Advanced Cross-Entropy in Closed-Loop Supply Chain Planning

Developing new methodologies for nondeterministic polynomial (NP-hard) problems such as supply chain network design is always a major consideration for academia and practitioners. In this paper a cross-entropy (CE) based solution methodology is developed in order to cope with complex combinatorial problems. The NP-hard problem of designing and planning a closed-loop supply chain (CLSC) is considered. Furthermore, a multi-product multi-period CLSC network in a mixed-integer programming structure is regarded. On the other side, cross-entropy is one of the newly developed and successful metaheuristic algorithms. Thus, in order to achieve better solutions in comparison with current solution methodologies, a cross-entropy algorithm is developed for the first time in CLSC design and planning. Then, the capabilities of the cross-entropy algorithm are elevated, in order to achieve solutions that are more robust. Therefore, an algorithm, which is called “advanced cross-entropy” (ACE) is proposed. Finally, two presented CE-based algorithms are compared with a developed genetic algorithm (GA) for the same problem. GA is the most well-known metaheuristic algorithm, which has been abundantly developed in CLSC. Results prove that both of proposed CE-based algorithms dominate current methodologies. Both can find acceptable solutions in comparison with GA. Furthermore, the proposed advanced cross-entropy performs even better than CE in the quality of solutions and time.