An effective methodology for the stochastic project compression problem

Abstract

In this paper, we consider the problem of planning a complex project when task durations are random. Specifically, we consider the problem of deciding how much to compress tasks in order to minimize the expected total cost that is defined by the sum of direct, indirect, and incentive costs. We initially consider this problem under the assumption that task durations can be modeled by a negative exponential distribution although we later relax this assumption and show that our methodology can be applied to any general distribution. To solve this problem, we develop an effective heuristic algorithm that we call the Stochastic COmpression Project (SCOP) algorithm; the SCOP algorithm is straightforward to implement and our numerical tests indicate that the algorithm performs significantly better than previously reported heuristics. In addition, we compare our approach to solutions found using expected values embedded in a deterministic approach (an approach that is frequently used to solve this problem in practice). Using our results, we show that the deterministic approximation approach, such as the classic PERT model, provides biased results and should be avoided.

Keywords:

• Project management
• project scheduling
• stochastic compression/crashing
• time-cost trade-offs

Acknowledgements

The authors gratefully acknowledge helpful comments from Professors K. Moinzadeh and T. Rockefellar as well as the Burlington Northern/Burlington Resources Foundation that provided support for the second author. The authors gratefully acknowledge the assistance of several anonymous referees whose comments have significantly improved this paper.

Notes

¹This assumption has been widely used in previous research, including papers on PM by Buss and Rosenblatt (1997) and also Kulkarni and Adlakha (1986).

²We conducted studies with as few as ten, and as many as 100, tasks per activity network. In all cases, the results were consistent with those presented here for 30-task networks.

³We conducted experiments with a variety of simulated trials from 100 to 25 000 activity time realizations per activity. The results were consistent with those reported here for 5000 simulated trials.

⁴Each experiment represents the results of 5000 randomly generated combinations of activity networks and indirect cost rates.