The robustness of schedule schemes plays an important role for the smooth execution projects under uncertain conditions. This paper presents a new stochastic programming model about the bi-objective robust resource-constrained project scheduling problem with random activity durations, which aims at maximizing the robustness and the probability of timely completion project simultaneously. The robust criterion is measured by the weight sum of buffer times of all activities under resource-constrained case. The method of obtaining time buffers is clarified, and some technical operations to solve the model are carefully addressed when adopting an improved non-dominated sorting genetic algorithm.
Finally, based on a numerical example, the sets of Pareto optimal schedule policies under different combinations of contract makespan and resource limit are gained. The results show that the probability of timely delivery and robust criteria are two mutually conflictive performances under uncertain environments. Therefore, project deciders can choose a proper schedule policy according to their attitudes towards risks and judgments on the extent of uncertainty. Moreover, the model can provide deciders with the set of Pareto optimal schedule policies when they execute projects.