A Simulation Approach to the PERT/CPM Time-Cost Trade-Off Problem

The traditional method of crashing Project Evaluation and Review Technique (PERT) networks ignores the stochastic nature of activity completion times, reducing the stochastic model to a deterministic Critical Path Method (CPM) model and simply using activity time means in calculations. The project is then arbitrarily crashed to some desired completion date, without consideration for what the penalty for late completion of the project is. Additionally, the method ignores the fact that reducing some activity times may reduce the mean project completion time more than others, due to such factors as bottlenecks. The authors use a computer simulation model to determine the order in which activities should be crashed as well as the optimal crashing strategy for a PERT network to minimize the expected value of the total (crash + overrun) cost, given a specified penalty function for late completion of the project. Three extreme network types are examined, each with two different penalty functions.