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On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Wu, Tao and Shi, Leyuan and Geunes, Joseph and Akartunali, Kerem (2012) On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times. Journal of Global Optimization, 53 (4). pp. 615-639. ISSN 0925-5001

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Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (l,S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures.

Item type: Article
ID code: 37400
Keywords: equivalence, strong formulation, capacitated, multi-level lot, sizing problems, setup times, Management. Industrial Management, Control and Optimization, Management Science and Operations Research, Applied Mathematics, Computer Science Applications
Subjects: Social Sciences > Industries. Land use. Labor > Management. Industrial Management
Department: Strathclyde Business School > Management Science
Depositing user: Pure Administrator
Date Deposited: 06 Feb 2012 12:08
Last modified: 12 Dec 2015 16:05

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