Optimal Crashing and Buffering of Stochastic Serial Projects

Crashing stochastic activities implies changing their distributions to reduce the mean. This can involve changing the variance too. Therefore, crashing can change not only the expected duration of a project but also the necessary size of its safety buffer. We consider optimal crashing of serial projects where the objective is to minimize total costs including crashing cost and expected delay penalty. As part of the solution we determine optimal safety buffers. They allow for activities that are statistically dependent because they share an error element (e.g., when all durations have been estimated by one person, when weather or general economic conditions influence many activities, etc). We show that under plausible conditions the problem is convex and thus it can be solved by standard numerical search procedures. The purpose of the paper is to encourage software development that will include valid stochastic analysis for scheduling and crashing using current estimates and historical performance records.