A stochastic bi-objective project scheduling model under failure of activities

In this paper, the research and development project scheduling problem ( RDPSP ) under uncertain failure of activities is formulated where an activity’s failure results in the project’s overall failure. A scenario-based bi-objective model to maximize the expected net present value ( eNPV ) and to minimize the NPV ’s risk by conditional value-at-risk ( CVaR ) measurement is presented. For this purpose, different modes of failure or success of activities have been considered as a stochastic parameter by a set of scenarios. To formulate the problem, a nonlinear model is first presented, then a mixed-integer programming ( MIP ) model of the problem is developed by piecewise approximation. Some valid inequalities are presented to improve the performance of the MIP model. A sequential sampling procedure is also used to approximate the solution of the MIP model with a large number of scenarios. The experimental results have shown that the sequential sampling procedure attains high-quality solutions in a reasonable CPU time.