We study single-item discrete multi-module capacitated lot-sizing problems where the amount produced in each time period is equal to the summation of binary multiples of the capacities of n available different modules (or machines). For fixed n≥2, we develop fixed-parameter tractable (polynomial) exact algorithms that generalize the algorithms of van Vyve (2007) for n=1. We utilize these algorithms within a Lagrangian decomposition framework to solve their multi-item versions. Furthermore, our algorithms are computationally efficient and stable, in comparison to Gurobi 9.0.
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