Using Combinations of Heuristics to Schedule Activities of Constrained Multiple Resource Projects

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Using Combinations of Heuristicsto Schedule Activities of Constrained Multiple Resource Projects


<ul><li><p>34</p><p>CPM are referred to jointly in this paper as dence conditions are satisfied and adequate</p><p>Usi oiv</p><p>Const ePERT/CPM.Network analysis is a decision-making tool for</p><p>all levels of management. It may be used at variousstages of project management, from initial plan-ning or analyzing of alternatives to scheduling andcontrolling activities that comprise the project.</p><p>Statement of the ProblemBasic PERT/CPM methods commonly used fornetwork analysis do not consider the availabilityof resources in the scheduling process. The con-</p><p>resources exist, these activities are scheduledaccording to the priorities. Scheduling an activitythat requires multiple resources is more complexthan those requiring only single resources. Allresources needed for the activity must be avail-able before an activity may occur. If only oneresource of several needed is unavailable, thatparticular activity is delayed, while other activi-ties continue to be scheduled according to thepriorities. A setback in any of the critical activi-ties may delay the entire project.CPM is strictly deterministic and with PERTthere is an uncertainty in the activity time esti-mates, the methods within these techniques arequite similar. Both are computer-oriented, definearrow network diagrams, and define the conceptof a critical path. For these reasons, PERT andLucy C. Morse, John O. McIntoshand Gary E. WhitehouseUniversity of Central Florida,Orlando, Florida</p><p>Project managers face ongoing challenges inmanaging projects. A project must beaccomplished in minimum time, with mini-mum cost, and limited resources. Because of eco-nomic factors, the project manager must makethe best use of these limited resources within aspecific time frame. Project managers use a vari-ety of techniques to accomplish this scheduling.</p><p>The most common approaches to projectscheduling are two traditional techniques thatdeveloped in the late 1950s. One is the CriticalPath Method (CPM), the other, Project Evalua-tion and Review Technique (PERT). Although</p><p>ng Combinationsto Schedule Act</p><p>rained Multiple RProject Management Journa</p><p>straints used with these networks are those ofprecedence only. Commercial microcomputerproject management software packages have theability to consider constrained resources. Theproblem according to Johnson [10] is that nopackage consistently finds a schedule in whichthe project completion time is minimized whenresources are considered.</p><p>When resources are taken into consideration,the constraints must consider both precedenceand resource requirements. With limitedresources the beginning time of some activitiesmay be delayed beyond the unconstrained sched-ule. Thus, if a resource is available only in limitedamounts, the schedule produced without consid-ering resources has the potential to be both inac-curate and unfeasible. When resources are limit-ed, the duration of the project could be longer.</p><p>When certain tasks must be coordinated toavoid resource and timing conflicts, the projectmanager seeks guidance on which activities toschedule and which to delay [4]. Also the projectschedule may be dynamic and have a direct rela-tionship with the availability of resources [15].</p><p>The general approach for allocating con-strained resources to activities is to assign priori-ties to the competing activities in the networkaccording to some criterion. When the prece-</p><p>f Heuristicsities of source Projectsl March 1996</p><p>According to Davis [5], existing constrained-resource scheduling procedures may be classifiedinto two major categories. One category is to use</p></li><li><p>er for Distance Learning. Prior toserving as a program manager inthe Engineering Directorate at the</p><p>National Science Foundation, shewas a member of the IndustrialEngineering and ManagementSystems (IEMS) faculty at theUniversity of Central Florida,</p><p>where she received her Ph.D.</p><p>John McIntosh is the assistant chair of the IEMSDepartment at the University ofCentral Florida, where he teachesengineering management cours-es, with an emphasis on costengineering. He has over 11 yearsof industrial management experi-ence with Texas Instruments,General Electric, and others.</p><p>Gary E. Whitehouse is provost and vice presidentfor academic affairs at the Univer-sity of Central Florida. He previ-ously served as dean in the Col-lege of Engineering and chair ofthe IEMS Department. He earnedhis Ph.D. at Arizona State andserved on the faculty at LeighMarch 1996 Proj</p><p>University.Heuristic procedures are capable of quicklysolving complex problems that would be extreme-ly difficult if not impossible to solve otherwise [3].Heuristics might lead to optimal solutions, butthey do not guarantee them. Using different heuris-tic procedures on the same constrained-resourcenetwork can easily produce different durationtimes, since rules that perform well on one prob-lem may perform poorly on another [12]. Manydifferent heuristics exist today. They include thoseoffered by commercial computer programs, elabo-rate and precise computer heuristics, and simplegeneral rules [7]. Since no single heuristic sched-uler is consistently best, commercial project man-agement packages usually do not create optimalschedules when resources are constrained [10].</p><p>Objective of the StudyThe main objective of this study is to find a sim-ple and quick procedure for scheduling activitiesof a constrained multiple-resource single-projectnetwork that will minimize project duration andlower project costs. Based upon the survey ofprevious research [1][3][7][8][13][14], ten simplerule-of-thumb heuristics are selected and appliedto 108 multiple-resource network problems.</p><p>This study then looks at determining the com-bination of heuristics giving the minimum delaytime rather than looking at the top ranking threeor four heuristics. The previous studies haveshown that no one heuristic always produces theminimum duration on every problem. Sincesome rules perform better on certain types ofproblems, a combination of heuristics shouldhave minimum durations for most types of net-work problems. The reason for using combina-tions of heuristics in this evaluation is an attemptto improve the solution of constrained multiple-resource networks.</p><p>This study evaluates constrained multiple-resource networks using combinations of two ormore heuristic methods to allocate theseresources and minimize the total project delay.This is accomplished by first determining projectdurations using a package network schedulingprogram in combination with an additional algo-rithm for allocating resources according to thedifferent heuristic methods. Then with theseresults a combination of two or more heuristicsthat give minimum delay time is determined.</p><p>Description of Network ProblemsFor evaluating the heuristic procedures selected,108 test problems from Pattersons benchmarkproblem set [obtained from James H. Patterson,optimal procedures that produce true minimumduration schedules. The other is to use some pre-determined rule-of-thumb or heuristic to set pri-orities for finding the duration of the project.</p><p>Although optimal procedures produce trueminimum durations, the disadvantage of usingoptimal procedures is the lengthy and complicat-ed computational time [7][9][12]. Optimal pro-cedures using the least computational time arethose involving some form of implicit enumera-tion, such as branch and bound procedures.</p><p>Since for any given problem there are a largenumber of possible combinations of activity starttime, these constrained-resource problems are ina field of mathematical problems known as com-binatorial problems. Analytical methods have notproven very successful on these combinatorialproblems, thus various heuristic-based proce-dures have been developed. Within this study theaccepted definition of a heuristic is Moders [12]:a rule of thumba simple, easy to use aid inproblem solving.</p><p>About the AuthorsLucy Morse is director of the Central Florida Con-sortium of Higher Education and is project manag-ect Management Journal 35</p></li><li><p>36</p><p>Using Combinations of Heuristics to Schedule Activities of Constrained Multiple Resource Projectsproblem set on disk, 1986] with optimal solu-tions and a heuristic solution were used. Accord-ing to Patterson [14], these problems representan accumulation of all readily available multipleresource problems existing in the literature. Thisproblem data set has been previously solved andanalyzed by others using various approaches[2][6][7][10][11][17]. Optimal durations includ-ed with the problem set were obtained by Stin-son Branch and Bound [16]. The number ofactivities included in the test problems variesbetween 7 and 51, with the number of resourcetypes required per activity varying between oneand three with only four networks having lessthan three resources. Of these problems, 89 havebetween 22 and 27 activities and ten problemsconsist of 51 activities.</p><p>In this study, ten simple priority-rule basedheuristics are used to determine priorities foractivities competing for constrained resources.They vary from simple single attribute heuristicto simple multiple attribute heuristic and includerules found effective in previous literature.</p><p>The heuristics used to determine the prioritiesand the explanation of their coding is:</p><p>1. Longest Activity First (LAF): Priority givento the activity with the longest activity.</p><p>2. Shortest Job First (SJF): Priority given tothe activity with the shortest duration.</p><p>3. First Come First Served (FCFS): Priority givento the activity with the lowest activity number.</p><p>4. Latest Finish Time (LFT): Priority given tothe activity with the earliest PERT/CPM calculat-ed late finish time.</p><p>5. Minimum Early Finish (MEF): Prioritygiven to the activity with the earliest PERT/CPMcalculated early finish time.</p><p>6. Minimum Slack First (MSF): Priority givento the activity with the least PERT/CPM calculatedslack time.</p><p>7. Maximum Slack First (Max SF): Prioritygiven to the activity with the greatest PERT/CPMcalculated slack time.</p><p>8. ACTIM: Priority given to the activity withthe maximum ACTIM value. The ACTIM valueof an activity is calculated as the maximum timethat the activity controls through the network onany one path [1].</p><p>9. ACTRES: Priority given to activity with themaximum ACTRES value. The ACTRES value iscalculated by multiplying each activitys time bythe sum of its resources and then finding themaximum ACTRES that an activity controls</p><p>through the network on any one path [1].</p><p>Project Management Journa10. Resources Over Time (ROT): Prioritygiven to the activity with the maximum ROTvalue. The ROT value is calculated by dividingthe sum of each activitys resources by the dura-tion of the activity and then finding the maxi-mum ROT that an activity controls through thenetwork on any one path [8].</p><p>The heuristics are used with the serial approach,with activity priority being determined during thescheduling procedure, but based on PERT/CPMcalculations obtained at the beginning of the sched-uling procedure. For all heuristics, ties are brokenby the lowest activity number first and then oncean activity is started it is not interrupted.</p><p>Formulation of AlgorithmThe project networks were scheduled using anexpanded version of Activity-on-Node NetworkAnalysis published in Project Management: IIEMicrosoftware [18]. Each of the 108 networkproblems was first solved independently usingthe ten heuristic methods previously described. </p><p>With a matrix of problem durations for eachof the ten scheduling heuristics, an attempt now ismade to find what combination of those heuris-tics gives the best results. Best is defined asthe minimum project duration. The combinationis a solution subset of two or more heuristics withgroups lowest mean, not necessarily the group ofheuristics with the lowest individual mean.</p><p>A heuristic computer algorithm was developedto find which combination of heuristics minimizesthe durations of constrained resource project net-works. An important difference between thisalgorithm and other methods used to find the topperforming heuristics for allocating constrainedresources is that the objective here is to findwhich combination or subset of heuristics mini-mizes project duration and meets this objective byfinding the average of the minimum durations.</p><p>ResultsUsing the computer algorithm to find the combi-nation of heuristics giving the best answer wasapplied to the durations of a group of 108 net-work problems. The means of the percentageincrease above optimum for each individualheuristic and each combination of heuristics isgiven in Table 1. As can be seen, the combinationof heuristics performed best. ACTIM with thelowest mean percentage increase is a 5.2 percentincrease above optimum compared to the combi-nation of two heuristics, which is 3.8 percent orthe combination of four heuristics, which is 2.9</p><p>percent above optimum.</p><p>l March 1996</p></li><li><p>tu</p><p>m. .. .. .. .. .. .. .. . . </p><p>l PTable 1. Percentage Increase Above Opand for the Combination of He</p><p>Heuristic Percentage Increase CoMAX SF . . . . . . . . . . . . . 19.9. . . . . . . . . . . . . . . SJF . . . . . . . . . . . . . . . . . 15.7. . . . . . . . . . . . . . . LAF . . . . . . . . . . . . . . . . . 12.5. . . . . . . . . . . . . . . ROT . . . . . . . . . . . . . . . . 12.2. . . . . . . . . . . . . . . MEF . . . . . . . . . . . . . . . . 12.1. . . . . . . . . . . . . . . MSF . . . . . . . . . . . . . . . . 10.9. . . . . . . . . . . . . . . FCFS . . . . . . . . . . . . . . . . 9.9 . . . . . . . . . . . . . . . LFT . . . . . . . . . . . . . . . . . 6.5 . . . . . . . . . . . . . . . ACTRES. . . . . . . . . . . . . . 5.4. . . . . . . . . . . . . . . .ACTIM . . . . . . . . . . . . . . . 5.2</p><p>Table 2. Solution Subset Results for AlA summary of the combination of heuristicsresults is given in Table 2. The size of the solu-tion subset is shown with the heuristic combi-nation for each subset. Also shown is the per-centage increase of the combination ofheuristics above the optimum duration. Thesevalues were obtained by computing the differ-ence (in time units) between the combination ofheuristics minimum duration and the optimumduration for each problem as a percentage ofthe optimum, and then taking the mean of thisdifference.</p><p>Table 2 shows, for example, that when thesolution subset size is four, the combination ofheuristics is ACTIM, LFT, ROT, and ACTRES.Using this combination the percentage increaseof the heuristics above optimum is 2.91 percent.</p><p>In comparing the combination of heuristics inthe solution subset of four to the four individualheuristics with the lowest mean, one heuristic is</p><p>March 1996 Pro</p><p>Subset size 1* 2 3</p><p>Heuristic ACTIM ACTIM ACTIM A</p><p>LFT LFT</p><p>ROT</p><p>A</p><p>Percent IncreaseAbove Optimum 5.2 3.79 3.23</p><p>*Heuristic with lowest mean, not found by algoriimum for Each Individual Heuristicristics</p><p>bination Size Percentage Increase . . . 2 . . . . . . . . . . . . . . . . . . . . 3.8 . . . 3 . . . . . . . . . . . . . . . . . . . . 3.2 . . . 4 . . . . . . . . . . . . . . . . . . . . 2.9 . . . 5 . . . . . . . . . . . . . . . . . . . . 2.8 . . . 6 . . . . . . . . . . . . . . . . . . . . 2.7 . . . 7...</p></li></ul>


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