Advanced Engineering Informatics 26 (2012) 737–748

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Advanced Engineering Informatics

journal homepage: www.elsevier .com/ locate/ae i

A genetic algorithm-based method for look-ahead scheduling in the finishingphase of construction projects

Ning Dong a,⇑, Dongdong Ge b, Martin Fischer a, Zuhair Haddad c

a Center for Integrated Facility Engineering (CIFE), Stanford University, 473 Via Ortega, Stanford, California, 94305, United Statesb Antai College of Economics and Management, Shanghai Jiao Tong University, 535 Fahua Zhen Road, Shanghai, 200052, Chinac Corporate Affairs and CIO, Consolidated Contractor’s International Company (CCC), 62B Kifissias Ave, Amaroussion, Athens, 15110, Greece

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

Article history:Received 30 September 2011Accepted 19 March 2012Available online 25 April 2012

Keywords:Look-ahead schedule (LAS)Genetic algorithm (GA)SimulationRCPSPRCMPSP

1474-0346/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.aei.2012.03.004

⇑ Corresponding author. Address: Center for Int(CIFE), Stanford University, 473 Via Ortega, Room 29United States. Tel.: +1 650 391 5599; fax: +1 650 723

E-mail addresses: ningdong@stanford.edu (N. Donfischer@stanford.edu (M. Fischer), zuhair@ccc.gr (Z. H

Genetic algorithms (GAs) are widely used in finding solutions for resource constrained multi-projectscheduling problems (RCMPSP) in construction projects. In the finishing phase of a complex constructionproject, each room forms a confined space for crews to conduct a series of activities and can thus be con-sidered as an individual sub-project. Generating the look-ahead schedule (LAS) which takes into accountthe limited resources available at the job site falls in the domain of RCMPSP. Therefore GAs can be used toaddress this scheduling problem and help construction managers to guide the daily work on site. How-ever, current GAs do not consider three key practical aspects that the project planers and constructionmanagers deal with frequently at the job sites: the engineering priorities of each individual sub-project,the zone constraint and the blocking constraint. By addressing these aspects, this paper proposes a GA-based method that takes them into account in the search process for optimum project duration and/orcost. Two examples are used for the discussion of the effectiveness of this method and to showcase itscapability in project scheduling when the scale of a project increases.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

LAS is a useful tool for general contractors in planning theirwork at the level of detail such that they can actually considerthe availability of crews and other resources on a daily basis [1].At this level, in the finishing phase of a construction project, theproject planner needs to make it clear to all members of the projectwhich crew (who) is working on what operation in which room(where) on which day (when), ensuring that everyone is on thesame page. At a university project, to generate such an LAS, the siteengineers needed to consider, on a daily basis, data sets includingmore than 15 types of rooms, more than 20 operations per room onaverage, their progress, more than 50 types of materials and theirquantities in each room, more than 10 types of crews and theirproductivities, and the engineering constraints on the job site [1].Generating a reliable LAS manually for a project this complex be-came such a challenge that the site engineers and project plannerseventually gave up. Therefore, they need an automated way for theLAS generation. In this paper, the term ‘‘operation’’ is used to rep-

ll rights reserved.

egrated Facility Engineering2, Stanford, CA 94305-4020,4806.

g), ddge@sjtu.edu.cn (D. Ge),addad).

resent a higher level of detail than ‘‘activity’’. Most operations canbe carried out in a given room (e.g., office rooms, conferencerooms, corridors, lobbies, toilets, etc.), which is basically a func-tional space. Therefore, space is a key factor we need to considerwhen generating LASs. Prior research relevant to space resourcemanagement can be categorized, as pointed out by Guo [2], intospace-scheduling, site layout planning, and path planning. This re-search focuses on space-scheduling. In this area, prior researchershave mostly concentrated on identifying and resolving space con-flicts by defining work spaces and then applying them to existingschedules [2–7]. On the other hand, Thabet and Beliveau [8] pro-pose a space-constraint and resource-constraint method to incor-porate the availability of space into scheduling. Such a methoddefines workspaces at the floor level, not the individual room level.In the finishing phase of complex projects, room is the basic pro-duction unit with specific work content. It provides a natural andconvenient representation for spatial reasoning [9], and accountsfor the spaces where the crews and equipment must be allocatedregardless of their shapes, unlike the work spaces defined andmeasured by length, width, and height [5,8]. Therefore, in this pa-per we consider room as the basic unit of work space and take intoaccount its availability in scheduling.

LAS generation considering limited resources can be catego-rized as a type of resource-constrained project scheduling problem(RCPSP) and can be addressed by genetic algorithms. For instance,

Fig. 1. The activity-on-node fragnets of the four sub-projects constituting a sampleconstruction project.

738 N. Dong et al. / Advanced Engineering Informatics 26 (2012) 737–748

Feng et al. [10] use a genetic algorithm to find the best LAS for thestructural phase of a construction project; Organización [11] com-bines simulation with genetic algorithm to generate LAS for berthallocation for containerships. However, as mentioned by Payne[12], up to 90% of all projects occur in a multi-project context. Un-der this context, a project is composed of multiple sub-projects andeach sub-project consists of an operation network (with embeddedoperation precedent constraints) that draws from shared pools ofmultiple types of resources which are normally not large enoughfor all the sub-projects, and thereby operations, to work concur-rently. LAS generation for the finishing phase of complex construc-tion projects conforms to this context. In the finishing phase, eachroom is relatively independent so that most operations in oneroom do not interfere with those in another. In addition, each typeof room entails a specific work sequence for crews to work on. If allrooms are entirely independent, each room can be considered as asub-project, thus making the LAS generation problem become a re-source-constrained multi-project scheduling problem (RCMPSP).

Such a problem has been first studied in the literature via thesingle-project approach, which adds dummy activities, i.e., ‘‘start’’and ‘‘end’’, and arcs to merge the sub-projects into a single mega-project. It reduces the RCMPSP to a RCPSP with a single criticalpath. Activity priority rule heuristics are the commonly used meth-ods in this approach [13–18]. As the complexity of a RCMPSP in-creases, researchers look into the multi-project approach, inwhich sub-projects are independent except that they draw froma common pool of resources of different types. Kurtulus and Davis[19] point out that certain priority rules deliver better results whenusing such a approach for scheduling. The use of a multi-projectapproach is further justified by Browning and Yassine [20]. Theydeem that this approach is more realistic and that it presents agreater opportunity for improvement. More importantly, theypoint out that compared to the single-project approach, it hasgreater potential to provide alternative decision guidance for dif-ferent management roles, e.g., individual project manager, generalproject manager, and portfolio manager.

Unfortunately, these approaches cannot be used directly to ad-dress the real-world LAS generation problem for the finishingphase of complex construction projects. One precondition ofRCMPSP is that resources cannot be shared by multiple operationsat the same time. But on a construction project, certain operationsin multiple rooms need to be synchronized with the same re-source(s) assigned to all such operations at the same time. This isreferred to as zone constraint; the rooms involved are grouped asa zone [1]. An example of a zone is a group of adjacent rooms shar-ing the HVAC system. The ‘‘HVAC duct installation’’ operation re-quires that a zone is formed so that all these rooms are reservedfor the HVAC crews/subcontractors to work in before being handedover to other disciplines. While the zone constraint renders roomsless independent, another constraint – blocking constraint [1] –adds further complexity to the spatial interactions. A typical block-ing operation is ‘‘Terrazzo flooring’’ in the corridor. When such anoperation starts in a corridor, the access to all its adjacent rooms issuspended and no other crews are allowed to step on the floor untilthe operation is finished. If interruption of an operation is not al-lowed, the blocking operation has to be squeezed into a schedulewhen no other operations are in progress in the adjacent rooms.In sum, a zone constraint requires that certain rooms/sub-projectsbe synchronized at a certain point, its corresponding zone opera-tions sharing the same resource(s); while the blocking constraint re-quires that no operation in certain rooms/sub-projects be starteduntil the blocking operation in a given room/sub-project is fin-ished. Both constraints break the paradigm of looking at a groupof rooms/sub-projects independently. The authors are not awareof prior research that has considered such practical constraintswhen using genetic algorithm to address RCMPSP.

Engineering priority is another factor existing literature has notyet taken into consideration when generating LAS. An LAS is nor-mally derived from the project master schedule which requirescertain project subareas to be completed first. Therefore, from timeto time, engineering priorities are given to certain rooms/sub-pro-jects, not individual operations. Without considering this factor,merely generating the best LAS using priority rule based geneticalgorithms becomes less attractive to practitioners.

In this paper, a genetic algorithm based method is described toautomate the LAS generation in the finishing phase of complexprojects with the objective of minimizing project duration or pro-ject cost. Such a method takes into account the engineering con-straints, i.e., blocking constraint and zone constraint, andengineering priorities in the schedule generation process so thatall the schedules created satisfy practical needs. In the sectionsthat follow, we consider the concepts of a room and a sub-projectas interchangeable. An operation is related to only one sub-projectin terms of materials to be installed/applied, although its execution(such as the execution of a blocking operation) might affect workin other sub-projects.

2. Problem description and mathematical formulation

2.1. Problem description

A complex construction project consists of N types of rooms,each of which requires a number of operations with unique worksequence for the finishing work. A fragnet [1] is used to modelthe finishing work of a type of room using activity-on-node net-work notation, where a set of M nodes represents M operationswith arcs between the nodes to represent their precedence rela-tions. In the research project this paper describes, only the ‘‘fin-ish-to-start’’ relation is used when developing the fragnets. The

N. Dong et al. / Advanced Engineering Informatics 26 (2012) 737–748 739

remainder of this paper refers to a room as a sub-project. Fig. 1shows an example which is a miniature of a construction projectin the finishing phase. The example consists of four sub-projects,each of which belongs to a particular type with a dummy startand a dummy finish operation. The duration of each operation isplaced on top of each operation and the resource required is placedbelow. The constraint-related operations are also shown in Fig. 1.Sub-project 4 contains a blocking operation and when it is started,all other sub-projects are blocked. Sub-projects 1, 2, and 3 eachcontain one zone operation (depicted as a gray node in Fig. 1)which requires two H crews. These operations must start at thesame time sharing the same crews and lasts for 3 days.

2.1.1. Precedence constraintsUnlike the multi-project genetic algorithm proposed by Kim

et al. [21], sub-projects in this paper do not have precedence con-straints. In other words, all sub-projects can start at the same timeas long as they are all ready (i.e., the structural related operationsare all completed in a sub-project) at the same time with enoughresources to get started. As to the precedence constraints of oper-ations, the start time of each operation is dependent upon the com-pletion of some other operations.

2.1.2. Resource considerationTo carry out an operation, multiple types of resources (e.g.,

crews, and equipment) should be employed together. However,only the most significant resource, i.e., crew, is associated withan operation assuming other types of resources are readily avail-able. Different types of crews are available in limited quantitiesbut renewable (i.e., can be reassigned) from period to period.

2.1.3. Crew productivity rateBy the time the site engineers start to create the LAS for the fin-

ishing phase of a construction project, the construction method foreach operation and the productivity rate of the correspondingcrews should already have been established. Therefore, the pro-ductivity rate for each crew for each type of operation is assumedto be fixed. Accordingly, the duration of each operation will notchange over time.

2.1.4. Project costThe project cost consists of two parts – direct cost and indirect

cost. The indirect costs refer to costs related with site supervision,field office costs (e.g., IT facilities, site QA program, payroll admin-istration, etc.), site cleanup and general housekeeping, etc. Here wecalculate this cost by multiplying the daily indirect cost by the pro-ject duration. The direct costs are costs that are directly associatedwith the project, including subcontractors, hired labor, materials,supplies, equipment, bonds and permits. In this paper the directcost is calculated in two parts. The first part is calculated by mul-tiplying a crew’s daily expense, including their salary, by the num-ber of days they are working on the job site. The second part is themobilization and demobilization costs, which are calculated bymultiplying a crew’s daily expense by the number of days the con-struction manager deems as the upper limit they can stay idlewhile getting paid. The cost calculation method is further ex-plained in Dong [1].

2.1.5. Single operation execution modeActivities in the RCPSP/RCMPSP setting can have single execu-

tion mode or multi-mode [21]. A mode is a processing alternativeof an activity. When generating LAS for operations on a daily basis,only one mode is allowed. Operations are not allowed to beinterrupted.

2.1.6. Zone constraintSub-projects form a zone when certain operations need to be

synchronized. Synchronization means that all such operationshave the same start and finish times and require the same crew(s). Such zone operations can be treated as one operation whichhas a lower level of detail compared to operations only being car-ried out in a given sub-project. A sub-project can be grouped to dif-ferent zones when two or more zone operations are defined in itscorresponding fragnet by the site engineers. Different zones do notnecessarily consist of the same sub-projects.

2.1.7. Blocking constraintA blocking operation is generally defined in a specific sub-pro-

ject which serves as the hub for the transportation of resources andmaterials required by its adjacent sub-projects. These sub-projectsform a blocked area. When a blocking operation occurs, the accessto the blocked area is not available, thus no operation can start inthe blocked area. Since operations are not allowed to be inter-rupted, the blocking operation requires the blocked area be clearedbefore it is started.

2.2. Mathematical formulation

The following notations are used for the formulation:

Indices:

i sub-project index, i ¼ 1; . . . ;M. M is index set of

sub-projects.

j operation index in each sub-project, j ¼ 1; . . . ; Ji.

Ji is the total number of operations in sub-project i.

t

periods, t ¼ 1; . . . ; T . In this paper, periods equalto days. T is the upper bound of the projectduration.

k

resource index, k ¼ 1; . . . ;K. K is the totalnumber of resource types needed for theconstruction project.

l

the index of a zone operation in related sub-projects.

Variables:

yt the binary variable with 1 indicating an

operation is performed in a sub-project on day t.

xi;j;t the binary variable indicating whether operation

j is performed in sub-project i on day t.

xc;b;t the binary variable indicating whether a

blocking operation b is performed in sub-projectc on day t.

zl;t

the binary variable indicating whether the zoneoperation l is performed on day t.

Parameters:

Rk the total number of resource type k available. ri;j;k the number of resource type k required by

operation j in sub-project i. Generally only onetype of crew is needed for an operation, butcertain operations might require multiple typesof crews to collaborate.

Ti

The date by which sub-project i won’t beavailable for the finishing work.

Hi

the set of operation pairs with precedenceconstraints in sub-project i.

Bc;b

the group of sub-projects blocked by theblocking operation b in sub-project c.

Zl

the set of sub-projects forming a zonecorresponding to the zone operation l.

(continued on next page)

740 N. Dong et al. / Advanced Engineering Informatics 26 (2012) 737–748

L

the total number of sub-projects in zone Zl.

RZl

Kl

the number of type-k resources required forzone operation l of zone Zl.

The mathematical formulation of this problem:

Minimize f ðtimeÞ or f ðcostÞ ð1Þ

Subject toXT

t¼1vi;j;t ¼ 1; i ¼ l; . . . ;M; j ¼ l; . . . ; Ji ð2Þ

XM

i¼1

XJi

j¼1ri;j;kvi;j;t 6 Rk; k ¼ 1; . . . ;K; t ¼ 1; . . . ; T ð3Þ

XTi

t¼1vi;j;t ¼ 0; t ¼ 1; . . . ; Ti ð4Þ

vi;j;t 6 yt; i ¼ 1; . . . ;M; j ¼ 1; . . . ; Ji; t ¼ 1; . . . ; T ð5ÞXm

j¼1

Xq

t¼1vi;j;t P

Xn

j¼1

Xq

t¼1vi;j;t 1 6 q 6 T; ðm;nÞ 2 Hi;

i ¼ 1; . . . ;M ð6Þ

vc;b;t

Xi2Bc;b

vi;j;t ¼ 0; j ¼ 1; . . . ; Ji; t ¼ 1; . . . ; T ð7Þ

1L

Xi2Zl

vi;l;t ¼ Zl;t ; t ¼ 1; . . . ; T ð8ÞP

i2Zlri;l;klvi;l;t

1L RZl

kl

¼ Zl;t; t ¼ 1; . . . ; T ð9Þ

vi;j;t;vc;b;t ; yt; Zl;t 2 f0;1g; i ¼ 1; . . . ;M; j ¼ 1; . . . ; Ji;

t ¼ 1; . . . ; T ð10Þ

The objective is to minimize the total project duration or projectcost as described in Eq. (1). The project duration can be expressedasPT

t¼1yt where T is the last date of the entire project; the cost cal-culation method is explained in Section 2.1.4. Eq. (2) dictates thateach operation can only be performed once in sub-project i. Tworesource constraints exist for this problem. The general constraintis that for a certain resource type k, the total amount of such re-source used by relevant operations in all projects cannot exceedthe total available amount Rk on a daily basis, as formulated inEq. (3). Another resource constraint is related with a zone and itis defined by Eqs. (8) and (9). The number of resources assignedfor a zone operation l is RZl

kl . Eq. (8) denotes that once a zone oper-ation l in a sub-project is started, all other zone operations in thesame zone must start as well. Eq. (9) describes the special resourceconstraint in a zone – all the zone operations in a zone must sharethe same resource(s). Therefore we need to divide RZl

kl by L, thenumber of zone operations in zone Zl. Eq. (5) implies that yt ¼ 1if any operation is done on day t. The constraint of room/sub-pro-ject availability is defined in Eq. (4), in which Ti is the date bywhich sub-project i won’t be available for the finishing work (be-cause of the incomplete structural work, such as concrete andblock work). The precedence constraint is defined in Eq. (6), inwhich operation n is the successor of m. Eq. (7) defines the blockingconstraint dictating that the blocking operation b in sub-project cand the operations in the blocked sub-projects (defined by B) aremutually exclusive.

After formulating this complex project management problemby integrating all its constraints, we observe that this mathemati-cal program is a quadratically constrained integer program. It iswell know that such a program is usually NP-hard: one cannotsolve it to the optimality in polynomial time. Such an intrinsicobstacle lies in most project management problems, which hasmotivated researchers to develop a great variety of approximationalgorithms and efficient heuristics to tackle the subject. Such algo-rithms include branch-and-bound [22], integer programing [23],sampling techniques [24] and local search (i.e., Tabu search [25],simulated annealing [26] and GA [27]).

3. The genetic algorithm-based method for look-aheadscheduling

In this paper we focus on a detailed GA-based approach thatintegrates more constraints, such as engineering priorities, zoneconstraints and blocking constraints, than the models previouslydiscussed in [12–21]. We use this approach because GA is moreflexible in accommodating additional constraints compared tothe other types of local search methods. GA is widely used inRCPSP/RCMPSP to find good solutions with few computationalrequirements within a reasonable time period. A GA applies theprinciples of biological evolution to solve optimization problemsby combining and altering existing solutions in order to formnew ones [27,28]. Scholars including Lee and Kim [29], Hartmann[30,31], Brucker et al. [32] and Özdamar [33] have conducted agreat deal of work to use GA to address RCPSP problems. Basedon their pioneering work, a number of studies [34–37] have beencarried out to use GA to address the RCMPSP by transferring theminto a RCPSP via the single-project approach. On the other hand,Kim et al. [21] propose a two-stage encoding to apply the multi-project approach to their GA. Tasan and Gen [38] and Xu and Zhang[39] improve the performance of this GA by introducing enhancedfuzzy logic controllers to regulate the GA parameters (generationnumber, population size, crossover ratio and others). Regardlesswhich approach is used, three main steps are used in GA in search-ing for the optimum solutions: initial population generation, repro-duction, and selection. After a certain number (POP, which isassumed to be an even integer) of individuals are generated, thepopulation is randomly partitioned into pairs of individuals. Wethen apply a crossover operator to such pairs to produce twonew individuals (children). Subsequently, a mutation operator isapplied to certain children to allow new features to appear in theoffspring. The crossover and mutation operators are the most com-monly used operators in the reproduction process. After the repro-duction, a population size of 2 � POP is reached. The selectionprocess reduces the population to its former size POP via certaincriteria based on each individual’s fitness. The reproduction andselection processes are repeated until a certain termination status(i.e., the maximum number of generations – GEN – is reached, theindividuals in the new generation are identical, the upper limit ofthe CPU time is reached, etc.) is met. Through certain schedulingalgorithms, individuals are created in both the initial populationgeneration and the reproduction processes.

3.1. Scheduling algorithm

Since we need to take engineering priority into account, priorityrule based heuristics become the starting point to create the sched-uling algorithm for the proposed problem. Kolisch [40] offers anextensive discussion regarding the two schedule generationschemes used by such heuristics – ‘‘serial’’ and ‘‘parallel’’, both ofwhich create valid schedules based on certain priorities assignedto the activities. The serial schedule generation scheme [41] is anactivity-oriented scheme and consists of M stages, where M is thenumber of activities to be scheduled. Each activity’s priority is cal-culated (using a given priority rule) only once before the schemestarts. At each stage, an activity is selected and scheduled as soonas possible, according to its priority, taking into account the prece-dence relationships and availability of resources. The parallel sche-dule generation scheme [40,41] is a time-oriented scheme andconsists of N time stages. At each stage, a set of activities is sched-uled and their priorities are determined at that stage. The parallelscheme is more appropriate for our proposed problem in whichwe need to address the two time-sensitive constraints – the zoneconstraint requires that a group of operations to be scheduled at

Table 1Data structure of the sample project for schedule generation.

Sub-project 1 Sub-project 2 Sub-project 3 Sub-project 4

Engineering priority 3 1 1 2Operation ID 1 2 3 4 5 1 2 3 4 5 1 2 3 4 1 2 3 4Zone constraint Zl½O13;O23;O33� Z1½O13;O23;O33� Z1½O13 ;O23;O33�Blocking constraint Bl½O44; ðP1; P2; P3Þ� Bl½O44; ðP1;P2; P3Þ� Bl½O44; ðP1;P2; P3Þ� Bl½O44; ðP1;P2;P3Þ�

Fig. 2. The proposed daily schedule generation procedure considering the engi-neering priority, zone, and blocking constraint.

N. Dong et al. / Advanced Engineering Informatics 26 (2012) 737–748 741

the same time at a certain stage, whereas the blocking constraint re-strains any operation in certain sub-projects to start while theblocking operation is being carried out. These two constraints alsojustify our choice of using the multi-project approach to address thisproblem as they introduce sub-project level interactions instead ofsub-project precedence relationships. The data structure represent-ing the multi-project example for the parallel scheme is shown inTable 1. All the information necessary for schedule generation canbe retrieved from this structure except the operation precedencerelationships shown in Fig. 1. Table 1 indicates that sub-project 2has the highest engineering priority and should be finished as earlyas possible. Sub-projects 1 and 3 have the same priorities which arethe lowest among all the sub-projects. Operations O13;O23 and O33

form a zone Z1, expressed by Z1 [O13;O23;O33]. Operation O14 willblock all the other sub-projects once it is started – we use B1[O44; ðP1;P2 and P3Þ] to represent such a blocking constraint.

Four operation sets are needed for the parallel scheme for theproposed problem: the complete set C for all the finished operations,the in-progress set I for all the scheduled but not yet finished opera-tions, the eligible set E for the operations of which all the predeces-sors are already in C, and the decision set D for the operations to bescheduled at a period. At each period (a day in this case), the schemefirst assigns resources to operations in I. If the remaining resourcesare sufficient for an operation to start, the scheme moves all suchoperations from E to D and ranks them according to their engineer-ing priorities. If an operation is linked to a zone, it will not be putinto D unless all other operations linked to the same zone are alsoin E. A blocking operation will only be selected into D if no otheroperations are ongoing in its corresponding blocked area. Next anoperation from D is selected to be scheduled. Note that a zone oper-ation, if any, will be selected before a regular operation if it has thesame highest priority in D. To ensure the two types of constraintsare satisfied, the selected operation will go through three steps:zone constraint processing, blocking constraint processing, and reg-ular operation processing. If the operation is linked to a zone, all itsrelated operations are scheduled as one zone operation regardlessthe priorities of these operations. If the selected operation is a block-ing operation, it will be scheduled in the second step. If the selectedoperation does not belong to the above two categories, it will bescheduled in the third step. Dong [1] gives an elaborate explanationregarding the details of these steps. The process of forming D andscheduling an operation will repeat as long as the remaining re-sources are sufficient for at least one operation in D to be scheduled.Such a daily schedule generation procedure is illustrated in Fig. 2.The scheme repeats the daily schedule generation procedure dayby day until all the operations are in the schedule (i.e., the wholeschedule). The scheme and the daily schedule generation procedure(Fig. 2) constitute our scheduling algorithm. In the rest of this paper,unless specifically stated otherwise, the term schedule refers to awhole schedule, not a daily schedule. The first two schedules inFig. 3 are two sample schedules generated using such an algorithmbased on the example shown in Fig. 1 and Table 1. It is notable thatin Schedule 1, the blocking operation starts from day 10; no opera-tions are allowed to start from this day on in sub-projects 1–3(marked by ‘‘b’’ in each cell) until it is completed. On the other hand,in Schedule 2, the blocking operation starts at the end of sub-project4, when all the other sub-projects are already finished. Schedule 2 is

Fig. 3. Two sample schedules (parents) and a child generated based on the proposed crossover operator.

742 N. Dong et al. / Advanced Engineering Informatics 26 (2012) 737–748

more desirable than Schedule 1 in terms of the total project durationas well as the completion time of the sub-projects with higher engi-neering priorities.

3.2. Crossover

The one-point crossover operator is one of the most popularoperators used in the literature for RCPSP [30,42]. It is derived fromthe permutation based crossover operator and can be tailoredaccording to specific features of a scheduling problem [43]. To ap-ply the one-point crossover to the proposed problem, we intend tofind a cutting point that can act on all the sub-projects. To achievethis goal, we cut all the sub-projects at the same time so thatchanges in activity sequence can happen in each sub-project afterthe crossover. Such a way of cutting is different from the conven-tional one-point crossover as it picks the cutting point based onthe position of a sorted activity list not time.

For any two given schedules F and M, we assume F costs n1 days,M costs n2 days. Then a number m from {1, 2, . . ., min{n1, n2}} israndomly chosen. Next we generate their children as follows:

Step 1: We choose the first m days in M as the first m days for thedaughter D. Therefore D inherits the partial schedule fromM up to day m.

Step 2: For each sub-project P_i, we sort its remaining work flowfollowing the work flow of F, knowing that the remainingwork sequence for P_i is still feasible (assuming that thereis no iterative effect from other sub-projects).

Step 3: Starting from day m + 1, we schedule all the work day byday. On day m + 1, we check the resource requirement ineach sub-project. If too many sub-projects ask for the sameresource, we give the resource to the first k sub-projects(ranked by engineering priorities) it can satisfy and letthe remaining sub-projects wait to try on the next day.The scheduling procedure is similar to that depicted inFig. 2, except that the work sequence in each sub-projectshould follow F.

When step 3 is finished, the operator will eventually generate afeasible LAS – a daughter D (child 1 shown in Fig. 3), taking the par-

tial schedule from S2 up to day m, then sorting the work flow foreach sub-project from day m + 1 following F. Similarly we can gen-erate a son S by switching the role of M and F in Steps 1–3.

This proposed crossover operator always generates legitimatechildren (although redundancy exists). We prove it with the fol-lowing theorems.

The work sequence of a sub-project P_o in a schedule I is givenby

WIO ¼ ðjIO1 ; . . . ; jIO

JOÞ

where Jo is the number of total operations in P_o. This work sequenceis assumed to be a precedence feasible permutation of the set ofoperations. We consider two individuals selected for crossover, amother M and a father F. The random cutting date m correspondsto a cutting position qMo in sub-project P_o in M and qFo in F, with1 6 qMo; qFo < Jo. Since we use date instead of position as the cuttingmeasurement, qMo and qFo are not necessarily the same. Through theproposed crossover operator, two children, a daughter D and a son S,are produced from the parents. In the work sequence of P_o in D, thepositions i ¼ 1; . . . ; qMo are taken from the mother, that is,

jDoi :¼ jMo

i :

The work sequence of positions i ¼ qMo þ 1; . . . ; Jo of P_o in D istaken from the father. However the operations that have alreadybeen taken from the mother are not considered again.

Theorem 1. If applied to precedence feasible parent individuals, theproposed crossover operator results in precedence feasible offspring.

Proof. Let the work sequence of the parents M and F conform tothe precedence assumption. We assume that child D produced bythe crossover operator is not precedence feasible. That is, in asub-project P_o, there are two operations jDo

i and jDok with

1 6 i < k < Jo; jDoi is before jDo

k , violating their precedence relations.Three cases can be distinguished [30]:

Case 1: We have i; k 6 qMo. Since all operations up to position

qMo are taken from M, operation jDoi precedes jDo

k in thework sequence of M, a contradiction to the precedencefeasibility of M.

N. Dong et al. / Advanced Engineering Informatics 26 (2012) 737–748 743

Case 2: We have i; k > qMo. As the relative positions are main-tained by the crossover operator, operation JDo

i precedesJDo

k in the work sequence of F, contradicting the prece-dence feasibility of F.

Case 3: We have i 6 qMo and k > qMo. Then operation JDoi pre-

cedes JDok in the work sequence of M, again a contradic-

tion to the precedence feasibility of M.

Similar discussions can be made for any sub-project(s) usingthese three cases, thus the daughter D produced by the crossoveroperator is precedence feasible. As to son S, the positions1; . . . ; qFo of the son’s work sequence are taken from the fatherand the remaining positions are determined by the mother. There-fore, Theorem 1 holds for both children.

Theorem 1 can be easily adapted to prove that the proposedcrossover operator does not violate the engineering priorities. Asto the zone constraint and the blocking constraint, we can use sim-ilar logic to testify the validity of the offspring. For instance we useTheorem 2 below to show how the zone constraint is fulfilled.

Theorem 2. If applied to zone feasible parent individuals, theproposed crossover operator results in a zone feasible offspring.

Proof. Let the parents M and F conform to the zone constraint. Weassume that child D produced by the crossover operator is not zonefeasible. That is, in sub-projects P_m and P_n, the zone operationsjDml and jDn

l for Zone Zl are not synchronized as they are supposed tobe. Assuming qMm

6 qMn, three cases can be distinguished:

Case 1: We have l 6 qMm. Then operations jDm

l and jDnl for Zone Zl

are not synchronized in M, a contradiction to the zonefeasibility of M.

Case 2: We have l P qMn. Since the zone constraint is main-

tained by the crossover operator, the assumption thatoperations jDm

l and jDnl for Zone Zl are not synchronized

in D contradicts the logic of the proposed daily schedulegeneration procedure in Fig. 2. This procedure guaran-tees that all zone operations for a zone are synchronizedin the schedule generation process.

Case 3: We have qMm< l < qMn

. Then operations jDml and jDn

l forZone Zl are not synchronized in M, again a contradictionto the zone feasibility of M.

These cases also hold if qMm> qMn

. Therefore the daughter Dproduced by the crossover operator conforms to the zone con-straint. The same logic can be applied to son S and father F. So The-orem 2 holds for both children.

Fig. 3 illustrates two parents (Schedule 1 and 2) and a child(Child 1) generated using the proposed crossover operator. FromFig. 3, it can be observed that Child 1 has the same total projectduration as Schedule 2. However, in terms of the degree of satisfac-tion to the engineering priorities, sub-project 2 (with the highestpriority) completes on day 14 in schedule 2, whereas day 15 inChild 1. Therefore, the degree of satisfaction to the engineering pri-orities can be integrated into the time-based objective (for now weuse only total project duration) if the project personnel deem itnecessary.

3.3. Mutation

To avoid local optima, we develop a two-tier mutation operator.First, after scanning a schedule, if multiple sub-projects are com-peting for the same resource at the same time, it assigns the re-source to a different sub-project of the same priority. At theoperation level, it randomly picks a sub-project and randomly

changes the order of two adjacent operations and test if the newschedule is still feasible. If so, the new schedule will be added tothe selection pool as the candidate to go into the next generation.If not, the operator will choose a cutting date and start to use theproposed schedule generation algorithm to generate the rest ofthe schedule after the cutting date. Such a mutation operator guar-antees the creation of a legitimate child every time the mutationoccurs. But this child does not necessarily have to be a new one– if it is exactly the same as one of its parents, it will not be addedto the selection pool.

3.4. Selection

We consider two alternative evolutionary mechanisms, namelyelite selection and roulette wheel selection. Both mechanisms fol-low the procedures of initialization, selection, crossover, and muta-tion [44]. In elite selection, after crossover and mutation, theoptimal solution with the highest fitness value, i.e., minimum pro-ject duration, minimum project cost, etc., is retained and dupli-cated in the new population. While in the roulette wheelselection [10], individuals with better fitness values have a higherprobability of being selected for the new population but there is achance that they might not get selected. Though optional, themutation operator is normally used to avoid the search beingtrapped in local optima. In the next section, we discuss its effecton search efficiency and whether it can help to find better solu-tions. In addition, the performance of the two selection methodsis compared.

4. Illustrative examples

We develop two examples with data extracted from an actualuniversity building project to validate the proposed GA-basedmethod for LAS generation. We do not use existing examples forthis purpose because, to our knowledge, these examples do notconsider engineering priorities, the blocking constraint, and thezone constraint. Therefore we compare the search results withthe data obtained via a simulation-based method, which auto-mates the generation of LAS taking into account the three typesof constraints. The simulation-based method is developed basedon the activity-based construction (ABC) modeling and simulationmethod, which is composed of an ABC modeling (ABC-Mod) com-ponent and an ABC simulation (ABC-Sim) component [45]. ABC-Mod models construction processes using an activity-centered ap-proach; ABC-Sim executes the ABC model using three steps inloops: schedule activities, advance simulation, and release re-sources. Our simulation-based method expands the ABC methodby (1) modeling construction processes in the finishing phase usinga three-tiered hierarchy: project, sub-project, and operation; and(2) accommodating the three types of constraints in the first stepof ABC-Sim. The design, implementation, and validation of thissimulation-based method are detailed in Dong [1]. The objectivefunctions of minimizing project duration and cost are both dis-cussed in the two examples. The proposed GA-based method canbe tailored in several ways. In terms of selection method, we dis-cuss the search results when different combinations of selectionmethod (Section 3.4) and mutation operator (Section 3.3) are used.

4.1. First example

4.1.1. Example setupDong [1] introduces a six-room example to showcase the simu-

lation-based LAS generation method. This example consists of onecorridor (COR1), two electrical rooms (ELE1 and ELE2), two IDFrooms (IDF1 and IDF2) and one plant room (PLT1). Therefore, four

744 N. Dong et al. / Advanced Engineering Informatics 26 (2012) 737–748

types of fragnets are introduced. In addition, one zone constraintand one corridor constraint are introduced. Sub-projects ELE2,IDF1 and IDF2 contain one zone operation ‘‘HVAC & Firefighting’’.Two blocking operations – ‘‘Suspended Ceiling’’ and ‘‘TerrazzoFlooring’’ in COR1 – block all other sub-projects thus no operationcan be carried out in them while the blocking operations are inprogress. Only one crew is available for each discipline. For projectcost items, we assign $100 to the daily indirect cost. As to the firstpart of direct cost, we assign $40 to the crew daily expense (assum-ing all disciplines cost the same). The second part of direct cost – acrew’s mobilization and demobilization cost – is considered to be8 days of a crew’s daily expense. If a crew do not have work formore than 8 days, they will be demobilized with 4 days’ expensesfor demobilization. Another 4 days’ expenses need to be paid forthis crew to come back to the job site to work again.

4.1.2. Computational resultsTable 2 compares the performance of the GA-based method

with the simulation-based method. Four experiments (i.e., runningthe simulation for 1000, 5000 and 10,000 times and running theprototype based on the GA-based method with POP equals 100and GEN equals 100) are conducted to compare their performance.Each is carried out 10 times to get an average result recorded. Thefirst row of Table 2 shows the average minimum project durationsfound by the four experiments and the corresponding project costs.The second row illustrates the average minimum project costsfound and the corresponding project durations. Unlike the simula-tion-based method, the GA-based method searches the optimalschedule(s) according to the specific objective function. Therefore,the data sets related with the GA-based method in the first row andthe second row are retrieved separately, while the data sets relatedwith the simulation-based method are retrieved at the same time.In terms of minimum project duration, the GA-based method doesnot outperform the simulation-based method significantly, but itdiscovers the relative optimal schedule(s) faster (93 vs. 390 s inthe 5000-time simulation). As to project cost, the GA-based meth-od discovers a slightly lower project cost ($20,152 vs. $20,378 inthe 10,000-time simulation) only using one fifth of the CPU time(161 vs. 802 s). Although the simulation-based method can findschedules with lower cost when the number of simulations in-creases, it will spend much more time to reach similar resultsfound by the GA-based method. Table 2 also indicates anothertwo findings. First, the GA-based method reached the close-to-optimum duration faster than the cost (93 vs. 161 s). This is be-cause of the current setting of the termination criteria. When nobetter result is reached within 20 generations, the prototype stops.

Table 2Comparison between the GA-based method and the simulation-based method in terms of

Simulation �1000 times Simulation – 5000 times S

Dur.(days)

Cost(USD)

CPU time (s) Dur.(days)

Cost(USD)

CPU time (s) D(

74.2 20,818 75 74.0 20,724 390 777.2 20,464 75 77.0 20,460 390 7

Table 3Computational results of four settings of the GA-based method – the six-room example.

Elite with mutation Elite without mutati

Av. Minimum project duration 74 days 74 daysAv. CPU time consumed 93 s 78 sAv. Minimum project cost 20,152 dollars 20,224 dollarsAv. CPU time consumed 161 s 125 s

On average it does not discover a better schedule in terms of dura-tion after the 40th generation. However, a lower cost keeps comingup until the final generation is reached. Second, both methods indi-cate that the relation between project duration and cost is not lin-ear; the schedule with minimum project duration does notnecessarily have the lowest project cost.

The results using GA-based method shown in Table 2 are gen-erated when the elite selection is chosen as the selection methodand 10% of the population go through mutation. We also collectedresults based on different combinations of selection method andmutation rate as shown in Table 3. The setting of elite selectionwithout mutation is the fastest in search of either minimum dura-tion or cost. But it does not deliver the best result for cost. Theroulette wheel selection takes more time than elite selection yetit does not give better results. The mutation operator appears tooffer slightly better results when searching for minimum cost($20,152 vs. $20,224 using elite selection; $20,158 vs. $20,166using roulette wheel selection) yet it increases the search time.In sum, the setting of elite selection with 10% mutation givesthe best results for the search of both duration and cost withoutincurring a major increase of CPU time compared to the otherthree settings.

The results shown in both Tables 2 and 3 are achieved assumingall operations have the same engineering priority. When we assignELE1 the highest priority, IDF1 the next highest, keeping all theothers the same, the lowest duration found by the GA-based meth-od becomes 76 days and the cost $21,324. This result indicates thatgiving certain rooms priority for the limited resource might ruleout the optimum resource allocation pattern, thus increasing pro-ject duration and/or cost.

4.1.3. ValidationTwo methods are used to validate the results discussed in Sec-

tion 4.1.2. First, we developed a schedule checking program tocheck the schedules in the following aspects: work sequence ineach sub-project, crew allocation conflicts on each day, confor-mance to engineering priorities and constraints, duration of eachoperation in the schedule, and the calculation of project durationand cost. The program was applied to test all the schedules gener-ated. No errors were found by the program. Second, the best sched-ules generated using the GA-based method and the 10,000-runsimulation were reviewed and approved by two planning engineersand one site engineer from Consolidated Contractors InternationalCompany. Before letting them review the schedules, they were firstasked to develop an LAS with all the relevant information (work se-quence, crew-operation-productivity connection, quantities, crew

project duration and cost for the six-room example.

imulation – 10,000 times GA – 100 � 100

ur.days)

Cost(USD)

CPU time (s) Dur.(days)

Cost(USD)

CPU time (s)

4.0 20,520 802 74.0 20,470 936.4 20,378 802 76.0 20,152 161

on Roulette wheel with mutation Roulette wheel without mutation

74 days 74 days99 s 86 s20,158 dollars 20,166 dollars183 s 157 s

N. Dong et al. / Advanced Engineering Informatics 26 (2012) 737–748 745

availabilities, engineering priorities and constraints, etc.) providedin Microsoft Excel spreadsheets [1]. Each spent an average of5980 s to generate one schedule, with an average duration of79.3 days (a different mobilization cost number was given to thepractitioners so project costs are not compared).

4.2. Second example

4.2.1. Example setupCompared to the simulation-based method, the GA-based

method discovers close-to-optimum schedules faster, but not sig-nificantly better, when applied to the six-room example. A key rea-son is that the scale of this example is not big enough so that close-to-optimum schedules can be found when the number of simula-tions becomes large enough without consuming too much CPU

Fig. 4. Activity-on-node network of the f

Table 4Operations, precedence relations and required resources for the faculty offic

Operation # Predecessors Operation name

1 – Conduit & box ab2 1 Electrical first fix3 1 HVAC, plumbing,4 2 Electrical second5 3, 4 Suspended ceiling6 5 First coating (sus7 6 Electrical final fix8 7 Second coating (s9 – Plumbing (precas10 9 Dry wall11 10 Conduit & box (d12 11, 17, 21 Electrical second13 5, 12, 16 First coating (all14 13 Electrical final fix15 14 Second coating (a16 – Window (precast17 – Glass wall18 – Screed19 18 Gypsum panel, fi20 1, 19 Conduit & box (g21 20 Gypsum panel, se22 8, 15, 18 Carpeting23 22 Wood skirting &24 23 Furniture25 24 Door

Table 5Comparison between GA-based method and simulation-based method in terms of project

Simulation �1000 times Simulation – 5000 times S

Dur.(days)

Cost(USD)

CPU time (s) Dur.(days)

Cost(USD)

CPU time (s) D(

114.6 70,363 1037 114.0 68,547 5102 1116.7 67,946 1037 117.4 67,422 5102 1

time (e.g., the shortest schedule can be found via the 5000-runsimulation using about 390 s). We expect that the GA-based meth-od outperforms the simulation method when it is applied to largerprojects. Therefore, we built the second example introducing a newfragnet – faculty office with a total of 25 operations (Fig. 4 and Ta-ble 4). This example consists of four electrical rooms, four IDFrooms, four plant rooms, one corridor, and seven faculty offices –a total of 20 rooms. Three zone operations are created related with‘‘HVAC & Fire Protection’’. Zone No.1 consists of rooms ELE1, ELE2,and IDF1; zone No.2 consists of rooms ELE3, IDF3, and IDF4, zoneNo.3 consists of rooms FAC1, FAC2, FAC3, and FAC4. Similar tothe first example, the two blocking operations – ‘‘Suspended Ceil-ing’’ and ‘‘Terrazzo Flooring’’ in the sub-project COR1 – block allother sub-projects once these operations start. All operations areassumed to have the same engineering priority. Two crews are

aculty office in the second example.

e.

Crew

ove ceiling 1 Electricalabove ceiling 1 Electricaland fire protection above ceiling 1 HVACfix – ceiling 1 Subcontractor

1 Carpenterpended ceiling) 1 Painting– ceiling 1 Electrical

uspended ceiling) 1 Paintingt wall) 1 HVAC

1 Carpenterry wall) 1 Electricalfix (all walls) 1 Subcontractorwalls) 1 Painting

(all walls) 1 Electricalll walls) 1 Paintingside) 1 Carpenter

1 Carpenter1 Screed

rst fix 1 Carpenterypsum panel) 1 Electricalcond fix 1 Carpenter

1 Tiling & Carpetingcladding 1 Carpenter

1 Carpenter1 Carpenter

duration and cost for the 20-room example.

imulation – 10,000 times GA – 400 � 200

ur.days)

Cost(USD)

CPU time (s) Dur.(days)

Cost(USD)

CPU time (s)

13.5 68,422 9883 112.0 67,954 723517.8 67,072 9883 119.3 66,014 7361

Fig. 5. Trends in search of project duration and cost using the simulation-based method and the close-to-optimum results found by the GA-based method.

Table 6Computational results of four settings of the GA-based method – the 20-room example.

Elite with mutation Elite without mutation Roulette wheel with mutation Roulette wheel without mutation

Av. Minimum project duration 112 days 112.7 days 112 days 112.2 daysAv. CPU time consumed 7235 s 6,502 s 8113 s 7024 sAv. Minimum project cost 66,014 dollars 66,236 dollars 66,004 dollars 66,012 dollarsAv. CPU time consumed 7361 s 6517 s 8185 s 7103 s

Fig. 6. Minimum project cost found at a 50-generation interval within 600 generations using the GA-based method.

746 N. Dong et al. / Advanced Engineering Informatics 26 (2012) 737–748

available for the disciplines including carpenter, electrical, plaster-ing, and painting. For the other disciplines, only one crew is avail-able. Compared to the six-room example, the indirect costincreases to $240 to echo the increase of project scale while the di-

rect cost remains the same for each crew. Since the project scalesup, the POP increases to 400. The search does not stop even if nobetter schedules are found within a certain number of generationsuntil the 200th generation (GEN) is reached.

N. Dong et al. / Advanced Engineering Informatics 26 (2012) 737–748 747

4.2.2. Computational resultsTable 5 compares the search results using the simulation-based

method and the GA-based method. All the searches were carriedout 10 times and the numbers in Table 5 are average numbers.As the number of simulations increases, better schedules are foundfor both project goals. This trend is illustrated in Fig. 5, based onthe data in Table 5. In terms of project duration, the GA-basedmethod outperforms the simulation-based method by 1.5 days(112 vs. 113.5 days in the 10,000-run simulation) while spending27% less CPU time (7235 vs. 9883 s) in the search. As to the projectcost, it discovers schedules with an average of $66,014, more thanone thousand less (1.58% less) than the average minimum costfound with the 10,000-run simulation, spending 26% less CPU time(7361 vs. 9883 s). The results found using the GA-based methodalso indicate that the schedule with shortest project duration doesnot necessarily have the lowest project cost (Table 5). In terms ofcost savings, the GA-based method offers better performance inthe 20-room example compared to the 6-room example (1.58%vs. 1.11% or $1,058 vs. $226). We expect that as the complexityof a project increases, the GA-based method continues to give bet-ter results compared to the simulation-based method.

The results found using the GA-based method shown in Table 5are generated when the elite selection is chosen as the selectionmethod and 10% of the population go through mutation. Similarto Table 3, we collect and show in Table 6 the results using differ-ent combinations of selection method and mutation rate. Compar-ing Table 6 to Table 3, elite selection without mutation is still theforerunner in terms of CPU time spent but delivers poorer resultscompared to others. When mutation is applied better results arereached for both project duration and cost. The power of roulettewheel selection combined with mutation rises to surface as itdelivers the best result in search of project cost, but spending11% more CPU time compared to elite selection with mutation,which gives the second best result.

Since the results using the GA-based method in Tables 5 and 6are obtained with the termination criteria of 200 generations (i.e.,GEN equals 200), we expect that lower project cost could be foundas the search goes on. Therefore, using the setting of roulette wheelselection with 10% mutation, we conducted a search to increaseGEN to 600 and the results are shown in Fig. 6. The lowest projectcost found is $65,840, by the 500th generation.

4.2.3. ValidationAll schedules generated for this 20-room example were exam-

ined by the schedule checking program described in Section 4.1.3and no errors were discovered.

5. Conclusion

This paper presents a new GA-based method which automatesLAS generation in the finishing phase of complex projects withthe objective of minimizing project duration or cost. Besides theconstraint of precedence relations between operations and theconstraint of resource availability, the method also deals withthree aspects that are common at the construction job sites of com-plex projects: engineering priorities, the blocking constraint andthe zone constraint. The consideration of these aspects extendsthe previous related work in the area of GA, especially the multi-project GA approach, to address RCMPSP. The current multi-projectGA literature either assumes each individual sub-project/room tohave the same priority (then dynamically determine their priori-ties in the scheduling process) or directly assigns precedence rela-tions between sub-projects according to particular projectrequirements. By considering the priority for each individual sub-project, the method allocates resources to the sub-projects in the

order of their level of ‘‘hunger’’ for resources. The current GA-basedRCMPSP literature only deals with the same level of detail in termsof activity/operation definition. By considering the zone constraint,the proposed method breaks this limitation and provides a newperspective to look at a group of sub-projects, which at certaintime, need to be synchronized for a particular type of work sharingthe same resources. It further extends the GA-based RCMPSP re-search by considering the blocking constraint, which presents an-other new perspective to look at a group of sub-projects – at acertain time, the work in one sub-project prevents all work in cer-tain other sub-projects from being carried out. The proposed meth-od can liberate the project planners from the tedious daily/weeklyLAS generation process and focus on other issues on the project; itcan benefit the construction managers by offering them alternativeschedules to achieve varied goals at different project stages; it canalso improve the efficiency of the site engineers in supervising thecrews’ daily work.

A six-room example is analyzed to validate the proposed meth-od, and another 20-room example is presented to illustrate itspower when a project scales up and its complexity increases. It isobserved that compared to the simulation-based method, the pro-posed method can find good solutions in terms of either projectduration or cost using less time. Comparing the two examples,the results denote that as the complexity of the project grows,the proposed method gives better results (i.e., more savings ofschedule duration or cost) than the simulation-based method. Bothexamples also indicate that a trade-off between duration and costexists for non-repetitive projects. The schedule results were gener-ated when no finishing-related work had started yet in any sub-project. Similar results can be obtained when the finishing workis in progress in certain sub-projects and the LAS are generatedbased on the work progress.

Although we formulate the scheduling problem based on anuniversity building project, the design of the proposed methodmakes it easily applicable to look-ahead scheduling in the finishingphase of various projects, such as hospitals and medical centers,offices, data centers, laboratories, and research facilities. Morebroadly speaking, since the proposed method utilizes a multi-pro-ject approach to address RCMPSP with more constraints, it can alsobe used to address multi-project planning problems, especiallywhen (1) individual projects have specific priorities, (2) interde-pendencies exist among these projects, and (3) they compete forscarce resources. The first and third factors are automatically con-sidered when addressing engineering priorities and resource con-straints. For the second, we will need to decompose differenttypes of interdependency into zone and blocking constraints andsee whether we need to add other constraints (such as staggeringof projects) to fully accommodate all the interdependencies. Inaddition, if the objective function is appropriately tailored, the pro-posed method can also be applied to project portfolio management[46,47] to help general contractors and subcontractors better selectprojects and properly prioritize them by going through multipleportfolio-mix scenarios.

In the current stage of development, the proposed method dealsonly with ‘‘finish-start’’ relations between operations because mostof the operations are carried out in rooms with specific equipmentand materials (and temporary structures) cramped inside, makingit very difficult for more than one operation to proceed at the sametime. The future research should take into consideration othertypes of relations when the rooms are big enough to allow multipleoperations to go in parallel. As to the priorities of sub-projects, wediscover that when resources are relatively rare (i.e., only one crewis available for each discipline), giving the resources first to thesub-projects with higher priorities does not necessarily guaranteethat they finish before those with relatively lower priorities. There-fore, deadlines should be considered along with priorities to satisfy

748 N. Dong et al. / Advanced Engineering Informatics 26 (2012) 737–748

the construction managers’ requirements. Thirdly, priority-rulebased heuristics are not considered in the proposed method be-cause we focus on addressing the engineering priorities as wellas the two constraints in the schedule generation process. Whenthere is a tie between two operations with the same engineeringpriority competing for the same resources, we randomly assignthe resources to one operation. In future research, when manysub-projects have the same priority, we can use priority-rules tobreak such ties and evaluate whether better schedules can bederived.

Finally, interruption of an operation is not allowed in the pro-posed method because suspending an operation to allow anotheroperation to start in a sub-project would result in additional crewmove-in, move-out, material/equipment in place and set-up timeleading to extra time and cost. But sometimes such interruptionsare unavoidable. Hence future research should take this factor intoaccount as well.

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