An effective methodology for the stochastic project compression problem

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.