Improved Lower Bounds for the Capacitated Lot Sizing Problem with Set Up Times

24 Pages Posted: 11 Apr 2006

See all articles by Zeger Degraeve

Zeger Degraeve

London Business School

Raf Jans

Erasmus University Rotterdam (EUR) - Rotterdam School of Management (RSM); HEC Montreal

Date Written: June 2003 5,

Abstract

We present new lower bounds for the Capacitated Lot Sizing Problem with Set Up Times. We improve the lower bound obtained by the textbook Dantzig-Wolfe decomposition where the capacity constraints are the linking constraints. In our approach, Dantzig-Wolfe decomposition is applied to the network reformulation of the problem. The demand constraints are the linking constraints and the problem decomposes into subproblems per period containing the capacity and set up constraints. We propose a customized branch-and-bound algorithm for solving the subproblem based on its similarities with the Linear Multiple Choice Knapsack Problem. Further we present a Lagrange Relaxation algorithm for finding this lower bound. To the best of our knowledge, this is the first time that computational results are presented for this decomposition and a comparison of our lower bound to other lower bounds proposed in the literature indicates its high quality.

Keywords: capacitated lot sizing, Dantzig-Wolfe decomposition, Lagrange relaxation, lower bounds

JEL Classification: M, M11, R4, C61

Suggested Citation

Degraeve, Zeger and Jans, Raf, Improved Lower Bounds for the Capacitated Lot Sizing Problem with Set Up Times (June 2003 5,). ERIM Report Series Reference No. ERS-2003-026-LIS, Available at SSRN: https://ssrn.com/abstract=411667

Zeger Degraeve

London Business School ( email )

Sussex Place
Regent's Park
London, London NW1 4SA
United Kingdom

Raf Jans (Contact Author)

Erasmus University Rotterdam (EUR) - Rotterdam School of Management (RSM) ( email )

P.O. Box 1738
Room T08-21
3000 DR Rotterdam, 3000 DR
Netherlands

HEC Montreal ( email )

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Montreal, Quebec H2X 2L3
Canada
+1 514 340 6834 (Phone)

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