A lexicographic approach to the robust resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) is one of the most studied problems in the context of project scheduling. Given the NP-hardness nature of the problem, the RCPSP has been solved mainly using heuristics. Moreover, most of the studies consider a single objective for the problem. This paper presents an exact approach based on two mixed-integer linear programming (MILP) models to solve the RCPSP. The first MILP aims to minimize makespan, while the second MILP maximizes the robustness of the schedule. The mathematical formulations are solved using a lexicographic approach. We illustrate the effectiveness of the proposed models by solving standard instances for the RCPSP available in the project scheduling problems library (PSLIB) library. Computational results show that it is possible to find alternate optimal solutions with the maximum robustness subject to the minimum makespan for instances with up to 90 activities.