Investigating the Effectiveness of Certain Priority Rules on Resource Scheduling of Housing Estate Projects
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Recep Kanit, Ph.D.1; Murat Gunduz, Ph.D.2; and Omer Ozkan3 Abstract: The heuristic method is one of the methods used for the scheduling of resource-constrained projects. This method is commonly used in programming the projects with high number of activities and resources such as construction investments. This paper investigates the effectiveness of three heuristic method priority rules applied in the resource scheduling of ten Turkish housing estate projects which were scheduled according to three preselected priority rules 关maximum remaining path length 共MRPL兲, latest finish time 共LFT兲, and minimum slack time 共MNSLCK兲兴 in resource-constrained conditions. The performance of each priority rule was evaluated in relation to the duration of the project. The results revealed that MRPL priority reduced the project duration to minimum in six projects, whereas LFT priority yielded the best duration results in three projects and MNSLCK priority in only one project. DOI: 10.1061/共ASCE兲CO.1943-7862.0000021 CE Database subject headings: Construction management; Algorithms; Housing; Scheduling; Turkey.
Introduction The heuristic method is one of the scheduling methods employed in resource-constrained conditions. The heuristic method can be defined as the method that facilitates the process of finding the solution group by means of a simple rule 共Demeulemeester and Herroelen 1992兲. It focuses on two basic concepts: minimizing the time 共Slowinski 1980; Talbot 1982兲 and minimizing the project cost 共Doersch and Patterson 1977; Padman and SmithDaniels 1993; Patterson et al. 1990; Russell 1986; Yang et al. 1993兲. Researchers define priority rules as solution algorithms which minimize project cost and time 共Bell and Han 1991; Boctor 1990; Ulusoy and Ozdamar 1989兲. The effectiveness of the heuristic method has been commonly measured in the literature through comparing certain priority rules 共Wiest 1967兲. When applying a scheduling scheme, priority rules are used in order to select the job to be scheduled next. The priority rules most commonly used in this paper are presented together with definitions in Table 1 共Ozdamar and Ulusoy 1994, 1996a, 1996b; Kolish and Hartman 1998兲. In the first column of Table 1, the name of each rule is given. The second column denotes whether the rule is applied to the job with the smallest 共min兲 or the largest 共max兲 priority value. Finally, the last column describes the computation of the priority rule. For the purposes of this study, a thorough literature review has been carried out, and three priority rules with high performance 1 Professor, Dept. of Technical Education, Gazi Univ., Ankara, Turkey. E-mail:
[email protected] 2 Associate Professor, Dept. of Civil Engineering, Middle East Technical Univ., Ankara, Turkey 共corresponding author兲. E-mail: gunduzm@ metu.edu.tr 3 Assistant Professor, Dept. of Construction Technology, Sakarya Univ., Sakarya, Turkey. E-mail:
[email protected] Note. This manuscript was submitted on March 18, 2008; approved on November 18, 2008; published online on March 27, 2009. Discussion period open until December 1, 2009; separate discussions must be submitted for individual papers. This paper is part of the Journal of Construction Engineering and Management, Vol. 135, No. 7, July 1, 2009. ©ASCE, ISSN 0733-9364/2009/7-609–613/$25.00.
have been selected for comparison. This study differs from the previous ones by the introduction explaining the application of mostly accepted priority rules on housing estate construction projects with resource constraints. Moreover, a clear comparison of maximum remaining path length 共MRPL兲 approach with other commonly used rules could not be found in the literature by the writers. Therefore, an aim of this study is to fill in that gap.
Literature Review The success ratio of the priority rules implemented in heuristic methods greatly depends on the number of available resources and the project size. Abbasi and Arabiat 共2001兲 analyzed 60 projects, in which the cash flow 共based on the present worth of cash requirements for the contractor兲 was classified according to a priority rule that can be described as a combination of the latest start time 共LST兲 and shortest processing time 共SPT兲 methods. This new method, namely late start and shortest processing time offered a higher performance when compared to some other priority rules—such as 共LFT兲 or LST. Ulusoy and Ozdamar 共1995兲 made a comparable analysis on 78 projects through parallel methods using four different priority rules in their study which was administered with nonrenewable resources. Parallel method is a programming strategy that takes into account multiple project decision criteria 共resource constraints, activity durations, slack, etc.兲 at the same time. Minimum slack time 共MNSLCK兲 and LFT gave the best present worth of cash requirements in 24 and 22 projects, respectively. Klein 共2000兲 used different priority rules and figured out that LFT priority yielded the best performance in 36 projects, most total successors 共MTS兲 priority in 20 projects, LST and greatest rank positional weight priority in 19 projects. When the parallel methods were implemented, the priority that produced the best success ratio was the LFT priority with 28 projects. In their research which included 83 different projects, Davis and Paterson 共1975兲 looked at the effectiveness of various priority rules. In their study, the MNSLCK priority gave the best result in 24 projects, and the LFT priority in 12 projects.
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Table 1. Priority Rules Priority rule
Order
Priority rule
Maximum remaining path length 共MRPL兲 Latest start time 共LST兲 Latest finish time 共LFT兲 Shortest processing time 共SPT兲 Most total successors 共MTS兲 Greatest rank positional weight 共GRPW兲 Late start and shortest processing time 共LSSPT兲 Minimum slack time 共MNSLCK兲
Max
TEP − TEi − Sij
Min Min Min Max Max Max
LS j LF j dj Fj d j + 兺i⑀Fid j Fij = T + dij
Min
LS j − ES j
Note: d j = activity time; F j = activity finish time; TEP = project time; and TIE = activity start time.
In their earlier studies, Kanit and Ozkan elaborated on the priority rules MRPL, LFT, and MNSLCK 共Kanit 2004a兲. Depending on the results of a study on road projects, they pointed out that MRPL priority offered the highest performance 共Kanit 2004b兲. Schirmer 共1999兲 scheduled his projects with 30 activities and used eight priority rules, out of which LFT priority showed the highest level of performance in 42 projects. Moreover, MTS and MNSLCK priority gave the best result in 23 and 24 projects, respectively. Hong et al. 共2001兲 presented a resource allocation point that took into account the dynamic and stochastic characteristics of simulation in order to enable the activity-based construction simulation system for the purpose of processing a decisionmaking ability, i.e., allocating the limited resources to the multiple computing activities during simulation. It is clearly seen in the literature that the effectiveness of the priority rules differs from project to project. The writers have conducted a significant amount of survey on the literature and concluded that the MRPL, LFT, and MNSLCK would give the best total project durations and present worth of cash requirements on construction projects. Therefore, the analysis of this study will be based on these three priority rules. In this study, the performance of these priority rules was tested on construction projects which had their own characteristics and resources. To these ends, ten different house estate projects with different numbers of blocks, stores, and apartments were scheduled according to the three aforementioned priority rules. Future studies by the writers will include more projects to draw stronger conclusions. The minimum number of activities in the database is 60.
tivity is defined by its i and j nodes兲 is used. In the second phase, the priorities 共MRPL, LFT, and MNSLCK兲 that will be used by activities are calculated. The activities are programmed in order according to these priorities. Finally, daily resources are checked for each activity: if they are sufficient, the activity is programmed; if not, the next day is checked, controlled, and programmed accordingly. The activity may stop for a day or more if necessary resources cannot be allocated for that day. The starting and stopping of activities could be easily followed by a scheduling software and incur no costs to the end-user. It should be noted that this process takes place before construction work starts. The details for the priority rules utilized in this study are given in the following: 1. In MRPL the time between the start and end of an activity is taken into consideration. This time for each activity is calculated with MRPL = TEP − TEi − Sij
共1兲
time 共the CPM solution value without any where kind of resource limitation兲; TEi = activity start time 共the CPM solution for early start time for the activity without any kind of resource limitation兲; and SiJ = activity slack. The superscript “E” refers to early start time; the subscript “P” refers to total project time; the subscript “i” refers to starting node of the activity; and the subscript “j” refers to ending node of the activity. The calculated MRPL time leads to the programming of the greater process. The activities are programmed according to this priority in order. This priority rule was first used by Brooks and White 共1965兲. LFT for each project is calculated, and the activity with the smallest value of LFT is programmed first. This priority rule was first used by Ahuja 共1976兲. MNSLCK is the ampleness amount of activities. This term can also be defined as the importance level of activities. The ampleness of each activity is calculated with Eq. 共2兲 and the activity with the least ampleness is programmed first. Davis and Patterson 共1975兲 used this priority rule in their studies to find the optimum project time, TEp = project
2.
3.
Sij = LSij − ESij
共2兲
where SiJ = activity slack; LSij = late start time 共the CPM solution for late start time for the activity without any kind of resource limitation兲; and ESij = early start time 共the CPM solution for early start time for the activity without any kind of resource limitation兲.
Project Algorithm and Priority Rules Research Methodology and Implementation For each project, the priority rule that minimizes the project duration should be determined. It should be noted that in resourceconstrained conditions, the priority rules give different results depending on the number of resources, quantity of limitation, and size of the project. The most well-known priority rules with implementation histories are used in the algorithm shown in Fig. 1. Project programming consists of two phases. In the first phase, the project’s CPM solution is programmed without any kind of resource limitation. Then, early start 共ES兲, early finish 共EF兲, lately start 共LS兲, lately finish 共LF兲, start 共S兲, and finish time 共F兲 of the activities are calculated. For critical path method 共CPM兲 calculations, “activity on arrow” notation 共where each ac-
Information about the characteristics of the housing estate projects implemented in this study is given in Table 2. The steps taken for project implementation are as follows: • Project costs were calculated according to the unit prices published periodically by the Turkish Ministry of Housing and Urban Development 共HUD兲. • Time and daily required resource for each activity were determined according to the standards of HUD 共1988兲. • Start and finish nodes of the project, and activity durations were uploaded to a program written in Visual Basic code, and this program determined the ES, EF, LS, LF, S, and F of each activity.
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Read the network data
Determine the priority rule
Reset the time to zero; equate the available resource amount to maximum value
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Make an active list
Choose the unscheduled activity with the highest priority
Calculate the remaining resources
Are there sufficient unutilized resources available to permit this activity to be scheduled over its total duration?
Y
Activity finish time (t)
Schedule the activity N
N
Calculate start and finish times
Calculate the amount of the remaining resources
Is this the last activity?
Y
Each activity scheduled or not?
N
Y
Schedule the next activity with priority
Stop
Fig. 1. Algorithm structure
Table 2. Housing Estate Projects’ Characteristics Project number 1 2 3 4 5 6 7 8 9 10
Project time 共months兲
Activity number
Project cost 共US$兲
Number of blocks
Number of stories
Number of Apartments
9 13 12 13 13 10 11 13 15 20
60 95 71 79 80 77 79 176 176 211
233,000 495,000 242,000 256,000 279,000 402,000 558,000 679,000 644,000 698,000
1 1 1 1 1 2 2 3 3 3
5 10 5 5 5 5 5 5 5 5-10
10 20 10 10 10 20 20 30 30 40
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Table 3. Information about Resource Constraints Materials
Iron 共4 t / day兲 Brick 共3000 unit/ day兲 Sand-crash stone 共40 m3 / day兲 Downloaded from ascelibrary.org by Qatar University Library on 04/17/16. Copyright ASCE. For personal use only; all rights reserved.
Machine equipment
Labor
Cement 共10 t / day兲
Iron craftsman 共8 person/ day兲 Wood craftsman 共8 person/ day兲 Wall craftsman 共8 person/ day兲 Worker 共15 person/ day兲
least project duration was accepted to be the optimal one. The results of the limitless resource and resource-constrained conditions of the projects are given in Table 4. The performance of each rule is tested in this section. Relative deviation for each project is calculated by Eq. 共3兲 in percentage values
Excavator 共1 unit/ day兲
RD共%兲 = 共RCD − d兲/d ⫻ 100
共3兲
where RD= relative deviation of resource constraint duration from original CPM duration with no constraints 共%兲; RCD= resource constraint duration calculated by each rule; and d = original CPM duration with no constraints. The projects with lowest RD values appear in bold in Table 4. It can be concluded from Table 4 that the MRPL priority has the lowest RD values in six projects. LFT and MNSLCK have the lowest RD values for three and one project, respectively. It appears in the related literature that MRPL priority has not been tested for construction projects before. Even though the LFT and MNSLCK priorities have always been known to be powerful in resource-constraint conditions 共Davis and Patterson 1975; Ulusoy and Ozdamar 1995; Schirmer 1999; Klein 2000兲, a clear comparison of these two priorities with the MRPL approach does not exist in the literature to the best of the writers’ knowledge. It should also be noted that the resource limitations for this study are gathered from the practical conditions and kept constant throughout the study. These limitations might differ for other construction projects. In the literature, there is no common rule on when it is best to use a specific priority rule. With this study, the MRPL approach performs better than LFT and MNSLCK approaches. Depending on the results, this study recommends the use of the MRPL approach in construction projects.
• Total resource constraints are presented in Table 3. These constraint values are kept constant for each project for better comparison of performance of priority rules. Resources for each project were allocated according to the values in Table 3. The resource requirements for project activities depend on the available daily total resources. If a project exceeded its resource limit, the required work was delayed to the next day. • The program needed for the analysis had been prepared in Visual Basic. The program took into account the priority rules and constraint conditions. It calculated the start and finish time for each activity, and the amount of resources needed on a daily basis. Then it scheduled the projects and determined each project’s duration 共day兲 by using MRPL, LFT, and, MNSLCK priorities.
Project Results To compare the effect of the priority rules on project duration, the housing estate projects were first scheduled in a limitless resource condition. Next, the critical paths of the projects 共CPM兲, ES, EF, LS, LF, S times, the starting and finishing times of the individual activities 共S and F, respectively兲 were calculated by the program. Afterwards, the projects were scheduled in resource constrained conditions according to the priority rules. The program took into account the daily resource requirements and checked each activity’s resource requirement on a daily basis. If the required resource was more than the available one, then the program delayed the activity to the following day. The resource limits are checked daily and the process is not stopped throughout the concerned day. The process continued until the calculation of the finish time of the last activity. After all these steps, the priority rule with the
Conclusion A thorough literature review reveals that there is no single, best priority rule in limited resource programming problems. Mathematical methods give accurate results when the number of resources is low. When the number of resources increases, heuristic methods do a better job in resource scheduling. In this study, ten different residence projects were programmed with three different heuristic priority rules to examine the project duration performance in construction projects.
Table 4. Projects Results Project number 1 2 3 4 5 6 7 8 9 10
Activity number
CPM duration 共day兲
MRPL
LFT
MNSLCK
MRPL
LFT
MNSLCK
60 95 71 79 88 77 79 176 176 211
170 306 259 312 319 186 226 309 365 522
226 378 324 427 439 235 260 486 595 679
267 394 326 414 422 231 259 537 606 681
255 415 359 411 446 280 262 515 597 706
32,94 23,53 25,10 36,86 37,62 26,34 15,04 57,28 63,01 30,08
57,06 28,76 25,87 32,69 32,29 24,19 14,60 73,79 66,03 30,46
50,00 35,62 38,61 31,73 39,81 50,54 15,93 66,67 63,56 35,25
Priority rules 共day兲
Relative deviation 共%兲
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MRPL priority yielded the shortest duration in six projects, LFT priority in three projects, and MNSLCK priority in one project. In other words, MRPL priority resulted in the shortest project duration in most of the projects in this study when limited resources were used. Therefore, depending on the findings, this study suggests the application of MRPL priority on construction projects. It should be noted that resource limitations for the analysis are from practice and kept constant throughout the study. This study differs from other studies in the literature by the introduction of MRPL into construction projects with high number of activities and resource constraints.
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