish the route generation step step 2 above we keep a Cost Label anda Trace Label for each edge i 2 E called cl(i t) and tl(i t) cl(i t) is the cost of theshortest route from edge sk that enters edge i at time t given that we enter sk at timed k tl(i t) is the trace label which specireg es the edge from which it arrived at edge i attime t I=(Ic Ip) represents the current incumbent solution where Ic is the cost ofthe path and Ip is the path itself e1 is the current end edge d k is the time when AGV kis reg rst available sk is the starting edge at which AGV k is located at time d k Mi is theset of edges in intersection i = f j 2 E| j is in intersection i g vik is the length segmentof edge i traversed by AGV k in a unit time ie the speed of the AGV cikt is the costof entering edge i at time t by AGV k

=livik if entering edge i causes no interference1 otherwise

G ij =1 if edge j is adjacent to edge i0 otherwise

We illustrate the implementation of this step with a numerical example belowStep 3 is the conmacr ict resolution step It is a direct application of the zone method

of control in that no two AGVs are allowed to be on the same edge at the same timeIf the edge belongs to an intersection we block out all the other edges at thatintersection Let us refer to this step as a special function called BL OCK which isinvoked each time we reg nish generating a path for an AGV The implementation ofthis function is as follows

Let Bijt =1 if edge i is occupied by AGV j at time t 0 otherwise `nowrsquo refers tothe current time


Algorithm BL OCK

If Bijt =1 then take care of piggy-back situations for all AGVs k such that k 6= j do

if agv_speed(k)gt agv_speed(j) thenLet v=agv_speed(k) - agv_speed(j)Let td =now + li vfor z=now td do

Set Bikz =1end for

end if

end for

take care of head-on collisions for all AGVs k such that k 6= j do

Let tc =now + liagv_speed(j)Let tb =now-1plusmn liagv_speed(k)for z= tb tc do

Set Bi 0 kz =1 where i 0 is the edge complement of iend for

end for

take care of intersections if edge i belongs in an intersection then

for all edges x 6= i such that x 2 MiSet Bxjt =1

end for

end if

end if

An example We illustrate the SPG heuristic procedure on the network shown inreg gure 3 Assume that the loading and unloading times at each workstation are 2 timeunits AGV speeds are one unit All edges are one unit length except edges 15 and 16which are two unit lengths We use two AGVs and the routing assignments to beaccomplished by them are as follows

Current location Pickup point Dropo pointAGV 1 12 17 31AGV 2 17 1 20

The SPG starts by computing the shortest distance paths for each of the AGVsFor AGV 1 the shortest distance path is 12 - 10 - 13 - 17 - 21 - 26 - 29 - 31 taking atotal duration of 9 time units For AGV 2 the shortest distance path is 17 - 14 - 9 -5 - 3 - 1 - 2 - 7 - 15 - 19 - 20 taking a total duration of 13 time units

We route AGV 2 reg rst (along its shortest distance path) and set the costs on theedges blocked by this path to inreg nity at the appropriate times We accomplish this asfollows

Initialization of cost and trace labels sk =17 d k =0 T =10Set cl(skd k)=0 and tl(skd k)=

2026 C Oboth et al

Set cl(it) =+ 1 and tl(it) = - i 2 E plusmn sk t = d k +1 TSet cl(skt)=+ 1 and tl(skt)= - t= d k +1 TSet Ic =+ 1 and Ip = -Set t= d k and x=1 t is the time counter and x is the edge counter

Updating of the cost and trace labels only edges 17 14 and 21 are adjacent to edge 17cl(171) =min cl(170) + c17 2 1 + 1 =min 0 + 1 + 1 =1 tl(171) =17cl(211) =min cl(170) + c21 2 1 + 1 =min 0 + 1 + 1 =1 tl(211) =17cl(141) =min cl(170) + c14 2 1 + 1 =min 0 + 1 + 1 =1 tl(141) =17cl(172) =min cl(171) + c17 2 2 + 1 =min 1 + 1 + 1 =2 tl(172) =17cl(212) =min cl(171) + c21 2 2 + 1 =min 1 + 1 + 1 =2 tl(212) =17cl(142) =min cl(171) + c14 2 2 + 1 =min 1 + 1 + 1 =2 tl(142) =17cl(173) =min cl(172) + c17 2 3 + 1 =min 2 + 1 + 1 =3 tl(173) =17cl(213) =min cl(172) + c21 2 3 + 1 =min 2 + 1 + 1 =3 tl(213) =17cl(143) =min cl(172) + c14 2 3 + 1 =min 2 + 1 + 1 =3 tl(143) =17

This process is continued until when t=10 Table 1 gives the rest of the costand trace labels The rest of the edges remain un-updated as they are not accessiblefrom edge 17 We next update cost and trace labels for edges adjacent to edges 14and 21

only edges 9 and 11 are adjacent to edge 14cl(92) =min cl(141) + c9 2 2 + 1 =min 1 + 1 + 1 =2 tl(92) =14cl(112) =min cl(141) + c11 2 2 + 1 =min 1 + 1 + 1 =2 tl(112) =14cl(93) =min cl(142) + c9 2 3 + 1 =min 2 + 1 + 1 =3 tl(93) =14cl(113) =min cl(142) + c11 2 3 + 1 =min 2 + 1 + 1 =3 tl(113) =14only edge 26 is adjacent to edge 21cl(262) =min cl(211) + c26 2 2 + 1 =min 1 + 1 + 1 =2 tl(262) =21cl(263) =min cl(212) + c26 2 3 + 1 =min 2 + 1 + 1 =3 tl(263) =21This process is also continued until t =10

The next labeling step updates the cost and trace labels for edges adjacent toedges 9 11 and 26 This procedure is continued until the minimum cost to reach thecurrent end edge and the associated path are identireg ed Table 1 gives a summary ofthe minimum costs of being on di erent edges at di erent times and the associatedtrace labels for AGV 2 the reg rst AGV to be routed

Identifying the best path that enters the current end edge by time T e1 =1 d k =0 T =10 From Table 1t =argmin cl(1t) for d k t T =5 tl(15) = 3Tracing this path backwards tl(34) =5 tl(53) =9 tl(92) =14 tl(141) =17Hence Ip =17 - 14 - 9 - 5 - 3 - 1 Ic =cl(15) =5

Checking if there is a better path that reaches e1 after Tfor x=1 |E| and x 6=e1 do

for i=1 lxvxk do

if cl(xT-lxvxk + i) + fx lt Ic then

a Set Ic =cl(xT-lxvxk + i) + fx

b Set Ip = the path traced from sk to x that corresponds to cl(xT)appended with the shortest time path from x to e1


end if

end for

end for

We summarize the computations in the following table

The values of cl(it) + f i for t =10 are 1 above the values in the tableSince Ic =5 is less than all these values we do not update Ic

Tracing and storing paths for starting at e1 at all times t t TTimes 5 and 6 will be spent loading the AGV So we trace the paths for starting

at edge 1 at times 7 8 9 and 10only edge 2 is accessible from edge 1cl(28) =min cl(17) + c2 8 2 + 1 =min 7 + 1 + 1 =8 tl(28) =1cl(29) =min cl(18) + c2 9 2 + 1 =min 8 + 1 + 1 =9 tl(29) =1cl(210) =min cl(19) + c2 10 2 + 1 =min 9 + 1 + 1 =10 tl(210) =1cl(211) =min cl(110) + c2 11 2 + 1 =min 10 + 1 + 1 =11 tl(211) =1edges 4 and 7 are adjacent to edge 2cl(49) =min cl(28) + c4 9 2 + 1 =min 8 + 1 + 1 =9 tl(49) =2cl(410) =min cl(29) + c4 10 2 + 1 =min 9 + 1 + 1 =10 tl(410) =2cl(411) =min cl(210) + c4 11 2 + 1 =min 10 + 1 + 1 =11 tl(411) =2cl(412) =min cl(211) + c4 12 2 + 1 =min 11 + 1 + 1 =12 tl(412) =2cl(79) =min cl(28) + c7 9 2 + 1 =min 8 + 1 + 1 =9 tl(79) =2cl(710) =min cl(29) + c7 10 2 + 1 =min 9 + 1 + 1 =10 tl(710) =2cl(711) =min cl(210) + c7 11 2 + 1 =min 10 + 1 + 1 =11 tl(711) =2cl(712) =min cl(211) + c7 12 2 + 1 =min 11 + 1 + 1 =12 tl(712) =2

This procedure is continued until the dropo edge e2 is reached Table 1summarizes the resulting cost and trace labels

Checking the paths which reach reg nal edge e2 by time Te2 =20 Ic =cl(2013) =13Tracing the path backward gives Ip =1 - 2 - 7 - 15 - 19 - 20 appended to the path

up to e1 We use the same procedure to generate a route for AGV 1 with the following cost

updates The cost of entering the intersection given by the edge set 8 9 10 11 1314 is set to at times 1 and 2 because AGV 2 uses this intersection at that Table 1summarizes the cost and trace labels for this AGV 1 The path obtained for thisAGV turns out to be 12 - 12 - 12 - 10 - 13 - 17 - 21 - 26 - 29 - 31 arriving at the

2028 C Oboth et al

i t cl(it) f i cl(it) + f i

17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10

destination after 11 time units These two paths constitute a feasible solution to thisrouting strategy

Current available routing strategies would start by routing the reg rst availableAGV (AGV 1) along its shortest path above taking 9 time units However theedges at the intersection above would also be blocked at times 1 and 2 Thereforethe path obtained for AGV 2 turns out to be 17 - 17 - 17 - 14 - 9 - 5 - 3 - 1 - 2 - 7 - 15 -19 - 20 arriving after 15 time units This is dereg nitely a worse performance than ourSPG strategy which accomplished the routing mission in 13 time units

References

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CALTEBERY G A 1991 The AGV Handbook (Ann Arbor Mich Braun-Brumreg eld)CHEN T C E 1987 AGV Dispatching in a macr exible manufacturing system International

Journal of Operations and Production Management 7 62plusmn 73COOKE K L and HANSLEY E 1966 The shortest path through a network with time depen-

dent internodal transit times Journal of Mathematical Analysis and ApplicationsDANIELS S G 1988 Real-time conmacr ict resolution in an automated guided scheduling

Doctorial dissertation Department of Industrial and Manufacturing EngineeringThe Pennsylvania State University

EGBELU P J 1987 The use of nonsimulation approaches in estimating vehicle requirementsin an automated guided vehicle based transport system Material Flow 4 17plusmn 32 1993Positioning of automated guided vehicles in a loop layout to improve response timeEuropean Journal of Operational Research 7 32plusmn 44

EGBELU P J and TANCHOCO J M A 1984 Characterization of automated guided vehicledispatching rules International Journal of Production Research 22 359plusmn 374 1986Potentials for bi-directional guidepath for auto mated guided vehicle based systemsIbid 24 1075plusmn 1097

EGBELU P J TANCHOCO J M A and TAGHABONI F 1987 Determination of the totalnumber of Vehicles in an AGV based material transport system Material Flow 433plusmn 52

FARAJI M and BATTA R 1994 Forming cells to eliminate vehicle interference and systemlocking in an AGVS International Journal of Production Research 32 2219plusmn 2241

FUJI S and SANDOH H 1987 A routing algorithm for automatic guided vehicles in FMSProceedings of the IXth International Conference on Production Research vol II pp2261plusmn 2267

HICKS R and CHARLES 1993 Fundamental Concepts in the Design of Experiments (NewYork Saunders College Publishing)

HOO-GON CHOI HYUK-JIN KWON and JIM LEE 1994 Traditional and tandem AGV systemlayouts a simulation study Simulation 63 85plusmn 93

KASILINGAM R G 1991 Mathematical modeling of the AGVS capacity requirements plan-ning problem Engineering Costs and Production Economics 21 171plusmn 175

KASILINGAM R G and GOBAL S L 1996 Vehicle requirements model for automated guidedvehicle systems International Journal of Advanced Manufacturing Technology 12 276plusmn279

KIM C and TANCHOCO J M A 1994 Bidirectional automated guided vehicle systemMaterial Flow Systems in Manufacturing Chap 9

KRISHNAMURTHY N N BATTA R and KARWAN M H 1993 Developing conmacr ict-freeroutes for automated guided vehicles Operations Research 41 1077plusmn 1090

LAW M L and KELTON D 1991 Simulation Modeling amp Analysis (New York McGraw-Hill)

MAHADEN B and NARENDRAN T T 1990 Design of an automated guided vehicle-basedmaterial handling system for a macr exible manufacturing system International Journal ofProduction Research 28 1611plusmn 1622

MAXWELL W L and MUCKSTADT J A 1982 Design of automatic guided vehicles IIETransactions 14


NARASIMHAN R T OBOTH C C BATTA R and KARWAN M H 1993 Dispatching andconmacr ict-free routing of automated guided vehicles with varying speeds 2nd IERC LosAngeles

NEWTON D 1986 Simulation model calculates how many automated guided vehicles areneeded Industrial Engineering 68plusmn 78

OBOTH C C 1996 Dispatching and conmacr ict-free routing of automated guided vehiclesETH anobject-oriented simulation study Doctoral dissertation Department of IndustrialEngineering State University of New York at Bu alo

SINRIECH D and TANCHOCO J M A 1992 The centroid projection method for locatingpickup and delivery stations in single-loop AGV systems Journal of ManufacturingSystems 11 297plusmn 307

TAGHABONI F and TANCHOCO J M A 1988 A LISP based controller for free-rangingautomated guided vehicle systems International Journal of Production Research 26173plusmn 188

VASSALLO M and KOHLI N 1993 Discussion of data collection and analysis at the harrisonradiator Report to the Department of Industrial Engineering SUNY AT BUFFALO

VOSNIAKOS G C and DAVIES J 1988 Simulation study of an AGV system in an FMSenvironment The International Journal of Advanced Manufacturing Technology 3 33plusmn46

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2030 Dynamic conmacr ict-free routing of AGVs

updated on all assignments It holds unused vehicles in specireg c locations in thesystem monitors the battery charging of the vehicles monitors problems thatoccur in the system re-starts the system after it has been shut down communicateswith the host computer compiles data for the host computer performs supervisoryfunctions for the AGV system and can maintain inventory records on the materialsin the material handling system

Scheduling several AGVs in a non-conmacr icting manner is a complicated real-timeproblem This is the job of the tra c controller which coordinates all tra c to makesure there are no vehicle collisions and the AGV tra c is e ciently managed If thereare any problems the tra c controller reroutes the vehicles and establishes newpriorities This controller holds all the information concerning the path networkroute and timetable of all the AGVs in the system Some tra c controllers coordi-nate the anti-collision blocking controls This paper presents the implementation of atra c controller system that can also perform a majority of the tasks of the centralcontroller

The on-board vehicle controller controls vehicle guidance steering speedacceleration stopping routing decisions safety monitoring collision and tra cavoidance interface with pickup and delivery stations doors alarms etc commu-nications with the central computer and interface with other material handlingequipment such as conveyors ASRS and robotic work cells

In the operation of an AGV based manufacturing system demands occur con-tinuously at random An e ective means must therefore be available for selectingthese demands from the set of available ones and once selected another e ectivemeans must be available for assigning the selected demands to available vehicles Thevehicles are then routed in a conmacr ict-free manner reg rst to their respective pickuppoints and then to the dropo points After demand delivery a means must beavailable to deal with empty vehicles if they cannot be immediately re-assignedother demands This process is continuously repeated during the manufacturingsystem operating period This paper presents a simulation of a dynamic batchtype manufacturing system incorporating all the above factors The performanceof the system is measured based on job system time mean number in queues vehicleutilization and mean response time

2 Literature review

Our literature review focusses only on papers that deal with research related toimplementations of a tra c controller system A detailed review of what has beendone to address the AGV routing problem can be found in Oboth (1996) Wenow summarize these works under two main categories macr ow path design issuesand operational control issues

21 Flow path design issuesIssues connected with macr ow path design like intersections and bu ers macr eet size

estimation and location of pickup and dropo stations have been addressed byMaxwell and Muckstadt (1982) Newton (1986) Egbelu and Tanchoco (19861987) Egbelu (1987) Usher et al (1988) and Sinriech and Tanchoco (1992)

22 Operational control issuesEgbelu and Tanchoco (1984) characterized dispatching rules for AGVs by com-

paring via simulation di erent combinations of workcentre and vehicle-initiated

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4][ 5

14]

[ 61

4][ 7

14]

[ 81

4][ 9

14]

[ 10

14]

10 11[ 2

14]

[ 31

4][ 4

14]

[ 51

4][ 6

14]

[ 71

4][ 8

14]

[ 91

4][ 1

014

]12 13

E14

[ 11

7][ 2

17]

[ 31

7][ 4

17]

[ 51

7][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]d

15[ 1

07]

[ 11

7][ 1

27]

[ 13

7]g

16e

17[ 0

17]

[ 11

7][ 2

17]

[ 31

7][ 4

17]

[ 51

7][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]18 19

[ 12

15]

[ 13

15]

20[ 1

319

]21

[ 11

7][ 2

17]

[ 31

7][ 4

17]

[ 51

7][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]22 23

[ 12

15]

[ 13

15]

24[ 4

28]

25 26[ 2

21]

[ 32

1][ 4

21]

[ 52

1][ 6

21]

[ 72

1][ 8

21]

[ 92

1][ 1

021

]27 28

[ 32

6]29

[ 32

6]30 31

[ 42

9]

(a)


ime

01

23

45

67

89

1011

1213

1 2 3 4 5[ 5

9]

[ 10

9]6 7 8 9

[ 41

0][ 5

10]

[ 61

0][ 7

10]

[ 81

0][ 9

10]

[ 10

10]

[ 11

10]

[ 12

10]

10[ 3

12]

[ 41

2][ 5

12]

[ 61

2][ 7

12]

[ 81

2][ 9

12]

[ 10

12]

[ 11

12]

11[ 9

14]

[ 10

14]

[ 11

14]

[ 12

14]

[ 13

14]

12[ 0

12]

[ 11

2][ 2

12]

[ 31

2][ 4

12]

[ 51

2][ 6

12]

[ 71

2][ 8

12]

[ 91

2][ 1

012

]13

[ 41

0][ 5

10]

[ 61

0][ 7

10]

[ 81

0][ 9

10]

[ 10

10]

[ 11

10]

[ 12

10]

E14

[ 81

7][ 9

17]

[ 10

17]

[ 11

17]

[ 12

17]

[ 13

17]

d15

g16

e17

[ 51

3][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]18 19

[ 13

15]

20[ 1

319

]21

[ 81

7][ 9

17]

[ 10

17]

[ 11

17]

[ 12

17]

[ 13

17]

22 23[ 1

315

]24 25 26

[ 92

1][ 1

021

][ 1

121

][ 1

221

][ 1

321

]27 28

[ 10

26]

[ 11

26]

[ 12

26]

[ 13

26]

29[ 1

026

][ 1

126

][ 1

226

][ 1

326

30 31[ 1

129

][ 1

229

][ 1

329

]

(b)

Tab

le1

Cos

tan

dtr

ace

labe

lsfo

r(a

)A

GV

2[cl

(it )

tl(i

t ) ](

b)A

GV

1[cl

(it )

tl(i

t ) ]









2012 C Oboth et al




186 340 9400340 475 7000475 602 7000602 729 6000729 853 11300853 885 16500885 898 7000898 904 7500904 907 4200907 910 9800910 1065 4100


392 725 5100725 886 2500886 894 5100

Workstation 3480 538 4700538 588 14500588 629 5400629 640 3100640 649 3500649 707 4700707 757 14600757 798 5400798 829 7000829 840 3100840 881 2200881 887 3500


552 805 4800805 935 3000935 1002 2900

1002 1020 7100


561 1020 7600


101 146 4900146 190 7200190 509 5400

509 511 6000511 686 4600


343 670 3700670 1053 6800

1053 1063 64001063 1116 12001116 1128 24001128 1130 2700


52 104 2600104 202 4800202 230 1600230 281 2500281 306 1500306 331 8600331 355 2400355 366 2900366 374 3000374 382 3700382 397 3300397 405 3800405 412 4500412 417 1600417 422 1000422 426 2000426 430 1400430 434 2400434 438 2800438 442 1700442 446 2700446 449 1800449 455 4800455 458 4300458 461 1400461 467 6300467 470 2400470 474 4800474 475 2000


770 1020 1600


81 1201 2700




482 708 3600

Workstation 14480 992 12800992 1142 14100

1142 1205 125001205 1260 12800




208 595 7000595 625 4700625 720 7100


434 539 8900539 604 10000604 654 15000654 718 9000718 720 10100


222 332 13500332 442 8600442 526 11300526 582 10000582 620 7300

Workstation 20480 511 11300511 529 9500529 537 11900537 540 6000


WS 1 2 3 4 5 6 7 8 9 10MCs 4 6 3 3 3 3 4 6 14 3

WS 11 12 13 14 15 16 17 18 19 20MCs 2 2 2 1 1 2 4 1 1 2





2014 C Oboth et al















systemJob related



2016 C Oboth et al

Workstation related


AGV related











Low Medium High


Table 3












2018 C Oboth et al


Fig

ure

6M

ean

SYST

IME

sum

mar

y

2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References















































2006 C Oboth et al












2008 C Oboth et al











2010 C Oboth et alT

ime

01

23

45

67

89

1011

1213

1[ 5

3]

[ 61

][ 7

1]

[ 81

][ 9

1]

[ 10

1]2

[ 81

][ 9

1]

[ 10

1][ 1

11]

3[ 4

5]

[ 55

][ 6

5]

[ 75

][ 8

5]

[ 95

][ 1

05]

4[ 9

2]

[ 10

2][ 1

12]

][ 1

22]

5[ 3

9]

[ 49

][ 5

9]

[ 69

][ 7

9]

[ 89

][ 9

9]

[ 19

9]7

[ 45

][ 9

2]

[ 10

2][ 1

12]

[ 12

2]8

[ 10

4]9

[ 21

4][ 3

14]

[ 41

4][ 5

14]

[ 61

4][ 7

14]

[ 81

4][ 9

14]

[ 10

14]

10 11[ 2

14]

[ 31

4][ 4

14]

[ 51

4][ 6

14]

[ 71

4][ 8

14]

[ 91

4][ 1

014

]12 13

E14

[ 11

7][ 2

17]

[ 31

7][ 4

17]

[ 51

7][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]d

15[ 1

07]

[ 11

7][ 1

27]

[ 13

7]g

16e

17[ 0

17]

[ 11

7][ 2

17]

[ 31

7][ 4

17]

[ 51

7][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]18 19

[ 12

15]

[ 13

15]

20[ 1

319

]21

[ 11

7][ 2

17]

[ 31

7][ 4

17]

[ 51

7][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]22 23

[ 12

15]

[ 13

15]

24[ 4

28]

25 26[ 2

21]

[ 32

1][ 4

21]

[ 52

1][ 6

21]

[ 72

1][ 8

21]

[ 92

1][ 1

021

]27 28

[ 32

6]29

[ 32

6]30 31

[ 42

9]

(a)


ime

01

23

45

67

89

1011

1213

1 2 3 4 5[ 5

9]

[ 10

9]6 7 8 9

[ 41

0][ 5

10]

[ 61

0][ 7

10]

[ 81

0][ 9

10]

[ 10

10]

[ 11

10]

[ 12

10]

10[ 3

12]

[ 41

2][ 5

12]

[ 61

2][ 7

12]

[ 81

2][ 9

12]

[ 10

12]

[ 11

12]

11[ 9

14]

[ 10

14]

[ 11

14]

[ 12

14]

[ 13

14]

12[ 0

12]

[ 11

2][ 2

12]

[ 31

2][ 4

12]

[ 51

2][ 6

12]

[ 71

2][ 8

12]

[ 91

2][ 1

012

]13

[ 41

0][ 5

10]

[ 61

0][ 7

10]

[ 81

0][ 9

10]

[ 10

10]

[ 11

10]

[ 12

10]

E14

[ 81

7][ 9

17]

[ 10

17]

[ 11

17]

[ 12

17]

[ 13

17]

d15

g16

e17

[ 51

3][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]18 19

[ 13

15]

20[ 1

319

]21

[ 81

7][ 9

17]

[ 10

17]

[ 11

17]

[ 12

17]

[ 13

17]

22 23[ 1

315

]24 25 26

[ 92

1][ 1

021

][ 1

121

][ 1

221

][ 1

321

]27 28

[ 10

26]

[ 11

26]

[ 12

26]

[ 13

26]

29[ 1

026

][ 1

126

][ 1

226

][ 1

326

30 31[ 1

129

][ 1

229

][ 1

329

]

(b)

Tab

le1

Cos

tan

dtr

ace

labe

lsfo

r(a

)A

GV

2[cl

(it )

tl(i

t ) ](

b)A

GV

1[cl

(it )

tl(i

t ) ]









2012 C Oboth et al




186 340 9400340 475 7000475 602 7000602 729 6000729 853 11300853 885 16500885 898 7000898 904 7500904 907 4200907 910 9800910 1065 4100


392 725 5100725 886 2500886 894 5100

Workstation 3480 538 4700538 588 14500588 629 5400629 640 3100640 649 3500649 707 4700707 757 14600757 798 5400798 829 7000829 840 3100840 881 2200881 887 3500


552 805 4800805 935 3000935 1002 2900

1002 1020 7100


561 1020 7600


101 146 4900146 190 7200190 509 5400

509 511 6000511 686 4600


343 670 3700670 1053 6800

1053 1063 64001063 1116 12001116 1128 24001128 1130 2700


52 104 2600104 202 4800202 230 1600230 281 2500281 306 1500306 331 8600331 355 2400355 366 2900366 374 3000374 382 3700382 397 3300397 405 3800405 412 4500412 417 1600417 422 1000422 426 2000426 430 1400430 434 2400434 438 2800438 442 1700442 446 2700446 449 1800449 455 4800455 458 4300458 461 1400461 467 6300467 470 2400470 474 4800474 475 2000


770 1020 1600


81 1201 2700




482 708 3600

Workstation 14480 992 12800992 1142 14100

1142 1205 125001205 1260 12800




208 595 7000595 625 4700625 720 7100


434 539 8900539 604 10000604 654 15000654 718 9000718 720 10100


222 332 13500332 442 8600442 526 11300526 582 10000582 620 7300

Workstation 20480 511 11300511 529 9500529 537 11900537 540 6000


WS 1 2 3 4 5 6 7 8 9 10MCs 4 6 3 3 3 3 4 6 14 3

WS 11 12 13 14 15 16 17 18 19 20MCs 2 2 2 1 1 2 4 1 1 2





2014 C Oboth et al















systemJob related



2016 C Oboth et al

Workstation related


AGV related











Low Medium High


Table 3












2018 C Oboth et al


Fig

ure

6M

ean

SYST

IME

sum

mar

y

2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References








































2008 C Oboth et al











2010 C Oboth et alT

ime

01

23

45

67

89

1011

1213

1[ 5

3]

[ 61

][ 7

1]

[ 81

][ 9

1]

[ 10

1]2

[ 81

][ 9

1]

[ 10

1][ 1

11]

3[ 4

5]

[ 55

][ 6

5]

[ 75

][ 8

5]

[ 95

][ 1

05]

4[ 9

2]

[ 10

2][ 1

12]

][ 1

22]

5[ 3

9]

[ 49

][ 5

9]

[ 69

][ 7

9]

[ 89

][ 9

9]

[ 19

9]7

[ 45

][ 9

2]

[ 10

2][ 1

12]

[ 12

2]8

[ 10

4]9

[ 21

4][ 3

14]

[ 41

4][ 5

14]

[ 61

4][ 7

14]

[ 81

4][ 9

14]

[ 10

14]

10 11[ 2

14]

[ 31

4][ 4

14]

[ 51

4][ 6

14]

[ 71

4][ 8

14]

[ 91

4][ 1

014

]12 13

E14

[ 11

7][ 2

17]

[ 31

7][ 4

17]

[ 51

7][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]d

15[ 1

07]

[ 11

7][ 1

27]

[ 13

7]g

16e

17[ 0

17]

[ 11

7][ 2

17]

[ 31

7][ 4

17]

[ 51

7][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]18 19

[ 12

15]

[ 13

15]

20[ 1

319

]21

[ 11

7][ 2

17]

[ 31

7][ 4

17]

[ 51

7][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]22 23

[ 12

15]

[ 13

15]

24[ 4

28]

25 26[ 2

21]

[ 32

1][ 4

21]

[ 52

1][ 6

21]

[ 72

1][ 8

21]

[ 92

1][ 1

021

]27 28

[ 32

6]29

[ 32

6]30 31

[ 42

9]

(a)


ime

01

23

45

67

89

1011

1213

1 2 3 4 5[ 5

9]

[ 10

9]6 7 8 9

[ 41

0][ 5

10]

[ 61

0][ 7

10]

[ 81

0][ 9

10]

[ 10

10]

[ 11

10]

[ 12

10]

10[ 3

12]

[ 41

2][ 5

12]

[ 61

2][ 7

12]

[ 81

2][ 9

12]

[ 10

12]

[ 11

12]

11[ 9

14]

[ 10

14]

[ 11

14]

[ 12

14]

[ 13

14]

12[ 0

12]

[ 11

2][ 2

12]

[ 31

2][ 4

12]

[ 51

2][ 6

12]

[ 71

2][ 8

12]

[ 91

2][ 1

012

]13

[ 41

0][ 5

10]

[ 61

0][ 7

10]

[ 81

0][ 9

10]

[ 10

10]

[ 11

10]

[ 12

10]

E14

[ 81

7][ 9

17]

[ 10

17]

[ 11

17]

[ 12

17]

[ 13

17]

d15

g16

e17

[ 51

3][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]18 19

[ 13

15]

20[ 1

319

]21

[ 81

7][ 9

17]

[ 10

17]

[ 11

17]

[ 12

17]

[ 13

17]

22 23[ 1

315

]24 25 26

[ 92

1][ 1

021

][ 1

121

][ 1

221

][ 1

321

]27 28

[ 10

26]

[ 11

26]

[ 12

26]

[ 13

26]

29[ 1

026

][ 1

126

][ 1

226

][ 1

326

30 31[ 1

129

][ 1

229

][ 1

329

]

(b)

Tab

le1

Cos

tan

dtr

ace

labe

lsfo

r(a

)A

GV

2[cl

(it )

tl(i

t ) ](

b)A

GV

1[cl

(it )

tl(i

t ) ]









2012 C Oboth et al




186 340 9400340 475 7000475 602 7000602 729 6000729 853 11300853 885 16500885 898 7000898 904 7500904 907 4200907 910 9800910 1065 4100


392 725 5100725 886 2500886 894 5100

Workstation 3480 538 4700538 588 14500588 629 5400629 640 3100640 649 3500649 707 4700707 757 14600757 798 5400798 829 7000829 840 3100840 881 2200881 887 3500


552 805 4800805 935 3000935 1002 2900

1002 1020 7100


561 1020 7600


101 146 4900146 190 7200190 509 5400

509 511 6000511 686 4600


343 670 3700670 1053 6800

1053 1063 64001063 1116 12001116 1128 24001128 1130 2700


52 104 2600104 202 4800202 230 1600230 281 2500281 306 1500306 331 8600331 355 2400355 366 2900366 374 3000374 382 3700382 397 3300397 405 3800405 412 4500412 417 1600417 422 1000422 426 2000426 430 1400430 434 2400434 438 2800438 442 1700442 446 2700446 449 1800449 455 4800455 458 4300458 461 1400461 467 6300467 470 2400470 474 4800474 475 2000


770 1020 1600


81 1201 2700




482 708 3600

Workstation 14480 992 12800992 1142 14100

1142 1205 125001205 1260 12800




208 595 7000595 625 4700625 720 7100


434 539 8900539 604 10000604 654 15000654 718 9000718 720 10100


222 332 13500332 442 8600442 526 11300526 582 10000582 620 7300

Workstation 20480 511 11300511 529 9500529 537 11900537 540 6000


WS 1 2 3 4 5 6 7 8 9 10MCs 4 6 3 3 3 3 4 6 14 3

WS 11 12 13 14 15 16 17 18 19 20MCs 2 2 2 1 1 2 4 1 1 2





2014 C Oboth et al















systemJob related



2016 C Oboth et al

Workstation related


AGV related











Low Medium High


Table 3












2018 C Oboth et al


Fig

ure

6M

ean

SYST

IME

sum

mar

y

2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References








































2010 C Oboth et alT

ime

01

23

45

67

89

1011

1213

1[ 5

3]

[ 61

][ 7

1]

[ 81

][ 9

1]

[ 10

1]2

[ 81

][ 9

1]

[ 10

1][ 1

11]

3[ 4

5]

[ 55

][ 6

5]

[ 75

][ 8

5]

[ 95

][ 1

05]

4[ 9

2]

[ 10

2][ 1

12]

][ 1

22]

5[ 3

9]

[ 49

][ 5

9]

[ 69

][ 7

9]

[ 89

][ 9

9]

[ 19

9]7

[ 45

][ 9

2]

[ 10

2][ 1

12]

[ 12

2]8

[ 10

4]9

[ 21

4][ 3

14]

[ 41

4][ 5

14]

[ 61

4][ 7

14]

[ 81

4][ 9

14]

[ 10

14]

10 11[ 2

14]

[ 31

4][ 4

14]

[ 51

4][ 6

14]

[ 71

4][ 8

14]

[ 91

4][ 1

014

]12 13

E14

[ 11

7][ 2

17]

[ 31

7][ 4

17]

[ 51

7][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]d

15[ 1

07]

[ 11

7][ 1

27]

[ 13

7]g

16e

17[ 0

17]

[ 11

7][ 2

17]

[ 31

7][ 4

17]

[ 51

7][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]18 19

[ 12

15]

[ 13

15]

20[ 1

319

]21

[ 11

7][ 2

17]

[ 31

7][ 4

17]

[ 51

7][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]22 23

[ 12

15]

[ 13

15]

24[ 4

28]

25 26[ 2

21]

[ 32

1][ 4

21]

[ 52

1][ 6

21]

[ 72

1][ 8

21]

[ 92

1][ 1

021

]27 28

[ 32

6]29

[ 32

6]30 31

[ 42

9]

(a)


ime

01

23

45

67

89

1011

1213

1 2 3 4 5[ 5

9]

[ 10

9]6 7 8 9

[ 41

0][ 5

10]

[ 61

0][ 7

10]

[ 81

0][ 9

10]

[ 10

10]

[ 11

10]

[ 12

10]

10[ 3

12]

[ 41

2][ 5

12]

[ 61

2][ 7

12]

[ 81

2][ 9

12]

[ 10

12]

[ 11

12]

11[ 9

14]

[ 10

14]

[ 11

14]

[ 12

14]

[ 13

14]

12[ 0

12]

[ 11

2][ 2

12]

[ 31

2][ 4

12]

[ 51

2][ 6

12]

[ 71

2][ 8

12]

[ 91

2][ 1

012

]13

[ 41

0][ 5

10]

[ 61

0][ 7

10]

[ 81

0][ 9

10]

[ 10

10]

[ 11

10]

[ 12

10]

E14

[ 81

7][ 9

17]

[ 10

17]

[ 11

17]

[ 12

17]

[ 13

17]

d15

g16

e17

[ 51

3][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]18 19

[ 13

15]

20[ 1

319

]21

[ 81

7][ 9

17]

[ 10

17]

[ 11

17]

[ 12

17]

[ 13

17]

22 23[ 1

315

]24 25 26

[ 92

1][ 1

021

][ 1

121

][ 1

221

][ 1

321

]27 28

[ 10

26]

[ 11

26]

[ 12

26]

[ 13

26]

29[ 1

026

][ 1

126

][ 1

226

][ 1

326

30 31[ 1

129

][ 1

229

][ 1

329

]

(b)

Tab

le1

Cos

tan

dtr

ace

labe

lsfo

r(a

)A

GV

2[cl

(it )

tl(i

t ) ](

b)A

GV

1[cl

(it )

tl(i

t ) ]









2012 C Oboth et al




186 340 9400340 475 7000475 602 7000602 729 6000729 853 11300853 885 16500885 898 7000898 904 7500904 907 4200907 910 9800910 1065 4100


392 725 5100725 886 2500886 894 5100

Workstation 3480 538 4700538 588 14500588 629 5400629 640 3100640 649 3500649 707 4700707 757 14600757 798 5400798 829 7000829 840 3100840 881 2200881 887 3500


552 805 4800805 935 3000935 1002 2900

1002 1020 7100


561 1020 7600


101 146 4900146 190 7200190 509 5400

509 511 6000511 686 4600


343 670 3700670 1053 6800

1053 1063 64001063 1116 12001116 1128 24001128 1130 2700


52 104 2600104 202 4800202 230 1600230 281 2500281 306 1500306 331 8600331 355 2400355 366 2900366 374 3000374 382 3700382 397 3300397 405 3800405 412 4500412 417 1600417 422 1000422 426 2000426 430 1400430 434 2400434 438 2800438 442 1700442 446 2700446 449 1800449 455 4800455 458 4300458 461 1400461 467 6300467 470 2400470 474 4800474 475 2000


770 1020 1600


81 1201 2700




482 708 3600

Workstation 14480 992 12800992 1142 14100

1142 1205 125001205 1260 12800




208 595 7000595 625 4700625 720 7100


434 539 8900539 604 10000604 654 15000654 718 9000718 720 10100


222 332 13500332 442 8600442 526 11300526 582 10000582 620 7300

Workstation 20480 511 11300511 529 9500529 537 11900537 540 6000


WS 1 2 3 4 5 6 7 8 9 10MCs 4 6 3 3 3 3 4 6 14 3

WS 11 12 13 14 15 16 17 18 19 20MCs 2 2 2 1 1 2 4 1 1 2





2014 C Oboth et al















systemJob related



2016 C Oboth et al

Workstation related


AGV related











Low Medium High


Table 3












2018 C Oboth et al


Fig

ure

6M

ean

SYST

IME

sum

mar

y

2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References































ime

01

23

45

67

89

1011

1213

1 2 3 4 5[ 5

9]

[ 10

9]6 7 8 9

[ 41

0][ 5

10]

[ 61

0][ 7

10]

[ 81

0][ 9

10]

[ 10

10]

[ 11

10]

[ 12

10]

10[ 3

12]

[ 41

2][ 5

12]

[ 61

2][ 7

12]

[ 81

2][ 9

12]

[ 10

12]

[ 11

12]

11[ 9

14]

[ 10

14]

[ 11

14]

[ 12

14]

[ 13

14]

12[ 0

12]

[ 11

2][ 2

12]

[ 31

2][ 4

12]

[ 51

2][ 6

12]

[ 71

2][ 8

12]

[ 91

2][ 1

012

]13

[ 41

0][ 5

10]

[ 61

0][ 7

10]

[ 81

0][ 9

10]

[ 10

10]

[ 11

10]

[ 12

10]

E14

[ 81

7][ 9

17]

[ 10

17]

[ 11

17]

[ 12

17]

[ 13

17]

d15

g16

e17

[ 51

3][ 6

17]

[ 71

7][ 8

17]

[ 91

7][ 1

017

]18 19

[ 13

15]

20[ 1

319

]21

[ 81

7][ 9

17]

[ 10

17]

[ 11

17]

[ 12

17]

[ 13

17]

22 23[ 1

315

]24 25 26

[ 92

1][ 1

021

][ 1

121

][ 1

221

][ 1

321

]27 28

[ 10

26]

[ 11

26]

[ 12

26]

[ 13

26]

29[ 1

026

][ 1

126

][ 1

226

][ 1

326

30 31[ 1

129

][ 1

229

][ 1

329

]

(b)

Tab

le1

Cos

tan

dtr

ace

labe

lsfo

r(a

)A

GV

2[cl

(it )

tl(i

t ) ](

b)A

GV

1[cl

(it )

tl(i

t ) ]









2012 C Oboth et al




186 340 9400340 475 7000475 602 7000602 729 6000729 853 11300853 885 16500885 898 7000898 904 7500904 907 4200907 910 9800910 1065 4100


392 725 5100725 886 2500886 894 5100

Workstation 3480 538 4700538 588 14500588 629 5400629 640 3100640 649 3500649 707 4700707 757 14600757 798 5400798 829 7000829 840 3100840 881 2200881 887 3500


552 805 4800805 935 3000935 1002 2900

1002 1020 7100


561 1020 7600


101 146 4900146 190 7200190 509 5400

509 511 6000511 686 4600


343 670 3700670 1053 6800

1053 1063 64001063 1116 12001116 1128 24001128 1130 2700


52 104 2600104 202 4800202 230 1600230 281 2500281 306 1500306 331 8600331 355 2400355 366 2900366 374 3000374 382 3700382 397 3300397 405 3800405 412 4500412 417 1600417 422 1000422 426 2000426 430 1400430 434 2400434 438 2800438 442 1700442 446 2700446 449 1800449 455 4800455 458 4300458 461 1400461 467 6300467 470 2400470 474 4800474 475 2000


770 1020 1600


81 1201 2700




482 708 3600

Workstation 14480 992 12800992 1142 14100

1142 1205 125001205 1260 12800




208 595 7000595 625 4700625 720 7100


434 539 8900539 604 10000604 654 15000654 718 9000718 720 10100


222 332 13500332 442 8600442 526 11300526 582 10000582 620 7300

Workstation 20480 511 11300511 529 9500529 537 11900537 540 6000


WS 1 2 3 4 5 6 7 8 9 10MCs 4 6 3 3 3 3 4 6 14 3

WS 11 12 13 14 15 16 17 18 19 20MCs 2 2 2 1 1 2 4 1 1 2





2014 C Oboth et al















systemJob related



2016 C Oboth et al

Workstation related


AGV related











Low Medium High


Table 3












2018 C Oboth et al


Fig

ure

6M

ean

SYST

IME

sum

mar

y

2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References






































2012 C Oboth et al




186 340 9400340 475 7000475 602 7000602 729 6000729 853 11300853 885 16500885 898 7000898 904 7500904 907 4200907 910 9800910 1065 4100


392 725 5100725 886 2500886 894 5100

Workstation 3480 538 4700538 588 14500588 629 5400629 640 3100640 649 3500649 707 4700707 757 14600757 798 5400798 829 7000829 840 3100840 881 2200881 887 3500


552 805 4800805 935 3000935 1002 2900

1002 1020 7100


561 1020 7600


101 146 4900146 190 7200190 509 5400

509 511 6000511 686 4600


343 670 3700670 1053 6800

1053 1063 64001063 1116 12001116 1128 24001128 1130 2700


52 104 2600104 202 4800202 230 1600230 281 2500281 306 1500306 331 8600331 355 2400355 366 2900366 374 3000374 382 3700382 397 3300397 405 3800405 412 4500412 417 1600417 422 1000422 426 2000426 430 1400430 434 2400434 438 2800438 442 1700442 446 2700446 449 1800449 455 4800455 458 4300458 461 1400461 467 6300467 470 2400470 474 4800474 475 2000


770 1020 1600


81 1201 2700




482 708 3600

Workstation 14480 992 12800992 1142 14100

1142 1205 125001205 1260 12800




208 595 7000595 625 4700625 720 7100


434 539 8900539 604 10000604 654 15000654 718 9000718 720 10100


222 332 13500332 442 8600442 526 11300526 582 10000582 620 7300

Workstation 20480 511 11300511 529 9500529 537 11900537 540 6000


WS 1 2 3 4 5 6 7 8 9 10MCs 4 6 3 3 3 3 4 6 14 3

WS 11 12 13 14 15 16 17 18 19 20MCs 2 2 2 1 1 2 4 1 1 2





2014 C Oboth et al















systemJob related



2016 C Oboth et al

Workstation related


AGV related











Low Medium High


Table 3












2018 C Oboth et al


Fig

ure

6M

ean

SYST

IME

sum

mar

y

2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References

































186 340 9400340 475 7000475 602 7000602 729 6000729 853 11300853 885 16500885 898 7000898 904 7500904 907 4200907 910 9800910 1065 4100


392 725 5100725 886 2500886 894 5100

Workstation 3480 538 4700538 588 14500588 629 5400629 640 3100640 649 3500649 707 4700707 757 14600757 798 5400798 829 7000829 840 3100840 881 2200881 887 3500


552 805 4800805 935 3000935 1002 2900

1002 1020 7100


561 1020 7600


101 146 4900146 190 7200190 509 5400

509 511 6000511 686 4600


343 670 3700670 1053 6800

1053 1063 64001063 1116 12001116 1128 24001128 1130 2700


52 104 2600104 202 4800202 230 1600230 281 2500281 306 1500306 331 8600331 355 2400355 366 2900366 374 3000374 382 3700382 397 3300397 405 3800405 412 4500412 417 1600417 422 1000422 426 2000426 430 1400430 434 2400434 438 2800438 442 1700442 446 2700446 449 1800449 455 4800455 458 4300458 461 1400461 467 6300467 470 2400470 474 4800474 475 2000


770 1020 1600


81 1201 2700




482 708 3600

Workstation 14480 992 12800992 1142 14100

1142 1205 125001205 1260 12800




208 595 7000595 625 4700625 720 7100


434 539 8900539 604 10000604 654 15000654 718 9000718 720 10100


222 332 13500332 442 8600442 526 11300526 582 10000582 620 7300

Workstation 20480 511 11300511 529 9500529 537 11900537 540 6000


WS 1 2 3 4 5 6 7 8 9 10MCs 4 6 3 3 3 3 4 6 14 3

WS 11 12 13 14 15 16 17 18 19 20MCs 2 2 2 1 1 2 4 1 1 2





2014 C Oboth et al















systemJob related



2016 C Oboth et al

Workstation related


AGV related











Low Medium High


Table 3












2018 C Oboth et al


Fig

ure

6M

ean

SYST

IME

sum

mar

y

2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References
































2014 C Oboth et al















systemJob related



2016 C Oboth et al

Workstation related


AGV related











Low Medium High


Table 3












2018 C Oboth et al


Fig

ure

6M

ean

SYST

IME

sum

mar

y

2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References











































systemJob related



2016 C Oboth et al

Workstation related


AGV related











Low Medium High


Table 3












2018 C Oboth et al


Fig

ure

6M

ean

SYST

IME

sum

mar

y

2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References






























Workstation related


AGV related











Low Medium High


Table 3












2018 C Oboth et al


Fig

ure

6M

ean

SYST

IME

sum

mar

y

2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References









































2018 C Oboth et al


Fig

ure

6M

ean

SYST

IME

sum

mar

y

2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References































Fig

ure

6M

ean

SYST

IME

sum

mar

y

2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References






























2020 C Oboth et al


Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References































Fig

ure

7M

ean

SYST

IME

with

inte

ract

ion

eec

ts



2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References
































2022 C Oboth et al



914 NV MFCFS







































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References













































6 Conclusions






Acknowledgments


2024 C Oboth et al

Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References






























Appendix


k2 ek


Algorithm SPG


i=1

de1i e1

( i+1)

n2shy 1

i=1

de2i e2

( i+1)

nkshy 1

i=1

deki ek

( i+1)















Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References






























Algorithm BL OCK



Set Bikz =1end for

end if

end for




end for



end for

end if

end if






2026 C Oboth et al








for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References





































for i=1 lxvxk do





end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References






























end if

end for

end for









2028 C Oboth et al


17 9 9 5 1414 9 9 4 1311 9 9 6 1512 9 1 1 110 9 1 1 19 9 9 3 125 9 9 2 113 9 9 1 10



References
































References






























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