Multi-mode resource-constrained project scheduling problem with material ordering under bonus–penalty policies

This study emphasizes that project scheduling and material ordering (time and quantity of an order) must be considered simultaneously to minimize the total cost, as setting the material ordering decisions after the project scheduling phase leads to non-optimal solutions. Hence, this paper mathematically formulates the model for the multi-mode resource-constrained project scheduling with material ordering (MRCPSMO) problem. In order to be more realistic, bonus and penalty policies are included for the project. The objective function of the model consists of four elements: the material holding cost, the material ordering cost, the bonus paid by the client and the cost of delay in the project completion. Since MRCPSMO is NP-hard, the paper proposes three hybrid meta-heuristic algorithms called PSO-GA, GA-GA and SA-GA to obtain near-optimal solutions. In addition, the design of experiments and Taguchi method is used to tune the algorithms’ parameters. The proposed algorithms consist of two components: an outside search, in which the algorithm searches for the best schedule and mode assignment, and the inside search, which determines the time and quantity of orders of the nonrenewable resources. First, a comparison is made for each individual component with the exact or best solutions available in the literature. Then, a set of standard PROGEN test problems is solved by the proposed hybrid algorithms under fixed CPU time. The results reveal that the PSO-GA algorithm outperforms both GA-GA and SA-GA algorithms and provides good solutions in a reasonable time.