The capacitated lot-sizing and energy efficient single machine scheduling problem with sequence dependent setup times and costs in a closed-loop supply chain network

In this paper, the capacitated lot-sizing and scheduling problem with sequence dependent setup times and costs in a closed loop supply chain is addressed. The system utilizes the closed-loop supply chain strategy so that the multi-class single-level products are produced through both manufacturing of raw materials and remanufacturing of returned recovered products. In this system, a single machine with a limited capacity in each time period is used to perform both the manufacturing and remanufacturing operations. The sequence-dependent setup times and costs (both between two lots of products of different classes and between two lots belonging to the same class of products produced through different methods) are considered. A large-bucket mixed integer programming formulation is proposed for the problem. This model minimizes not only the manufacturing and remanufacturing costs, the setup costs and the inventory holding and backlogging costs over the planning horizon, but also the energy costs paid for the utilization of machine and the compression of processing times. Since the problem is NP-hard, a matheuristic and a grey wolf optimization algorithm are proposed to solve it. To evaluate the efficiency of the proposed algorithm, some experimental instances are generated and solved. The obtained results show the effectiveness of the proposed algorithms.