Towards a More Effective Method of Scheduling
Resource-Constrained Multiple Projects
Operations Planning, Scheduling and Control
There has been much research examining the issues of planning and controlling projects in the multiple project resource constrained environment but little agreement on the best method to schedule such projects. In 1998 Rob Newbold published Project Management in the Fast Lane in which he applied the principles of theory of constraints to the management of single projects and revolutionized the way single projects are managed. This presentation will present a DBR-based approach to scheduling resource-constrained multiple projects and will also present the results of a simulation comparing the proposed heuristic with more conventional methods.
Edward D. Walker II, P.O. Box 8152, Dept. of IS & L, Georgia Southern University, Statesboro, GA 30460, Phone (912) 681-5085,
In this paper a resource scheduling heuristic and a buffering heuristic for resource-constrained multiple projects are presented. The results of a simulation comparing the execution PERT-based and Drum-Buffer-Rope(DBR)-based plans is presented. The statistical analysis provides evidence that a multiple project DBR-based approach might be more effective than methods previously examined.
First a brief review of the literature is presented followed by a presentation of the projects and planning parameters. The results of a simulation comparing PERT-based and DBR-based methods of project management are presented. Finally, the results are interpreted and discussed.
Upon examining recent research on multiple projects with constrained resources, it is readily apparent that the assumption made by most researchers is that once a “proper plan” is created there is little need for control. Recent research in the area of multiple project planning and control has recognized several shortcomings of the PERT/CPM method. Researchers have explored resource assignment rules to better execute multiple projects (e.g. Abdel-Hamid, 1993; Allam, 1988; Bock and Patterson, 1990; Dean, et al., 1992; Deckro, et al., 1991; Kim and Leachman,1993; Kurtulus and Davis, 1982; Kurtulus, 1985; and, Kurtulus and Narula, 1985; Lawrence and Morton, 1993; Lee, et al.,1978; Mohanty and Siddiq, 1989; Speranza and Vercellis, 1993; Trypia, 1980; Tsai and Chiu ,1996; Vercellis, 1994; Yang and Sum,1993) and have investigated the issue of multiple project control on both an organizational basis (e.g. Coulter, 1990; Payne, 1995; Platje and Seidel, 1993) and a tactical basis (e.g. Dumond and Dumond, 1993; and, Tsubakitani and Deckro, 1990). With the exception of Dumond and Dumond (1993) and Tsubakitani and Deckro (1990), the recent research has examined a static multiple project environment.
The investigations into the planning and control functions have found several fundamental characteristics inherent in multiple projects:
1.Multiple projects are interdependent due to the use of common resources.
2.Some method must be used to prioritize the use of resources among multiple projects.
3.There is some trade-off between utilization of resources and the on-time completion of individual projects.
4.Whether organizational or tactical, a control mechanism must exist to reduce the variance between planned and actual project completion dates.
These characteristics reflect fundamental problems in the way that multiple projects are currently planned and controlled.
In above research, the authors have uniformly tested resource assignment rules that have been applied as the projects are executed. It is the position of this author that creating a plan for resource assignment a priori might be a better approach. The heuristic used to create such a plan is presented below.
1.Assemble all known projects.
2.Calculate the PERT critical path for each project i to establish ES/EF and LS/LF dates for each activity.
3.Assemble the planned start date for each projecti — i.e., the date on which the individual project is to be started.
4.Let Tnow = 0. For each projecti let Psi equal the number of periods into the future that projecti is planned to start.
5.For each projecti let
ES = ES + Psi (1)
EF = EF + Psi (2)
LS = LS + Psi (3)
LF = LF + Psi (4)
for all activities in projecti. This adjusts all PERT plans to reflect the staggered start dates.
6.Create a dummy activity named “start of planning horizon” prior to the earliest start date among all activities from all projects and create a dummy activity named “end of planning horizon” after the latest early finish date among all activities from all projects.
7.Assign resources across all projects using a resource leveling heuristic. Figure 1 shows a modified Wiest and Levy heuristic.
8.Add start and end nodes for each projecti. Calculate the individual project critical chain in a multiple project environment completion (CCMPC) for each projecti and the slack associated with each activity from the “start of planning horizon” node to the “end of project i” node using PERT/CPM-style forward and backward passes considering resource contention (indicated by dummy arrows – Figure2).
9.Insert appropriate buffers (convergence, resource contention, and project completion) to protect the CCMPC of each projecti (Figure 3). Execute. STOP.
See Figure 1
See Figure 2
See Figure 3
Simulation Comparison of PERT-based and DBR-based Project Management
An AweSim simulation compared two PERT-based and two DBR-based project management methods. The four methods are as follows: all projects scheduled and executed as if they were independent PERT projects (SPPERT); all projects scheduled and executed as if they were independent DBR-based projects (SPDBR); all projects scheduled and executed as if they were a set of PERT projects (MPPERT); all projects scheduled and executed as if they were a set of DBR-based projects (MPDBR). The projects used for the simulation were developed by the author as representative of large projects with moderate resource contention.
The treatment of certain parameters within each project plan were addressed: when activities would be started; how would the resources be leveled; and, how large should the various buffers be. Each of these three questions is addressed in Table I for each of the four project management schemes. After each plan was developed, the AweSim simulation language was used to simulate the execution of each plan on the selected set of projects. No effort was made to control the projects during execution.
See Table I
Presentation of Results
The descriptive statistics are reported in Table II for each of three primary measures upon which the project planning heuristics were to be evaluated — percent of projects completed before the planned completion date (% early completion); mean lateness as a percent planned project duration (mean % late); and, mean earliness as a percent planned project duration (mean % early). [Also reported in Table II are the descriptive statistics of mean project tardiness in days (Yang & Sum, 1993).]
The basic design of the experiment was a 2x2 ANOVA and the two factors were: 1), the factor considering the planning method used — PERT/CPM-based planning method or DBR-based planning method (PLAN); and 2), the factor considering the network of the projects as single projects or as a mega-project (NETWORK). Table III reports that the interaction effects for all measures are significant to = .001. Two of these measures (% early completion and mean % early) have an Fmax > 9; therefore all statistical comparisons must be interpreted carefully. To be assured of a level of significance of = .05, the critical values of F are reported for = .05, = .01, and = .001.
By examining Table II one can determine that the interactions are ordinal when comparing DBR-based plans to PERT-based plans. In the case of ordinal interactions the main effects may be interpreted directly (Keppel, 1991, p. 235). The calculated F values for the main effects are reported in Table III. The main effects of PLAN and NETWORK for each of the three summary measures were found to be significant ( = .001). There is a difference between the type of PLAN used (PERT v. DBR) and also the type of network used (SP v. MP).
Table IV reports the F values for the cell means comparisons. Recall that a buffer was added to the planned project completion date (25 days for the single project NETWORK and 30 days in the mega-project NETWORK) under both planning methods (DBR-based PLAN and PERT-based PLAN). These buffers were inserted to protect the projects from the uncertainty of activity duration. It is also worth noting that the buffers inserted into the PERT-based plans represent a larger percentage of planned project duration than the buffers inserted into the DBR-based plans.
Discussion of results
The interaction effects were found to be significant for all of the summary measures. Since the interactions of the three measures were ordinal, one can proceed to the interpretation of main effects. The fact that the main effects for each of the summary measures was significant demonstrates that there are differences associated with the PLAN and NETWORK factors in the analysis. The DBR-based methods had: a greater percentage on early project completions; had a smaller mean project lateness as a percent of planned project duration; and, a larger mean project earliness as a percent of planned project duration.
Overall, the newly developed heuristic performed better than the competing heuristics on all summary measures in the multiple project environment. A strong indication for this conclusion is provided by the extremely high F values. It is also worth noting that the significant interaction effects provide evidence that the single project DBR-based method also performed better than either of the PERT-based methods.
The proposed heuristic performed better than any of the other treatments on the measures of mean percent of early project completions, mean lateness as a percent of planned project duration, and mean earliness as a percent of planned project duration.
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Figure 1: Wiest and Levy resource leveling heuristic modified to accomodate multiple copies of each resource and multiple projects.
Figure 2: Identifying the individual project critical chain in a multiple project environment completion (CCMPC).
Figure 3: Buffering points of convergence with the CCMPC of individual projects in a multiple project environment.
Table I: Project planning parameters for each of the four treatments.Treatment / When activities start / Resources leveling / Buffer size
SPPERT / Critical – no sooner than early start;
Non-critical – consume ½ PERT slack / First-come/first-served / 25-day project completion
MPPERT / Critical – no sooner than early start;
Non-critical – consume ½ PERT slack / First-come/first-served / 30-day project completion
SPDBR / Critical – upon completion of prior activity;
Non-critical – no sooner than early start modified to reflect buffer size / Wiest and Levy within projects;
First-come/first-served across projects / 25-day project completion;
MPDBR / Critical – upon completion of prior activity;
Non-critical – no sooner than early start modified to reflect buffer size / Modified Wiest and Levy within and across projects / 30-day project completion;
* Unless existing natural buffer was smaller.
Table II: Descriptive statistics of the summary measures reported by planning heuristic.MPPERT / MPDBR / SPPERT / SPDBR
Mean / StdDev / Mean / StdDev / Mean / StdDev / Mean / StdDev
% early completion / 0.00% / 0.0000 / 15.24% / 0.0775 / 0.00% / 0.0000 / 0.32% / 0.0121
mean % late / 196.62% / 0.1341 / 18.61% / .03652 / 62.59% / 0.6201 / 54.01% / 0.0532
mean % early / 0.00% / 0.0000 / 3.79% / 0.0154 / 0.00% / 0.0000 / 0.10% / 0.0045
Days late / 387.83 / 25.91 / 41.26 / 10.09 / 109.52 / 27.57 / 98.60 / 18.77
Table III: The calculated F values for the interaction effect of PLAN x NETWORK and for the main effects of PLAN and NETWORK for each of the summary measures. (All are significant at = .001)Summary Measure / Interaction effect / Main effect PLAN
(PERT v. DBR) / Main effect NETWORK
(SP v. MP)
% early completion / 108.578 / 118.0153 / 108.5780
mean % late / 3294.360 / 3996.7010 / 1112.5110
mean % early / 158.204 / 175.9867 / 158.2042
Table V: The calculated F values for cell means comparisons for each of the summary measures. (* Significant at = .001)Summary Measure / SPDBR v. MPDBR / SPPERT v. MPPERT / SPDBR v. SPPERT / MPDBR v. MPPERT
% early completion / * 217.1559 / 0.0000 / 0.0983 / * 226.4949
mean % late / * 289.0133 / * 4117.8570 / * 16.9534 / * 7274.1070
mean % early / * 316.4084 / 0.0000 / 0.2367 / * 333.9542
Proceedings of the Twelfth Annual Conference of the Production and Operations Management Society, POM-2001, March 30-April 2, 2001, Orlando FL