integration of multi-mode resource-constrained project scheduling under bonus-penalty policies with material ordering under quantity discount scheme for minimizing project cost

In this paper a mixed binary integer mathematical programming model is developed for integration of multimode resource-constraint project scheduling problem (mrcpsp) under bonus–penalty policies and quantity discount problem in material ordering (qdpmo) with the objective of minimizing the total project cost. by proving a theorem, an important property of the optimum solution of the problem is found which reduces the search space significantly compared to previous studies. since the rcpsp belongs to the class of problems that are np-hard, four hybrid meta-heuristic algorithms called coa-ga, gwo-ga, pso-ga and ga-ga is developed and tuned to solve the problem. each of the proposed algorithms consists of outside and inside search components, which determine the best schedule, and materials procurement plan respectively. finally a set of standard progen test problems is solved by the proposed hybrid algorithms under fixed cpu time. the results show that the coa-ga algorithm outperforms others.