Integrated lot sizing and energy-efficient job shop scheduling problem in manufacturing/remanufacturing systems

In this paper, a system designed to produce multi-class single-level products through both manufacturing of raw materials and remanufacturing of return products is taken into consideration, with the aim of defining and solving an integrated lot sizing and energy-efficient job shop scheduling problem. A mixed-integer programming formulation is proposed for the problem. This model minimizes not only the manufacturing and remanufacturing costs, the setup cost and the inventory holding and backlogging costs over the planning horizon, but also the energy costs paid for the utilization of machines and the compression of processing times. Since the model is NP-hard, a relax-and-fix heuristic is proposed to solve the problem. The proposed algorithm is illustrated with a numerical example, and its performance is tested on a set of randomly generated experimental problems. The results show the efficiency of the algorithm. Besides, the performance of the proposed energy-efficient model has been compared with classical models (that consider only the minimization of manufacturing/remanufacturing, holding and setup costs); the results indicate that the proposed model not only diminishes the energy consumption and the machines idle times, but it actually reduces the overall cost of the system.