This research studies production planning problems which appear in manufacturing environments designed to simultaneously produce products of different types. Machines are set up according to specific patterns, templates, or, in general, process configurations. The planning decisions focus on deciding the configurations for the machines and the production level for each configuration to fulfill the given demand in order to minimize the total cost. We propose general decomposition approaches based on the logic-based Benders techniques, which decompose the problem into a master, where configuration decisions are determined, and a set of sub-problems, where production planning decisions are determined. These reformulations are solved using a cutting plane approach, which corresponds to the original logic-based Benders implementation, and a branch-and-check algorithm. Computational experiments on three variants of cutting problems in the steel industry and a planning problem in the printing industry are carried out. Results show that the developed methods generally outperform the benchmark approaches in terms of computing time to find optimal solutions, total number of optimal solutions found, and quality of the solutions.
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