An embedded simulation approach for optimal activity crashing in stochastic networks

This paper presents a simulation based method for activity crashing in stochastic networks where the activity durations are uncertain. The objective is to minimize the expected total cost of crashing activities as well as project tardiness. Project evaluation and review technique (PERT) is a well-known deterministic method for dealing with such problems. It usually underestimates the project completion time and does not care about the penalty of project tardiness. Other existing methods for solving this problem are heuristics. We have studied the analytical aspects of the problem and proved the convexity and differentiability of the cost function. We use a sequential quadratic programming (SQP) framework to solve the problem up to the optimality. Monte-Carlo simulation is then applied to evaluate the objective function coefficients and its derivatives at each SQP iteration. The computational results show the advantages of our proposed method in terms of both time and total cost as compared with those of an existing method.