Using a meta-heuristic algorithm for solving the multi-mode resource-constrained project scheduling problem

Resource‐constrained project scheduling problem (RCPSP) is one of the most important problems in the context of project scheduling. It consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimised. Robustness is an objective that recently has been noticed. Robustness of the scheduling means that if some activities take more time than the estimated of the scheduling phase, project finish date will not change without any cost. In this paper, a bi‐objective single mode RCPSP is expanded to the multi‐mode resource‐constrained project scheduling problem (MRCPSP) with robustness and makespan criteria. Taking these two objectives in the MRCPSP as a bi‐objective problem and using metaheuristic algorithms to solve it has not been studied until now. A new bi‐objective mathematical model for the problem is presented. The problem formed in this way is NP‐hard, so we apply an evolutionary algorithm named sub‐population genetic algorithm (SPGA) to find Pareto solutions. Standard sets of instances from the project scheduling problem library (PSPLIB) are used and solved by the proposed algorithms to show the efficiency of our algorithm to solve the problem.