In this work, we model the production planning problem of a supply chain as an extension of the capacitated lot-sizing problem (CLSP). In particular, we consider the problem with setup times and alternative capacity resources at varying cost rates. The goal is to seek a flexible framework that is easily implemented on commercial mathematical programming software systems, and which can be extended to complex variants of the CLSP without changing its underlying approach. We discuss the fundamental structure of the framework which tries to improve the performance of an LP-based approach by reducing the integrality gap through the manipulation of the setup forcing constraints. We also identify the characteristics of good heuristics based on this framework. These characteristics are investigated through a series of computational experiments. The computational experience helps to give insights into the design of heuristics that can be deployed for a large variety of CLSP extensions. Finally, we stress that this framework is only in its embryonic stage and we identify areas for future investigations.
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