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A batch sizing and scheduling problem on parallel machines with different speeds, maintenance operations, setup times and energy costs

This paper considers a production scheduling problem in a Chilean company from the metalworking industry. This company produces steel balls of different diameters on parallel production lines. There are different types of production lines and each production line may have a different speed for producing each diameter. Furthermore a setup time occurs when changing the diameter produced on each machine. Besides these production and setup operations, maintenance operations have to be scheduled. These electrical machines yield high energy demands. It is therefore crucial to minimize total energy consumption, which depends on batch/machine assignment, and maximum demand on peak hours. We consider the batch sizing and scheduling problem involving electricity costs in a non-uniform parallel machine context. Given a demand for each family of steel balls, the problem consists in splitting the demand in sublots (batches) that have to be assigned and scheduled on the parallel machines together with the required maintenance operations. The goal is to complete the schedule before a common deadline while minimizing electricity costs. We propose to tackle this problem through mixed integer linear programming. We propose a global formulation and a two-phase matheuristic. Computational results on realistic instances are provided.