Distributed Scheduling Model for Infrastructure Networks

Distributed Scheduling Model for Infrastructure NetworksTarek Hegazy, M.ASCE1; Ahmed Elhakeem2; and Emad Elbeltagi, M.ASCE3

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Abstract: This paper presents an innovative model for scheduling, resource planning, and cost optimization of large constructiomaintenance programs that involve multiple distributed sites. The proposed distributed scheduling model~DSM! employs an informationsystem to store data related to various work sites, activities’ optional construction methods, and available resources. The Dincorporates a scheduling algorithm that is resource focused, and maintains crew work continuity under any sequence of distribuTo minimize cost and meet project time and resource constraints, the DSM uses genetic algorithms to determine the optimuconstruction methods and the optimum routing order among sites. Details of the DSM formulation are presented in this paperbenefits to municipalities and contractors are outlined.

DOI: 10.1061/~ASCE!0733-9364~2004!130:2~160!

CE Database subject headings: Computer applications; Construction management; Algorithms; Optimization; ScheduInfrastructure; Cost control.

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Introduction

Infrastructure networks such as highways, pipelines, buildingand water/sewer systems have recently been at the center otention for contractors and owner organizations. Not only infrstructure needs to be built, but also the current aging infrastrture needs to be repaired, upgraded, or expanded. Commcharacteristics of infrastructure projects are being huge in siinvolve many repetitive tasks, scattered across many spatially dtributed sites, and require a large amount of resources for thconstruction/maintenance operations. With the prevailing privazation pressures, municipalities and contractors strive to condthese operations in a timely and cost effective manner with mimum service interruption to the public through efficient useresources.

Infrastructure management systems are concerned mainly wlife cycle analysis and continuous assessment of network permance so that a properly budgeted construction/maintenancegram can be decided. When a municipality budgets its yeamaintenance/construction program, the detailed execution plausually left to internal departmental decisions based on expeence in past years. This, however, represents a major challe

1Associate Professor, Civil Engineering Dept., Univ. of WaterlooWaterloo ON, Canada N2L 3G1~corresponding author!. E-mail:[email protected]

2Graduate Student, Civil Engineering Dept., Univ. of WaterlooWaterloo ON, Canada N2L 3G1. E-mail: [email protected]

3Assistant Professor, Mansoura Univ., Mansoura, Egypt; presenPost Doctoral Fellow, Civil Engineering Dept., University of WaterlooWaterloo ON, Canada N2L 3G1. E-mail: [email protected]

Note. Discussion open until September 1, 2004. Separate discussmust be submitted for individual papers. To extend the closing dateone month, a written request must be filed with the ASCE ManagiEditor. The manuscript for this paper was submitted for review and posible publication on May 30, 2002; approved on November 19, 200This paper is part of theJournal of Construction Engineering and Man-agement, Vol. 130, No. 2, April 1, 2004. ©ASCE, ISSN 0733-93642004/2-160–167/$18.00.

160 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMEN

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since maintenance operations for infrastructure networks areally carried out under stringent resource and time constraiMost maintenance operations for municipal highway networksCanada, for example, are carried out during the mild sprisummer season. Similarly, maintenance operations for schbuildings are carried out during the short summer vacation.dustrial facilities are also maintained under strict constraints, pticularly when a plant is shut down during maintenance opetions.

The planning challenge in construction/maintenance opetions is exacerbated in wide infrastructure networks that stretcthe municipal, provincial, or the federal levels. In such caslocal conditions, including weather, vary from one site to tother. An efficient plan, in this case, is one that scheduleswork at each site when its productivity is highest. As such,order by which the different sites are constructed has to be omally decided, considering the time and cost of transportingsources from one site to the other. As such, the key consideratthat relate particularly to infrastructure networks include: tnumber of crews to use, the construction methods to employeach activity, the varying nature of work conditions at each sand the site construction order.

Most of the planning and scheduling tools available at tcommercial and research levels address some but not all asof infrastructure project management. Almost all commercproject management software systems, for example, are basethe critical path method~CPM! and, as such, exhibit some serioudrawbacks. Despite their multiproject and resource leveling cabilities, they are mainly duration driven, are not formulatedrespect a given deadline and resource limits, and do not guaracrew work continuity~Reda 1990; Suhail and Neale 1994!. Inaddition, their schedule presentation does not legibly showlarge amount of data involved in repetitive projects or thesource movements throughout the construction program. Thlimitations are mainly due to inadequate resource managemwhich is crucial for infrastructure projects.

In recognition of the disadvantages of network techniquesnumber of research-based methods for scheduling linear andpetitive projects have been developed since the 1960s, inclu

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Fig. 1. Using resource depository to automate estimate generation

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the line of balance~LOB! ~Lumsden 1968; Reda 1990!. Being aresource-driven technique, the objective of the LOB techniqueto determine a balanced mix of resources and to synchronize twork so that they are fully employed and noninterrupted. As sucit is possible to benefit from repetition, and the crews will likelspend less time and money on later units once they develolearning momentum. The traditional LOB technique, however, asumes purely sequential activities and has a simplistic formution to maintain crew work continuity. One notable effort to combine the benefits of the CPM and the LOB techniques is tmodel developed by Suhail and Neale~1994!. The model is agood framework for CPM/LOB integration, however, it does noconsider work interruptions, resource constraints, or cost optimzation. More importantly for infrastructure networks, no modehave considered distributed sites, site order, or the time/costcrews’ movement among sites.

A limited number of mathematical models have been devoped for cost optimization in repetitive projects, including the twmodels of Moselhi and El-Rayes~1993! and Senouci and Eldin~1996!. For large-scale projects, however, the mathematical opmization techniques they used may not guarantee an optimsolution and may be trapped in local optima~Li and Love 1997!.With recent developments in artificial intelligence and computtechnology, a nontraditional optimization technique, genetic algrithms ~GAs!, has emerged and can potentially be used for scheule optimization in large projects/networks. Genetic algorithmwork by emulating the natural evolution and ‘‘survival of thefittest’’ mechanism in living organisms. It incorporates cycles ogenerating and testing random solutions until a global optimumfound. Genetic algorithms have already been applied successfto numerous areas in civil engineering and construction, includitime–cost tradeoff analysis of nonrepetitive projects~Li and Love1997; Hegazy and Ayed 1999!.

This paper presents the formulation of a new distributescheduling model~DSM! that facilitates the planning and scheduling of resources in large networks with repetitive nontypictasks and spatially distributed sites. The DSM is flexible and cosiders all project parameters as variables to be optimized usthe GA technique.

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Basis of Distributed Scheduling Model: Focus onResources

With infrastructure networks involving spatially distributed sitethat have different work conditions, activities, and quantities,proposed DSM model is developed to address these particneeds. Distributed scheduling model is a resource-driven mothat balances the resources at both the global and the detactivity levels, and determines the optimum quantity of resourto be employed in a construction/maintenance program witlarge number of spatially distributed sites. The DSM formulatiis flexible and incorporates various practical features, includin1. Incorporation of a resource depository with automated e

mate generation;2. Allows for up to three methods of construction for each a

tivity, with variable quantities from one site to the other;3. Allows for varying the site order, and accounts for the co

sequent time/cost of crew moving among sites;4. Allows for site-dependent productivity factors;5. Incorporation of an algorithm for crew assignment amo

the spatially distributed sites;6. Use of an improved schedule presentation that shows co

coded crews and their movement among sites; and7. Use of GA optimization to minimize total cost of the who

construction/maintenance program.

Resource Depository and Estimate Generation

At the core of the DSM is a simplified storage of the basicsources that are usable in various construction activities~Fig. 1!.Labor and equipment can be used to form crews. Also, crematerials, and/or subcontractors can be used to form stanconstruction methods with resource production rates, similarthe Means approaches~RS Means 2000!. All basic resources andconstruction methods are stored independently for any probeing constructed.

Using the resource depository, the estimating task becomemore than identifying each construction activity~in a given site!,associating one of the construction methods stored in the sysand specifying the quantity of work. At the planning stage, it

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Fig. 2. Activity identification parameters

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possible to specify up to three construction methods for eacactivity and accordingly each activity will have various construction options with their associated resources, durations, and cosas shown on the right side of Fig. 1. For estimating, the followinequations are used, with activity parameters shown in Fig. 2:

Activity duration

di jk5Qi jk

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wheredi jk5duration for activityi using methodj in site k @Eq.~1!#; i5activity number;j5index to the construction method usedin activity i ( j 51, 2, or 3!; k5site number;L5month number~1,2,...,12! in which the activity is scheduled;Qi jk5quantity ofwork for activity i using methodj in site k; Pj5production ratefor the resources involved in methodj, according to the resourcetype ~crew, subcontractor! and their working hours per day; andf kL5productivity factor~.0–1!, depending on the working con-ditions in sitek during monthL, 1> f kL.0.

Activity direct cost


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Ci jk5di jk3ci j (2)

where ci j 5sum of the cost per day for the resources involvesin method j of activity i ~depending on the resource type andits working hours per day!. For example, consider the fourthsite ~k54! in an activity i ( i 51) as shown in Fig. 2, uses itsfirst construction method (j 51) with resource production(P1525 units/day), quantity of work (Q1145100 units), sched-uled approximately in February (L52), and a 0.7 productivityfactor for site 4 in month 2 (f 4250.7). Accordingly, usingEq. ~1!, duration of site 4 of activity 1 using method 1 (d114)5100/(2530.7)55.7 days.

Improved Schedule Presentation

With a large number of sites each having its CPM network, pre-senting the whole schedule in a legible format becomes difficultand bar charts become inadequate. The DSM, therefore, uses aline-of-balance presentation with several improvements as shown

Fig. 3. Flexible options in distributed scheduling model schedule representation


Fig. 4. Impact of site order, considering crew moving time and cost

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in Fig. 3. Fig. 3 shows a schematic schedule for nine sites wvarious flexible features for scheduling an activity: color-codedpattern-coded crews; crew moving time; varying quantities; prductivity impact; crews interruption; crew staggering; crew worsequence; and activities relative speeds~slopes of lines!. Also, toview the nonsequential~parallel! activities, the DSM presents theproject data one path at a time to avoid overlapping.

Site Order: Scheduling Variable

The essence of the DSM is to have the site order as a variablethe schedule formulation. Since any changes in site order resula different project duration and cost, the scheduler has factoriaSways to scheduleS different sites. The effect of varying the siteorder can be clearly observed when crew moving time and coin addition to site productivity factors, are considered in thscheduling process. An example to illustrate this situationshown in Fig. 4, where two site orders were used to schedulework among four sites~A, B, C, and D!. In each site order, thetime and cost to mobilize a crew from one site to the next isdirect function of the distance between the two sites, as follow

Moving time

MT5distance

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Moving cost

MC5distance3moving cost/km (4)

As shown in Fig. 4, site order~b! has shorter distances among thesites and accordingly exhibits a net time saving to the schedulAs such, the best site order can minimize the total project duration and cost. It is noted here that the quantity of work and accordingly activity duration is constant in all sites and only onecrew is employed.

As opposed to constant activity duration, let us consider theffect of site productivity factors on the schedule. For simplicitylet us assume that each site can have one of three productivlevels, depending on the time of the year during which the activity is scheduled: high; medium; and low. Accordingly, activityduration will vary, according to Eq.~1!, depending on the siteproductivity level. Since the quantity and the production rate arconstant, high site productivity translates into a shorter durationFor the same example in Fig. 4, site-specific productivity factorwere introduced as shown in Fig. 5. In this case, varying the sitorder results in changes to activity duration at the individual sitesaccordingly affecting project duration and cost. In Fig. 5, siteorder~a! gives better project duration than site order~b!, althoughthe latter was better in terms of crew moving time~shorter dis-tances!. As such, a proper site order can offset the impact o

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Fig. 5. Impact of varying site order, considering site productivity factors

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productivity factors on project duration. Similarly, selectingfaster construction method can be a measure against project deDetermining the best site order, however, is not an easy taparticularly if all aspects of multiple crews, productivity factorsand optional construction methods are considered together.

Distributed Scheduling Model Formulation

The DSM formulation to construct the schedule has two compnents: crew synchronization calculation to determine the numbof crews for each activity needed to meet project deadline; aassigning the crews to specific sites, according to a given sorder.

Crew Synchronization Calculation to Meet ProjectDeadline

Given a total ofS sites, it is possible to use CPM calculations todetermine the time it takes to complete the first site~CPM dura-tion!. Then, given a deadline duration~DL!, the remaining (S21) sites have to be completed in the remaining time~DL


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2CPM!. As shown in Fig. 6, the desired progress rate cancalculated as follows~Hegazy 2002!:

R5remaining sites

remaining time5

S21

~DL2CPM!(5)

Knowing the desired progress rateR, it is possible to enforce it onall critical activities in order to meet the prespecified deadlinNoncritical activities, on the other hand, can be relaxed and givslower progress rates commensurate with their respective to

Fig. 6. Calculating desired progress rate~R!


Fig. 7. Proposed crew scheduling approach

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float values~Suhail and Neale 1994!. Accordingly, the progresrate needed for any activityi can be calculated as

Ri5S21

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where TFi5total float of activity i. Eq. ~6!, thus, is a generaformula that considers CPM-based float calculations in the scule development and can be applied to both critical and noncal activities. For critical activities, total floats are zeros and~6! is, therefore, reduced to Eq.~5!.

Once the required progress rates for all repetitive activhave been calculated, the number of crews required to acthose rates can be calculated, taking into consideration worktinuity and crew synchronization. A basic relationship that demines the required crews for an activityi to achieve a certaiprogressRi , given the durationdi j that a crew takes to finish onsite without interruption~depending on the method of constrution j used!, is expressed as follows~Hegazy 2002!:

Cri5Ri3di j (7)

The number of crews Cri obtained from Eq.~7!, basically, forcescritical activities to progress in parallel with a rateRi that ensuresmeeting the specified deadline. An important consideration, hever, is that in most cases the number of crews calculated uEq. ~7! is not an integer value. The actual number of crews todeployed, therefore, needs be adjusted and rounded up to thwhole number. Another consideration is that available crewssometimes less than those needed. In this case, the actual nof crews to be used must be limited to the maximum availablesuch, the actual number of crews Crai to be used in any activityibecomes:

Crai5RoundUp~Cri); (8)Crai<maximum available crews

Consequently, the actual progress rate of each activityRai needsto be adjusted based on the actual number of crews Crai as fol-lows:

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It is noted that whenever changes are made to the theorenumber of crews determined by Eq.~7!, due to either rounding orresource limits, the revised crew numbers and progress rates~8! and~9! no longer guarantee that the specified deadline is mWhen resource limits are enforced, some activities will haveuse a smaller number of crews, which will relax their progrerates and cause delays. Based on this discussion, Eqs.~5!–~9! arethe basis for DSM formulation.

Detailed Schedule with Crew Assignments

In the proposed DSM algorithm, one important and useful feais that sites are assigned to the crews, not the opposite. Inapproach, a site is assigned to the first crew that becomes aable for work. As shown in Fig. 7~b!, Crew 1 proceeds to Site 5immediately after it finishes Site 4, because other crews arebusy in other sites. This approach has its potential time savingillustrated in Fig. 7.

During the process of crew assignment, crew movement tiand cost among sites, Eqs.~4! and ~5! are considered. Accordingly, detailed start~ST! and finish~FN! times of each activityi atevery sitek ~notations described in Fig. 8! are calculated as fol-lows:

STiK5min@CFNqp1MTpK# Iq1I>finish time of predecessors

(10)

FNiK5STiK1di jK (11)

wheredi jK 5duration of activityi using construction methodj insite K, this value should be calculated from Eq.~1! consideringproductivity factors.

Cost Optimization Using Genetic Algorithms

The presented DSM model is capable of generating schedulemanually changing the options for construction methods, numof crews, the site order, and the amount of interruption at varisites. However, with the large number of possibilities, even fosmall network of sites, a cost optimization model becomes nessary to identify the optimum combination of these variables


Fig. 8. Calculating start and finish times

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meet schedule constraints. The optimization model involvessetup of the objective function, optimization variables, and opmization constraints, as follows:

Objective Function

The objective function of the model is to minimize total constrution cost, encompassing:~1! direct cost;~2! indirect cost;~3! liq-uidated damages;~4! incentive for early completion; and~5! crewmoving cost.

Variables

The independent variables in the present model areconstruction-method indices for the activities, number of crefor the activities, work interruptions at various sites, and sorder indices. As shown in Fig. 9, the number of variable is larand can be represented by the following equation:

Optimization variables52N1S1~S3N! (12)

166 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEME

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whereN5number of activities andS5number of sites involved.Given that each variable can have different possible values, thsolution space can be extremely large and thus the GAs providemajor advantage over mathematical optimization in finding a so-lution.

ConstraintsAlong with proper ranges for the variables, two soft constraintsare used:1. Project duration should be less than or equal to the deadlin

duration; and2. Total aggregated amount of a given resource is less than o

equal to the amount available.For flexibility, and to reflect the project manager’s objective, allvariables and scheduling options such as considering crew moving time/cost or site productivity factors can be set to on/off dur-ing the optimization.

The cost optimization was implemented as a procedure in thepresent scheduling model. The procedure uses the GA techniqu

Fig. 9. Schedule variables and genetic algorithm representation of solution

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Unlike traditional optimization programs that utilize a hill climbing routine, GA based techniques create an environment whhundreds of possible solutions to a problem can compete with oanother and only the ‘‘fittest’’ survive. Such techniques employpowerful mechanism that searches a wider spectrum of the sotion space to arrive at the global optimum~or near optimum!solution. Using the Visual Basic for Application~VBA ! macrosavailable in Microsoft Project software~MS 2000!, the developedmodel along with the optimization procedure were coded.

Perceived Benefits of Proposed Model

At the network level, developing efficient management systemfor all types of infrastructure networks has attracted, and wcontinue to attract, many researchers from diverse domains.the management side, the work done by Kleiner~2001! andGuignier and Madanat~1999!, for example, presents budget allocation models for infrastructure maintenance, centered oncycle cost analysis. On the technology side, also, extensive sties currently focus on new materials and mechanisms for rehabtation. The work of Srensen and Engelund~1997!, for example,focuses on finding the optimum rehabilitation method~amongthree options! for concrete structures, considering corrosion proability. Such studies are necessary, in conjunction with new dvelopments for facility-condition assessment, to decide on thepropriate technology and the eligible and feasible list of facilitieto be included in municipal construction/maintenance programThe DSM, then, becomes the necessary supplement tool for sporting the actual execution of such programs in a cost effectmanner so that perceived benefits can materialize.

With labor and equipment being the largest contributors to tcost of construction operations, efficient utilization of such rsources becomes a crucial factor for success and profitability.large owner organizations such as municipalities and governmagencies, the proposed DSM model provides many potential befits related to resource management. Determining the numbecrews and their detailed work plan, for example, are beneficialmanpower-planning and financing decisions, particularly whin-house resources are utilized. The DSM model is also beneficin sensitivity analysis studies related to determining the moproper time to start the execution of a construction program.addition, the useful schedule representation used in the DSMthe powerful optimization feature provide a dynamic environmeneeded to meet constraints and decide on proper correctivetions during execution.


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Conclusion

This paper presented the formulation of a DSM for scheduresource planning, and cost optimization in large construcand/or maintenance programs that involve multiple distribsites. The DSM uses GAs to determine the optimum set ofstruction methods and the optimum routing order among sconsidering crew work continuity, crew moving time/cost, asite-dependent work conditions. The proposed model is beneto municipalities and construction/maintenance contractors,can work as a powerful supplement to infrastructure managesystems.

References

Guignier, F., and Madanat, S.~1999!. ‘‘Optimization of infrastructuresystems maintenance and improvement policies.’’J. Infrastruct. Syst.5~4!, 124–134.

Hegazy, T.~2002!. Computer-based construction project managem,Prentice-Hall, Upper Saddle River, N.J.

Hegazy, T., and Ayed, A.~1999!. ‘‘Simplified spreadsheet solutions: Moels for critical path method and time–cost trade-off analysis.’’CostEng.,41~7!, 26–33.

Kleiner, Y. ~2001!. ‘‘Scheduling inspection and renewal of large infstructure assets.’’J. Infrastruct. Syst.,7~4!, 136–143.

Li, H., and Love, P.~1997!. ‘‘Using improved genetic algorithms to fcilitate time-cost optimization.’’J. Constr. Eng. Manage.,123~3!,233–237.

Lumsden, P.~1968!. The line of balance method, Pergamon, London.Microsoft Corporation~MS!. ~2000!. Microsoft project 2000, Redmond

Wash.Moselhi, O., and El-Rayes, K.~1993!. ‘‘Scheduling of repetitive project

with cost optimization.’’J. Constr. Eng. Manage.,119~4!, 681–697.Reda, R.~1990!. ‘‘RPM: Repetitive project modeling.’’J. Constr. Eng

Manage.,116~2!, 316–330.RS Means Company.~2000!. Means building construction cost da,

R. S. Means Company, Kingston, Mass.Senouci, A., and Eldin, N.~1996!. ‘‘A time-cost trade-off algorithm fo

nonserial linear projects.’’Can. J. Civ. Eng.,23, 134–149.Srensen, J. D., and Engelund, S.~1997!. ‘‘Optimal planning of mainte

nance of concrete structures.’’Proc., Int. Workshop on Optimal Peformance of Civil Infrastructural Systems, ASCE, Reston, Va., 169180.

Suhail, S., and Neale, R.~1994!. ‘‘CPM/LOB: New methodology to integrate CPM and line of balance.’’J. Constr. Eng. Manage.,120~3!,667–684.


Distributed Scheduling Model for Infrastructure Networks

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