Logic-based Benders reformulations for integrated process configuration and production planning problems

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We propose a generalized decomposition approach for production planning problems with process configuration decisions. These problems appear in contexts where the machines are set up according to specific patterns, templates, or, in general, process configurations that allow to simultaneously produce products of different types. The problem consists of determining feasible process configurations for the machines and the production level for each used configuration to fulfill the given demand at the minimum total cost. The proposed approaches make use of logic-based Benders reformulations, which decompose the original problem into a master problem, where the configurations are determined, and a set of subproblems, where production planning decisions are determined. These reformulations can either be solved using a cutting plane algorithm or a branch-and-check algorithm. Reformulation enhancements through logic-based inequalities generated for subsets of products with common characteristics are proposed. Computational experiments on applications from the literature in the steel industry and the printing industry are carried out. Results show that the proposed methods find optimal solutions much faster than the benchmark approaches, and have a superior performance in terms of the number of instances optimally solved and solutions quality.

, 21 pages

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