a decision-making system for construction site layout planning

nono, Ch

whul

pletimalgo) praluaance of the proposed decision-making system, which was veried by a residentialthe practitioners in the construction industry to deliver construction projects in aman

1. Introduction

CSLP) hy pract, whicng soluereforerocesswhich acation

the available site space (sometimes it is une

managers and p

Automation in Construction 20 (2011) 459473

Contents lists available at ScienceDirect

Automation in

e lsand constraints, and nally evaluating and selecting the best sitelayout plan for implementation.

In our previous research [1], a new method using continuousdynamic searching scheme to guide themaxmin ant system (MMAS)algorithm, which is one of the ant colony optimization (ACO)algorithms, to solve the dynamic CSLP problem under the twocongruent objective functions of minimizing safety concerns andreducing construction cost is proposed. This paper aims to develop a

that most of the previous CSLP research works concentrated on thestatic CSLP problems [24].

Second, reviews of previous CSLP research works [57] showedthat the site facilities had been shaped as rectangular blocks, by whichthey could be assigned to any location. Academically it is termed asequal-area CSLP problem. However, this theoretically convenientapproach did not consider whether those locations could actuallyaccommodate the assigned facilities in reality. This hypotheticalcomputationally intelligent CSLP decision-consists of four stages: the input stage,evaluation and selection stage, and the outp

Corresponding author. Tel.: +852 2788 7238; fax: +E-mail address: [email protected] (K.-C. Lam).

0926-5805/$ see front matter 2010 Published by Edoi:10.1016/j.autcon.2010.11.014qual-area site), which isThird, generation of thelll the layout objectives

during the progress of a construction project, the site layout should bealtered accordingly. Under this situation the CSLP problems should beregarded as dynamic problems. However, literature reviews showeddynamic during the construction progress.construction site layout alternatives, which fuConstruction site layout planning (critical step in construction planning bCSLP is a decision-making processproblems and opportunities, developialternative and implementing it. Thlayout plan is a decision-making pdetermination of the CSLP objectives,the layout constraints. Second, identias been recognized as aitioners and researchers.h involves identifyingtions, choosing the best, designing a good sitethat involves rst there usually multiple, andof the site facilities and

problems under multiple objectives.

2. Construction site layout planning

After extensive literature reviews of previous CSLP research worksand discussionswith projectmanagers and practitioners of constructionoperations, some CSLP problems are identied as follows:

First, if the requirements of the construction work were changedmaking system whichthe design stage, theut stage to help project

assumption is falimited researchCSLP problemsunequal-area CS

Third, mostimprovement ofalgorithms, by wgenerated for ev

852 2788 7612.

lsevier B.V.lanners to solve dynamic and unequal-area CSLPA decision-making system for constructio

Xin Ning a, Ka-Chi Lam b,, Mike Chun-Kit Lam b

a School of Investment & Construction Management, Dongbei University of Finance and Ecb Department of Building and Construction, City University of Hong Kong, Hong Kong SAR

a b s t r a c ta r t i c l e i n f o

Article history:Accepted 4 November 2010Available online 9 December 2010

Keywords:Decision-making systemConstruction site layout planningMaxmin ant systemPareto-based ant colony optimizationalgorithm

A decision-making system,proposed to solve dynamic, mIn the input stage, the multistage, two mathematical opcolony optimization (ACO)objective optimization (MOOTOPSIS method is used to evthe design stage. The performbuilding project, shall assistmore efcient and effective

j ourna l homepage: www.ner, and thus construction costs could be reduced signicantly. 2010 Published by Elsevier B.V.site layout planning

mics, Dalian, Liaoning Province, Chinaina

ich consists of input, design, evaluation and selection, and output stages, isti-objective and unequal-area construction site layout planning (CSLP) problem.objectives, schedule planning and site condition are determined. In the designization models maxmin ant system (MMAS) and modied Pareto-based antrithm are employed to solve single objective optimization (SOO) and multi-oblem respectively. In the evaluation and selection stage, the intuitionistic fuzzyte and select the best layout plan among the generated layout alternatives from

Construction

ev ie r.com/ locate /autconr away from the real-life situation in CSLP. Moreover,works had been carried out to solve unequal-area[8]. Therefore, there is a research gap in solvingLP problems.of the CSLP research works concentrated on thethe computational capability of various optimizationhich a number of site layout alternatives could bealuation and selection. Nevertheless little research

effort has beenplacedonhowtoevaluateand select thenal, or the best,construction site layout from the generated site layout alternatives. As amatter of fact that CSLP is basically a trade-off problem, in whichconstruction managers and site planners need to make a decision toselect the best construction site layout among the site layoutalternatives generated from various optimization algorithms. Thisapproach requires construction managers and planners to considerand balance all the important attributes, such as minimizing costs, safeworking environment and efcient material transportation, withoutsacricing the required quality. Moreover, some of these importantattributes, such as security and noise control are not easy to handle andit is extremely difcult for decisionmakers to justifywhich constructionsite layout should be selected.

Finally, many researchers treated CSLP as a single-objectiveoptimization (SOO) problems, for instance, minimizing the frequencyof trips made by construction personnel, minimizing the totaltransportation costs of resources between facilities, and minimizingthe cost of construction facilities or the interactive costs betweenfacilities. Until now, only few researchers have treated CSLP as amulti-objective optimization (MOO) problem, which involves morethan a single objective function [9].

In order to solve the aforementioned problems, this study aims todevelop a computationally intelligent CSLP decision-making systemwhich consists of four stages: the input stage, the design stage, theevaluation and selection stage, and the output stage (see Fig. 1) tohelp project managers and planners to solve dynamic, multipleobjective and unequal-area CSLP problems.

In this study, the multiple objectives dened in the input stage areminimizing the likelihood of accidents happened to improve thesafety level (f1) and minimizing the total handling cost of interactionows between the facilities associated with the construction sitelayout (f2), which is based on interaction relationship between thefacilities.

In the design stage, two optimization models, one is SOO modeland the other is MOOmodel, are employed to solve multiple objectiveCSLP problems, which could be treated as either SOO problem orMOOproblem. Maxmin ant system (MMAS) and Pareto-based ACOalgorithm are deployed into the SOO model and MOO model tosolve the multiple objective CSLP problems respectively. Moreover,the unequal-area grids recognition strategy and continuous dynamicsearching scheme [1] are adopted to guide the two ACO algorithms tosolve dynamic, multiple objective and unequal-area CSLP problems.

Input stage

Site condition

Schedule planning

Construction objectives

Available space

Assigned facilities

Layout constrains

Objectives

Interaction relationship

Design stage

SOO model using MMAS

MOO model using Pareto-based ACO algorithm

ide

st

areod

ou

Inpu

t sta

ge

e

460 X. Ning et al. / Automation in Construction 20 (2011) 459473Evaluation and selection stage

f1: Minimize the likelihood of accto improve the safety level;

f2: Minimize the total handling coflows between the facilities

By weighted sum metho d

By Pmeth

MADM model using intuitionistic fuzzy TOPSIS

Output Final site layFig. 1. The owchart of the proposednts happened

of interaction

to optimization

Cons

truct

ion

site

layo

ut

t plan

Des

ign

stag

Eval

uatio

n an

d &

sele

ctio

n st

age

Out

put

stag

eCSLP decision-making system.

When solving multiple objective CSLP problems, a number ofconstruction site layout alternatives are generated in the design stageof the proposeddecision-making system. In the evaluation and selection

stage, a multiple attribute decision making (MADM) model usingintuitionsitic fuzzy TOPSIS is employed to evaluate and select the bestconstruction site layout plan from the site layout alternatives generatedin the design stage. The evaluation attributes such as security, easysupervision and control, ease of expansion, which are neglected in theprevious CSLP studies and difcult to quantify, are considered in thisstudy. The rest of this paper is organized in the following manner: rst,the structure of the proposed CSLP decision-making system isintroduced. Second, the functions and the algorithms used in eachstagewill be discussed one by one in the following sections. Third, a casestudy of the residential building project is used to verify the proposedCSLP decision-making system. Finally, a conclusion is drawn.

3. The structure of CSLP decision-making system

The system structure of the proposed CSLP decision-makingsystem is summarized as below:

The components and methods employed at each stage of theproposed CSLP decision-making system would be discussed below.

3.1. Input stage

There are three components: site conditions, schedule planning andconstruction objectives in the input stage. From the site conditions andthe schedule planning of the construction project, the space availability,the site facilities, the dynamic site layout time interval and the layout

Table 1The pseudo-code of MMAS.

Step Function

1 Select assignment sequence for the facilities2 Initialize pheromone information and dene heuristic information 3 Determine the maximum iteration number N4 Determine the total ant number m5 Initialize the iteration number n=16 Initialize pheromone information and dene heuristic information 7 For each ant k8 Set a parameter q

0between [0, 1].

9 Generate a random variable q, which is uniformly distributed over [0,1]10 If qq0, an ant k assigns the next unassigned facility i to a free location j in

terms of arg max lNik{ij[ij]}; otherwise, the probability rule

pkij t =ij t ij

lNk

iil t il

is adopted. and are the parameters that

determine the relative inuence of the pheromone information and the

heuristic information respectively, Nik is the feasible neighborhood of node i11 Update the pheromone information, If after the pheromone update we have

max, we set =max; if min, we set =min.12 Update the iteration number n=n+113 If ibN, go to step 714 Output the solution (site layout alternatives)

Start

Generate initial colony POP randomly with number

Calculated associated value of objective functions offi (x),i = 1,2,K , k and the constrained functions of e j , j = 1,2,K ,J.

Initialize external set BP , which consists of non-dominated feasiblesolutions

on

461X. Ning et al. / Automation in Construction 20 (2011) 459473Set maximum iterati

t = 1i = 1

Generate variable P randomly within inparameter P0 , P0[0,1]

P P0

Local pheromone communication (mode 1)

G

Update external set

t < Nmax

End

NO

YES

NO

Fig. 2. The workow of the modieNi

t , Nmax

terval [0, 1] and set a

lobal optimum searching history (mode 2)

1+= ii

1+= tt

YES YES

NOd Pareto-based ACO algorithm.

Step 1: Divide the whole construction sitento two blocks (B1 and B2) by the maximumacilities sizes. In this case, the maximum sizef the two facilities is 100 .Thus the wholeonstruction site is divided into two blocks (B1nd B2) with an area of 100 .

Step 2: Assign the facilities of FA1 withizentoith

oca

y tith

locloc

462 X. Ning et al. / Automation in Construction 20 (2011) 459473ifo

c

a

s

iw

l

FA1

B2

B1

FA2

bw

SB1 SB2

FA1 SB2 bb

FA2 constraints are rstly derived. From the component of constructionobjectives, the multiple objectives are dened and the interactionrelationships are then calculated. In the case study of the proposeddecision-making system, the multi-objective functions dened wereminimizing the likelihood of accidents happened and minimizing thetotal handling cost of interactionowsbetween the facilities. The factorsconsidered in the interaction relationship were material ows,information ows, personnel ows, equipment ows, safety/environ-ment concerns and users' preference) [10,11]. Having the data of thequalitative factors involved in the interaction relationships derived via aquestionnaire, the fuzzy rule-based system [12,13] was employed tocalculate the interaction relationships between the facilities.

3.2. Design stage

Themain function of the design stage of the proposed CSLP decision-making system is the generation of construction site layout alternatives,in terms of the objective functions, for the evaluation and selectionstage. In order to have more quality candidate solutions or alternativesfor evaluation and selection, the two ACO algorithms were applied tooptimize objective functions in the dynamic site layout time interval. Inthe SOOmodel,MMAS,which is oneof the extensionsof ACOalgorithms[14] conjoins the weighted sum method, is used to solve the multipleobjective CSLP problems, by which the multi-objective functions aretransformed into single objective function, and thus MOO problemwasmitigated as SOO problem. In the MOO model, the Pareto-based ACOalgorithmconjoins the Pareto optimizationmethod [9], which is used tosolve continuous combinatorial optimizationproblem, is beingmodiedto solvediscrete CSLPproblem in this study.Moreover, theunequal-areagrid recognition strategy and continuous searching scheme are

FA2 facilassig

Fig. 3. Unequal-area grid recognition strategy ems of 50 and FA2 with sizes of 100 two blocks with size of 100 randomlyout considering the constraints oftions sizes.

Step 3. Divide the block of B1 occupiedhe FA1 into smaller blocks (SB1 and SB2) area of 100 equal to area of FA1.

Step 4. Assign the facility of FA1 to theks of SB1 and SB2 randomly. The smallerks SB1 and SB2 have areas of 50 . The employed to guide the two ACO algorithms to solve unequal-area anddynamic CSLP problems.

3.2.1. SOO model using MMASIn the SOO model MMAS conjoins the weighted sum method,

which is a method that scalarizes a set of objectives into a singleobjective by pre-multiplying each objective with a user-suppliedweight, is employed to solve the dynamic, multiple objective CSLPproblems. By the weighted summethod, the two objectives ( f1 and f2)are transformed into single objective function fas follows:

f = w1f1 + w2f2 1

Where w1 and w2 are the weights of objective functions. The taskof MMAS is to nd the optimal solution for the single objectivefunction fin accordance with the principle of ants' searching food. Thesteps to realize MMAS [15,16] is introduced in Table 1.

ity FA1with an area of 50 can bened to any small blocks randomly.

ployed in the SOO model and MOO model.

F1 F2

F3

F1

F3

F1 F2

F4

(a) Phase 1 (b) Phase 2

F4 F3

(c) Final layout plan

Locationoccupied by the F2 in the Phase 1 Location fixed

Location fixed

+

=

Fig. 4. The continuous dynamic searching scheme employed in the SOO model andMOO model.

The capabilities of MMAS outperformed the other two main ACOalgorithms (ant colony system and ant system) as MMAS rstenhances the optimization searching capability by exploiting thebest solution found during iteration or during the run of the algorithm.

The modied Pareto-based ACO algorithm consists of two

Operation 20082007

Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov

FoundationUnderground woksSuperstructure

Fitting out

External works

Phase 1 Phase 2 PhStart time Finish time Start time Finish time Start time Finish time

(MM-DD-YY) (MM-DD-YY) (MM-DD-YY) (MM-DD-YY) (MM-DD-YY) (MM-DD-YY)04-15-07 08-17-07 18-08-07 02-02-08 02-03-08 11-23-08

Fig. 5. The key date in each construction phase of residential building.

463X. Ning et al. / Automation in Construction 20 (2011) 459473After each iteration, only one best single ant (iteration-best ant orglobal-best ant) adds pheromone. Second, MMAS limits the range ofpossible pheromone trails on each solution component to an interval[min,max] to avoid stagnation of the searching process [15,16].

3.2.2. MOO model using the Pareto-based ACO algorithmZhang and Huang [17] proposed the Pareto-based ACO algorithm,

in which the principle of Pareto optimization was applied into ACOalgorithm, to solve continuous combinatorial optimization problem.In order to modify the original Pareto-based ACO algorithm to solvediscrete CSLP problem in this study, two modications are needed.First, the searching space in CSLP problem is the discrete location inthe construction site. In themodied Pareto-based ACO algorithm, thearticial ants shall search from one location to another locationdirectly within the discrete searching space. Second, the parameter ofrandom disturbance factor deed in the original Pareto-based ACOalgorithm to solve continuous optimization problem is not applicablein thismodiedmodel as the searching location is limited and discretein the construction site.

Table 2Site facilities and their dimensions of residential building.Temporary and xedfacilities (facility number)

Facilitytype

Number offacilities

Dimension offacilities (m2)

Servicedphase

Sample room (F1) non-xed 1 25 3Equipment maintenanceplant (F2)

1 25 1,2,3

Electrician hut (F3) 1 25 1,2,3Tool shed (F4) 1 50 1,2,3Rebar bending yard (F5) 1 100 1,2Carpentry workshop (F6) 1 100 1,2,3#1 Material (laydown)area (F7)

1 100 1,2,3

#2 Material (laydown)area (F8)

1 100 1,2,3

#1 Tower crane (F9) xed 1 50 1,2#2 Tower crane (F10) 1 50 1,2#1 Material hoist (F11) 1 25 2,3#2 Material hoist (F12) 1 25 2,3#3 Material hoist (F13) 1 25 2,3#4 Material hoist (F14) 1 25 2,3Site ofce (F15) 1 50 1,2,3Security hut at siteentrance (F16)

1 9 1,2,3

Security hut at site exit (F17) 1 9 1,2,3searching modes: searching mode based on the local pheromonecommunication (mode 1) and searching mode based on the globaloptimum searching history (mode 2). The workow of the modiedPareto-based ACO algorithm is shown in Fig. 2.

For the mode 1 (see the owchart of Fig. 2), the choice of the ant iis related to the pheromone density of the ant j released and thedistance between the ant i and the ant j. The higher the pheromonedensity, the closer the distance and the greater the probability of ant jis selected. The probability Pj of choosing ant j is

Pj =jij

m

j=1jij

; ji; j = 1;2; ;N: 2

Where ij=1/dij, where dij is the distance between xi and xj. j ispheromone density released in terms of

j =

1; if xj is non feasible solution;2; if xj is feasible solution and xi xj;3; if xj is feasible solution and

xi ; xj is non constrianed dominated relation;4; if xj is feasible solution and xj xi:

8>>>>>>>:

3

Where xi and xj is the associated solution of the ant i, j=1,2, ,N,(i j,N is the ant number); 1,2,3,4 are the four parameters forTable 3aThe optimal results via SOO model in phase 1.

Constructionphasing

Parameterssetting

Convergence statuswithin 100 steps

Optimalresults

Best results ofxed value

1 =0.5 =2 Y 9939 9750.2=1=2 Y 9750.2=2=1 N 12952=2

1 =0.7 =2 Y 9941 9941=1=2 Y 9983=2=1 N 10971=2

1 =0.9 =2 Y 9855.8 9714.4=1=2 Y 9714.4=2=1 N 10648=2

Table 3bThe optimal results via SOO model in phase 2.

Constructionphasing

Parameterssetting


Optimalresults


2 =0.5 =2 Y 33725 33536=1=2 Y 33536=2=1 N 32499=2

2 =0.7 =2 Y 32661 32661=1=2 Y 32768=2=1 N 35137=2

2 =0.9 =2 Y 32415 32415=1=2 Y 33642=2=1 N 33746=2

464 X. Ning et al. / Automation in Construction 20 (2011) 459473the pheromone density due to relationship between xi and xj and4N3N2N1; xixj means solution xi dominates solution xj; xjximeans solution xj dominates solution xi. The amount of pheromonedensity j released is determined by comparing the qualities of thesesolutions in terms of Pareto dominance relationship between them.

For the searching mode 2, it is assumed that there are p non-dominated solutions x=(x1,x2,,xp) in the set BP, which is an externalset to keep all non-dominated solutions found during the run of thealgorithm. The distance fdij between the objective function of xi to theother ants can be calculated using the following equation:

fdij =

K

t=1ft xi ft xj

2s 4

where i=1,2,,p, j=1,2,,p, i j.And then calculate the shared function value S( fdij)

S fdij

=1fdij = share; fdijb share;0; fdij share:

5Table 3cThe optimal results via SOO model in phase 3.

Constructionphasing

Parameterssetting


Optimalresults


3 =0.5 =2 Y 25214 25206=1=2 Y 25206=2=1 N 29160=2

3 =0.7 =2 Y 25902 25596=1=2 Y 25596=2=1 N 27918=2

3 =0.9 =2 Y 25876 25872=1=2 Y 25872=2=1 N 25411=2Where share is niching radius. The niche of non-dominatedsolution is given

niche i = p

j=1S fdij

; i = 1;2; ;p; ij 6

The smallest niche(i)of the non-dominated solution ideterminesthe searching direction of the ants.

3.2.3. Unequal-area grid recognition strategy used in the SOO model andMOO model

In solving unequal-area CSLP problem, the dimensions or the sizes ofthe facilities and the locations should be considered during theassignment of facilities in the construction site. Using unequal-areagrid recognition strategy, an unequal-area CSLP problem can be reducedinto an equal-area CSLP problem by assigning the biggest facility arearst in the construction site and thus the searching scope is then reducedstep by step. Using the sequence of the descending ranking orderof facilities' dimensions, the locations for all facilities shall be found.

A brief description of the unequal-area grid recognition strategyemployed in the SOO model and MOO model is given in Fig. 3.Suppose there is a construction site with area of 200 m2, which isdivided by grid units of each 25 m2 area, the two facilities of FA1 witharea of 50 m2 and FA2 with area of 100 m2 thus occupied two gridsand four grids respectively (see step 2 of Fig. 3). Now, the two facilitieswill be assigned to construction site step by step (see step 3 and step 4of Fig. 3) accordingly.

3.2.4. The continuous dynamic searching scheme employed in the SOOmodel and MOO model

In order to guide the SOOmodel andMOOmodel to solve dynamicCSLP problem, the continuous dynamic searching scheme wasadopted (see the Fig. 4 for details).

Suppose there were four facilities needed to be assigned on aconstruction site (see Fig. 4), the facilities of F1, F2 and F3 wereinvolved in the construction operation in Phase 1 and the facilities ofF1, F3 and F4 were needed in the construction phase 2. The locationsfor F1, F2 and F3were assigned to corresponding locations via the SOOmodel andMOOmodel in phase 1. The locations for facilities of F1 andF3 were xed in the phase 2, the task for the SOO model and MOOmodel was to nd the location for facility of F4 and the location forfacility F2 was removed from the assignment process in this phase.With the locations xing for facilities of F1 and F3 during the phase 2,no double handling cost occurred. Finally, the two layout plans inphase 1 and phase 2 were merged into one layout plan [1]. Just likeTommelein [18] said that there was a single-site layout drawing usedthroughout the project to include such information regarding facilitieson the site at successive time intervals during project construction.

3.3. Evaluation and selection stage

At this stage theMADMmodel using intuitionistic fuzzy Techniquefor Order Preference by Similarity to Ideal Solution (TOPSIS) methodwas employed to evaluate and select the most satisfying, or the best,construction site layout in accordance with the pre-determinedattributes, which can be determined by the survey conducted amongthe management team of a specic contractor. Modied from Li [19]and Tan and Zhang [20], the intuitionistic fuzzy TOPSIS methodadopted in this research is explained below.

3.3.1. Intuitionistic fuzzy TOPSISIntuitionistic fuzzy sets (IFS), which are the extension of traditional

fuzzy sets [21], constitute a generalization of the concept of fuzzy sets.In traditional fuzzy set [22], a membership function is assigned to eachelement of the universe of discourse a number, which is from an unit

interval, to indicate the degree of belongingness to the set under

Table 4The construction site layout alternatives generated by the SOO model.

Construction sitelayout alternatives

Adoptedparameters setting

Value of f in different phases Total valueof f

Total valueof fin original layout

Reduction rate (%)

Phase 1 Phase 2 Phase 3 f f1 f2

Alternative 1 (L1) =0.9 9714.4 32418 26279 68411.4 86851 21.2 17.9 25.0=2=2

Alternative 2 (L2) =0.9 9815.6 32415 25301 67531.6 86851 22.2 18.1 27.0=2=1

Alternative 3 (L3) =0.5 9720.3 32362 25206 67288.3 86851 22.5 18.4 27.2=2=2

kelihciate

465X. Ning et al. / Automation in Construction 20 (2011) 459473consideration. However, in real-life problems, sometimes people arehard to dene imprecise and uncertain situations by membershipfunctions. It is because, in some cases, people can clearly describe theirnegative feelings rather than the positive feelings. Moreover, one caneasily gure out which alternatives one likes or does not like or onedoes not knowhowmuch one really likes it or not. Since IFS give both adegree ofmembership and a degree of non-membership, therefore, IFSare helpful to model many real-life problems.

Based on the principle of choosing the best alternative which has theshortest distance from the positive ideal solution (PIS) and the longestdistance from the negative-ideal solution (NIS), TOPSIS was proposed byHwangandYoon [23] to solveMADMproblems. Inspiredby theworkof Li[19], who use linear program to calculate optimal weights between theattributes instead of personnel preference to avoid evident preference onsome alternatives and the research works of IFS and TOPSIS done by Tanand Zhang [20], the proposed intuitionistic fuzzy TOPSISmethod adoptedin this research can be realized by the following successive steps:

Step 1 Calculate intuitionistic fuzzy set decision-making matrix D.

a1 a2 am

D =

x1x2xn

r11 r12 r1mr21 r22 r2m rn1 rn2 rnm

2664

3775

a1 a2 am

=

x1x2xn

11;11 12;12 1m;1m 21;21 22;22 2m;2m

n1;n1 n2;n2 nm;nm

2664

3775

7

W = w1 w2 wm 8

Note: scalarized single objective function f is the weighted representative score for liconstruction site. f1 is the representative score for likelihood of accidents happened assofacilities associated with the construction site layout.Where analternative setX=[x1,x2,,xn] consists ofn alternativecandidates in which the most preferred alternative need to beselected, a attribute set Acan be expressed as A=[a1,a2,,am],which is based on mattributes, each alternative candidate's

Table 5The Pareto optimal results via MOO model.

Construction sitelayout alternatives

Value of MOF in different phases

Phase 1 Phase 2 Phase 3

f1 f2 f1 f2 f1

Alternative 4 (L4) 10976 13118 42496 29640 32991Alternative 5 (L5) 10965 12490 42298 28959 32636Alternative 6 (L6) 10831 11969 41890 27538 34321

Note: MOF stands for multiple objective functions, f1 (multiple objective function 1) is the rep(multiple objective function 2) is the representative score for the total handling cost betweperformance is evaluated; rij; i = 1;2;;n; j = 1;2;;m isthe rating of alternative candidate xiwith respect to the attributeaj; ij, (0ij1) and ij (0ij1) are the degree ofmembership and the degree of non-membership of the alterna-tive candidate xiwith respect to the attribute ajunder the conceptof intuitionistic fuzzy set respectively, where 0ij+ij1.wj j = 1;2;;m is the weight of the attribute aj. Dand W are the intuitionistic fuzzy decision matrix and weightvector respectively.

Step 2 Calculate the attribute weight.The evaluation of alternatives in term of attribute is an IFS, whichcan be denoted as X={bxi, ij,ij,ijN}, where intuitionistic indexij=1 ijij is the uncertainty membership of alternativecandidate xi with respect to the attribute aj, which will biasdecisionmaker's choice. The best result of ijwill increase to ij+ij if the decision maker considers the situation in an optimisticway. So the decisionmaker's positive evaluationwill fall into theinterval [ ij, ij+ij]. Similarly, the decision maker's negativeevaluation will fall into the interval [ij,ij+ij].As for the attribute weight, let j, j and j to be the degree ofmembership, the degree of non-membership and intuitionisticindex of the fuzzy concept of importance of the attribute ajrespectively, where j=1jj. The weight wj(0 wj 1;

m

j=1wj = 1) lies in the closed interval [j,j+j] if the

decision maker takes into consideration of j.

In order to get PIS, the alternative should fulll the followingequations:

max

(m

j=1ij + ij

wj

)

9

ood of accidents that happened and total handling cost between the facilities in thed with the site layout. f2 is the representative score for total handling cost between thes:t fj wjj + j; j = 1;2;;mmj=1

wj = 1

Total value of MOF Total value of MOFin original layout

Reduction rate(%)

f2 f1 f2 f1 f2 f1 f2

22558 86463 65316 96585 77867 10.5 16.122626 85899 64075 96585 77867 11.1 17.723967 87042 63474 96585 77867 9.9 18.5

resentative score for likelihood of accidents happened associated with the site layout, f2en the facilities associated with the construction site layout.

466 X. Ning et al. / Automation in Construction 20 (2011) 459473Building 1

#1 towercrane

Security hut

#1 material hoist

F7

Siteexitmin

(m

j=1ij wj

)

s:t fj wjj + j; j = 1;2;;mmj=1

wj = 1

10

Where ij=1 ijij, is the degree of hesitation of thealternative candidate xi with respect to the attribute aj underthe concept of IFS.Integrate Eqs. (9) with (10), we have the following equation

max

(m

j=1 ij + ijij

wj

)

s:t fj wjj + j; j = 1;2;;mmj=1

wj = 1

11

Building 4

Building 3

Site office

#3 material hoist

#4 material hoist

F8

F1

Fig. 6. The original consBuilding 2

F1: Sample roomF2: Equipment maintenance plantF3: Electrician hutF4: Tool shedF5: Rebar bending yardF6: Carpentry workshopF7: #1 material laydown areaF8: #2 material laydown areaBased on the Eq. (11), the attribute weight problem canbe solved by transforming into a linear programming.

Step 3 Calculate weighted IFS decision-making matrix D (see Eqs. (7)and (8))

rij = rij wj; i = 1;2;;n; j = 1;2;;m: 12

Step 4 Identify the positive-ideal intuitionistic fuzzy solutions (A+)and negative-ideal intuitionistic fuzzy solutions (A)

A =

(maxj

ij;

; minj

ij

; j = 1;2;;m j i = 1;2;;n

)

13

A =

(minj

ij;

; maxj

ij

; j = 1;2;;m j i = 1;2;;n

)

14

#2 towercrane

Security hut

#2 material hoist

F4

F5

F6

F2

F3

Site entrance

truction site layout.

F7

F8

467X. Ning et al. / Automation in Construction 20 (2011) 459473Building 1

#1 towercrane F1 F3 F2

Security hut

#1 material hoist

SiteexitStep 5 Calculate the distance of each alternative to positive-ideal andnegative-ideal intuitionistic fuzzy solutions.In this research, thedistances betweenalternative candidates andpositive-ideal andnegative-ideal intuitionistic fuzzy solutions aremeasured by Euclidean distance. The distances from positive-ideal andnegative-ideal intuitionistic fuzzy solutions are denotedas E+ and E respectively.

Step 6 Calculate the closeness coefcient of each alternative.The closeness coefcient Ciof each alternative can be calculated by

Ci = Ei

Ei + E

i

; i = 1;2;;n: 15

Step 7 Rank the preference order of alternatives.A set of alternatives shall be ranked in accordance to thedescending order of Ci. The best alternative is the one with thehighest relative Ci.

Building 4

Building 3

Site office

F6

F5

F4

#3 material hoist

#4 material hoist

S

Fig. 7. Construction site lBuilding 2

F1: Sample roomF2: Equipment maintenance plantF3: Electrician hutF4: Tool shedF5: Rebar bending yardF6: Carpentry workshopF7: #1 material laydown areaF8: #2 material laydown area3.4. Output stage

The output stage is the nal step of the proposed CSLP decision-making system. The best construction site layout selected should fulllboth quantitative requirements of multiple objective functions andqualitative requirement of attributes such as security, noise control.

4. Application of the proposed CSLP decision-making system

The proposed CSLP decision-making systemwas tested and veriedby the case study of residential building. The project is located in the cityof Beijing, China. There are four residential buildings (Building 1 andBuilding 4 are sixty stories high; Building 2 and Building 3 are eightystories high), site ofces and construction operational facilities locatedwithin the construction site. Other temporary living facilities are locatedoutside the construction site. The task of the proposed model is to ndthe corresponding locations for the temporary construction operationalfacilities in the construction site.

#2 towercrane

Security hut

#2 material hoist

ite entrance

ayout alternative-L1.

F5

F7


#1 tower

Security hut

#1 material hoist

Siteexit4.1. Input stage

The construction project started in 15 April 2007 and is scheduledto nish by 28 November 2008. The whole construction process isdivided into three construction phases for this case study. The starttime and nish time of each construction phase are shown in Fig. 5.

In Fig. 5, the site layout plan used in the original contractor's plandocument consisted of ve construction phases, namely, foundationconstruction phase, underground section construction phase, super-structure construction phase, nishing works phase and externalworks phase. In the case study, the three construction phases are usedas the dynamic schedule intervals to lay out the site in terms of thetime duration and the amount of the facilities serviced in each originalconstruction phase. The main works done in each construction phaseare foundation and underground works (Phase 1), superstructure(Phase 2), nishing works and external works (Phase 3). In theoriginal plan, the foundation phase lasted for almost 2 months andthere were few facilities serviced in this phase, so there was no need

Building 4

Building 3

Site office

crane

F3 F2 F1

F6

F8

F4

#3 material hoist

#4 material hoist

S


F1: Sample roomF2: Equipment maintenance plantF3: Electrician hutF4: Tool shedF5: Rebar bending yardF6: Carpentry workshopF7: #1 material laydown areaF8: #2 material laydown areato treat it as a separate phase. In this case study, the foundation phaseand the underground section construction phase are merged into onedynamic schedule interval and termed as Construction Phase 1.Superstructureworkswere nishedwhen thework on thewaterproofroof was completed; the period of the superstructure work was usedas the dynamic schedule interval and termed Construction Phase 2.The nishing work (masonry, installation of door and window,interior decoration, outer-eave decoration, etc.) began when thewaterproof roof was completed; therefore, the nishing works andthe external works were merged into Construction Phase 3.

The temporary facilities (xed and non-xed facilities) and theircorresponding dimensions, serviced phase are shown in Table 2.

In Table 2, tower cranes, material hoists, site ofce and securityhuts are xed. It is because tower cranes are always xed during thebuilding construction for the high installation fees. Thematerial hoistsare used for the transportation of materials to the superstructure andtheir location are dependent on the structural elements to which theyare tied, thus planners always freeze these facilities in certain

#2 towercrane

Security hut

#2 material hoist

ite entrance


F5

F8


1# towercrane F4

1# material hoist

Siteexit

Security hutlocations rst. The location of the main gate is usually pre-determinedwith reference to the external transportation system. Moreover,security huts are commonly assigned to the site entrance and site exitfor ease of supervision and to avoid theft. The site ofce is usually nearthe main gate, also for the sake of safety.

4.2. Design stage

In the proposed CSLP decision-making system, there are twomodels (the SOO model and the MOO model) employed to solve theMOO problem in the design stage. The CSLP problem of this case studywas predominantly a MOO problem, in which the multiple objectivefunctions dened are intended tominimize the likelihood of accidentsoccurring and to minimize the total handling cost between thefacilities. In the SOOmodel, MMAS is used to solve the MOO problemsby the weighted summethod. TheMOOmodel is based on the Pareto-based ACO algorithm to solve the MOO problems by Paretooptimization method. The applications of both models are discussedas follows.

Building 4

Building 3

Site office

F2 F3 F1

F6

F7

3#material hoist

4#material hoist

Si


F1: Sample roomF2: Equipment maintenance plantF3: Electrician hutF4: Tool shedF5: Rebar bending yardF6: Carpentry workshopF7: #1 material laydown areaF8: #2 material laydown area4.2.1. Optimization process by the SOO modelThe three key parameters in the SOOmodel are the persistence of the

pheromone trails (), the relative inuences of the pheromone strengths() and the relative inuences of the heuristic information (). In order toinvestigate the impact to the results caused by the parameter settings, theSOO model was tested under the three sets of parameters in this casestudy (see Table 3). According to the continuous dynamic searchingscheme, when the SOOmodel was applied to nd locations for the sevenfacilities (F2~F8) in the construction phase 1, the locations for the sevenfacilities were found. The optimal results via SOO model in phase 1 weredocumented inTable3a. In this Table, the layoutwith the smallest valueoff(see Eq. (1)) in which seven facilities were assigned to correspondinglocations is selected for further optimization. It is because there were atotal of eight temporary facilities (F1~F8) involved in the wholeconstruction process. In order to search the location for the sampleroom (F1) which is only existed in Phase 3, optimization process wasconducted inPhase3. Thus, the layout alternative tomerge the layoutplanin construction phase 1 and phase 3, named as Alternative 1 (L1), wasgenerated. If the continuous dynamic searching schemewas started from

2# towercrane

2#material hoist

te entrance

Security hut



#1 tower

Security hut

#1 material hoist

Siteexitthe construction phase 2, in which there are seven facilities (F2~F8)involved, the locations for the seven facilities were determined. Theoptimal results via SOOmodel in phase 2weredocumented in Table 3b. Inorder to the location for the sample room(F1)whichonly existed in Phase3, optimization processwas conducted in Phase 3. In thisway, Alternative2 (L2) was generated. So as the continuous dynamic searching schemestarted from construction phase 3. Firstly the locations for the seventemporary facilities (F1 to F4, F6 to F8)were assigned (please see Table 3cfor the optimal results via SOOmodel in phase 2) and then the location forfacility rebar bending yard (F5) was identied by optimizing process onPhase 2 and Phase 1, separately. Finally, the third layout alternative-Alternative 3 (L3) was determined. The optimal results (construction sitelayout alternatives) and their respective representative scores for f(seeEq. (1)) are shown in Table 4.

4.2.2. Optimization process by the MOO modelThe key parameters in the MOO model are N, which is the ant

colony population (solution population N) and the four parameters

Building 4

Building 3

Site office

crane

F14

#

#1 material hoist

F2

F4

F5

F8

F6

F7

F1

Fig. 10. Construction siteBuilding 2

F3

F1: Sample roomF2: Equipment maintenance plantF3: Electrician hutF4: Tool shedF5: Rebar bending yardF6: Carpentry workshopF7: #1 material laydown areaF8: #2 material laydown area1, 2, 3 and 4 for the different levels of pheromone density. TheMOO model was tested under the four sets of parameters. When Nwas set to 100, the optimization processes by the MOO model wereconducted under 1=0.01, 2=0.1, 3=2, 4=5 and 1=0.01,2=0.2, 3=8, 4=32, respectively. When N was set to 200, theoptimization processes of MOO model were conducted under1=0.01, 2=0.1, 3=2, 4=5 and 1=0.01, 2=0.2, 3=8,4=32, respectively. After setting the parameters, the optimalconstruction site layouts were processed by the MOO model via thesame searching process in SOO model. Therefore, the alternative 4(L4), alternative 5 (L5), alternative 6 (L6) were generated by thecontinuous dynamic searching scheme started on the constructionphase 1, construction phase 2 and construction phase 3 respectively.The optimal construction site layout alternatives generated by theMOO model, with their corresponding representative scores for fareshown in Table 5.

For the comparison and evaluation, the original site layout and sixlayout alternatives are illustrated in Fig. 6 to Fig. 12.

#2 towercrane

Security hut

#2 material hoist

3 material hoist

Site entrance

layout alternative-L4.

F6


#1 tower

#1 material hoist

Security hutSite e

xit4.3. Evaluation and selection stage

In the evaluation and selection stage, the six construction site layoutalternatives were evaluated and selected using the intuitionistic fuzzyTOPSISmethod in terms of the ten attributes, whichwere identied from23 common attributes from literature used to evaluate the constructionsite layout alternatives. In order to identify the essential attributes fromthe 23 common attributes, the 5-point scale questionnaire (not importantis set to 1 and extremely important is set to 5)was designed to survey thekey personnel of this project. The aim was to survey to what extent theyconsidered these attributes important in the evaluation of the construc-tion site layouts. For the ten attributes, please see the Table 6.

At this stage of the proposed CSLP decision-making system, theintuitionistic fuzzy TOPSIS method was used to evaluate and select thebest construction site layout plan from the six construction site layoutalternatives (L1 to L6generated by theprevious stage). The intuitionisticfuzzy set was rst determined by the survey to describe the extent ofhow these six alternatives could fulll the requirements of a good site

Building 4

Building 3

Site office

crane

F14

#3 material hoist

#4 material hoist

F4

F8

F7

F1

S

Fig. 11. Construction siteBuilding 2

F1: Sample roomF2: Equipment maintenance plantF3: Electrician hutF4: Tool shedF5: Rebar bending yardF6: Carpentry workshopF7: #1 material laydown areaF8: #2 material laydown arealayout in terms of the ten essential attributes surveyed and dened.Then, the positive-ideal (best solution) and the negative-ideal (worstsolution) intuitionistic fuzzy solutions could be found from theintuitionistic fuzzy sets. The positive-ideal and the negative-idealintuitionistic fuzzy solutions under the ten essential attributes arerecorded in Table 7.

Having the positive-ideal and the negative-ideal intuitionisticfuzzy solutions determined, the task for the following intuitionisticfuzzy TOPSIS method is used to nd the best of the best solutions,which has both the nearest Euclidean distance from the positive-idealsolution (the best solution) and the longest Euclidean distance fromthe negative-ideal solution (the worst solution). The ratio betweenthe longest distance from the negative-ideal solution and the nearestdistance to the positive-ideal solution is the closeness coefcient ofeach alternative. So, the best construction site layout alternative is theone which has the highest closeness coefcient. The alternatives ofthis case study then could be ranked in terms of their closenesscoefcients as shown in Table 8.

#2 towercrane

#2 material hoist

F5

F2

F3

Security hut

ite entrance


Building 1

F4

Security hutSite

exit

472 X. Ning et al. / Automation in Construction 20 (2011) 459473#1 towercrane

#1 material hoist

F5

F24.4. Output stage

The result of the preference ranking order of the six alternativesgenerated by the SOO model and the MOO model is in descending

Building 4

Building 3

Site office

F14

#3 material hoist

#4 material hoist

F1

F3

F8

F7

F6

S

Fig. 12. Construction site

Table 6Ten key attributes to evaluate construction site layout alternatives in residentialbuilding.

Attribute no. Ten attributes

1 Efcient movement of materials2 Tie-in with external transportation3 Good space utilization and conguration4 Ease of expansion5 Safety6 Effective movement of personnel7 Efcient operations8 Frequency and seriousness of potential breakdowns9 Security10 Easy supervision and controlBuilding 2

F1: Sample roomF2: Equipment maintenance plantF3: Electrician hutF4: Tool shedF5: Rebar bending yardF6: Carpentry workshopF7: #1 material laydown areaF8: #2 material laydown areaorder of L2NL3NL1NL6NL5NL4. Therefore, Alternative L2, which hasthe highest closeness coefcient (0.966) among the six alternatives,was selected as the output of the proposed CSLP decision-makingsystem. Alternative L2 is the best site layout which has the shortestdistance from the positive ideal site layout and the longest distancefrom the negative ideal site layout in terms of the ten essentialattributes among all the alternatives. In addition, the construction sitelayout of L3 (Ci=0.908) could also be used as another option by theproject manager. The closeness coefcients for L2 and L3 are veryclose, and there is not a big difference between them. In L2, the #1 and#2 material lay-down areas are located around Building 3 andBuilding 4, and Building 1 and Building 2, respectively. Thus, the #1material lay-down area could service Building 3 and Building 4 andthe #2 material lay-down area could service Building 1 and Building 2effectively. The centralized locations for all the facilities in the middlearea between the four buildings should boost the constructionoperation efciency. The compact arrangement of the facilities shouldfacilitate the construction site expansion on the left-hand side area ofthe construction site.

#2 towercrane

#2 material hoist

Security hut

ite entrance


Table 7Positive-ideal and negative-ideal intuitionistic fuzzy solutions.

Ideal intuitionistic Project-specic attributes

(5)a (6)a (7)a (8)a (9)a (10)a

(0(0

473X. Ning et al. / Automation in Construction 20 (2011) 4594735. Conclusion

The CSLP decision-making system is proposed to solve dynamicand unequal-area, multi-objective optimization CSLP problems in thisstudy. The performance of CSLP decision-making system was testedand veried by the case study of a residential building. Therepresentative score of likelihood of accident happened and totalhandling cost could be reduced from 9.9% to 18.4% and from 16.1% to27.2% respectively if the proposed CSLP decision-making systemrecommendations were adopted. The gures showed that an optimalconstruction site layout planning has a great, positive impact onconstruction cost. Furthermore, the best construction site layout inthe output stage could satisfy both the quantitative aspect of costreduction and the qualitative aspect of the other attributes, whichhave been neglected in previous studies.

The grids-recognition strategies used to solve the unequal-areaCSLP problem by the SOO model and the MOO model could also beemployed using other advanced algorithms and their applications can

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

A+ (1,0) (1,0) (0.9,0) (0.9,0)A (0.7,0.1) (0.9,0) (0.7,0.2) (0.6,0.2)

a Attribute no.

Table 8Rank the alternatives in terms of closeness coefcient.

Alternative Distance frompositive-idealintuitionistic fuzzysolution E+

Distance fromnegative-idealintuitionistic fuzzysolution E

Closenesscoefcient ofeach alternative Ci

Ranking

L1 0.093 0.249 0.727 3L2 0.011 0.310 0.966 1L3 0.030 0.295 0.908 2L4 0.270 0.053 0.165 6L5 0.122 0.205 0.628 5L6 0.109 0.226 0.675 4also be extended e.g. from static to dynamic CSLP problems. At thesame time, the strategy would offer an innovative way to solve theunequal-area CSLP problem without increasing the computationalcomplexities.

With the adoption of continuous dynamic search scheme in thisdecision-making system, the re-handling cost could be avoided, thesafety level could be improved and the work productivity could beincreased. This continuous dynamic searching scheme could beapplied to solve static to dynamic CSLP problems using otheradvanced algorithms.

Moreover, the MOO problems in the CSLP were solved by the SOOmodel and MOO model using the weighted sum method and thePareto-based optimization method respectively. With the applica-tions of the two methods to solve the MOO problems, more qualitysolutions (L1, L2, L3, L4, L5 and L6) were generated for the evaluationand selection stage using the intuitionistic fuzzy TOPSIS method.

The proposed CSLP decision-making system can be used as a toolto help project managers and planners to design their constructionsites under conicting multiple objectives or congruent objectives,

[17] Y.D. Zhang, S.B. Huang, One ant colony algorithm for solving multi-objective

optimization problems, Control and Decision 20 (2) (2005) 170176.

[18] I. D. Tommelein, SightPlan: An expert system that models and augments humandecision making for designing construction site layout, Ph.D. thesis, Departmentof Civil Engineering, Stanford University, 1989.

[19] D.F. Li, Multi-attribute decision making models and methods using intuitionisticfuzzy sets, Journal of Computer and System Sciences 70 (1) (2005) 7385.

[20] C.Q. Tan, Q. Zhang, Intuitionistic fuzzy set method for fuzzy multiple attributedecision making, Fuzzy Systems and Mathematics 20 (5) (2006) 7176.

[21] K.T. Atanassov, Intuitionistic fuzzy sets, theory and applications, Physica-Verlag,which involve more than one objective functions consisted ofquantitative factors, such as handling cost of material. Moreover, theproposed decision-making system will help project managers andplanners to design a good construction site layout with considerationof other qualitative factors, such as ease of supervision and controlwhich are neglected in the previous studies.

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.9,0) (0.9,0) (0.9,0) (0.9,0) (1,0) (1,0)

.8,0.1) (0.3,0.6) (0.5,0.4) (0.6,0.2) (0.4,0.4) (0.3,0.6)solutions a a a aNew York, 1999.[22] L.A. Zadeh, The concept of a linguistic variable and its application to approximate

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state-of-art survey, Springer-Verlag, New York, 1981.

A decision-making system for construction site layout planningIntroductionConstruction site layout planningThe structure of CSLP decision-making systemInput stageDesign stageSOO model using MMASMOO model using the Pareto-based ACO algorithmUnequal-area grid recognition strategy used in the SOO model and MOO modelThe continuous dynamic searching scheme employed in the SOO model and MOO model

Evaluation and selection stageIntuitionistic fuzzy TOPSIS

Output stage

Application of the proposed CSLP decision-making systemInput stageDesign stageOptimization process by the SOO modelOptimization process by the MOO model

Evaluation and selection stageOutput stage

ConclusionReferences

a decision-making system for construction site layout planning

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