Relaxations for two-level multi-item lot-sizing problem

Mathieu van Vyve (), Laurence Wolsey () and Hande Yaman
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Mathieu van Vyve: Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium.
Laurence Wolsey: Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium.
Hande Yaman: Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium and Bilkent University

No 2012031, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: We consider several variants of the two-level lot-sizing problem with one item at the upper level facing dependent demand, and multiple items or clients at the lower level, facing independent demands. We first show that under a natural cost assumption, it is sufficient to optimize over a stock-dominant relaxation. We further study the polyhedral structure of a strong relaxation of this problem involving only initial inventory variables and setup variables. We consider several variants: uncapacitated at both levels with or without start-up costs, uncapacitated at the upper level and constant capacity at the lower level, constant capacity at both levels. We finally demonstrate how the strong formulations described improve our ability to solve instances with up to several dozens of periods and a few hundred products.

Keywords: mixed-integer programming; lot-sizing; extended formulation; multi-level; multi-item (search for similar items in EconPapers)
Date: 2012-09-14
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Citations: View citations in EconPapers (1)

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