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Improved Lower Bounds For The Capacitated Lot Sizing Problem With Set Up Times

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  • Degraeve, Z.
  • Jans, R.F.

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.

Suggested Citation

  • Degraeve, Z. & Jans, R.F., 2003. "Improved Lower Bounds For The Capacitated Lot Sizing Problem With Set Up Times," ERIM Report Series Research in Management ERS-2003-026-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:326
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    File URL: https://repub.eur.nl/pub/326/ERS-2003-026-LIS.pdf
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    References listed on IDEAS

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    1. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    2. Prabhakant Sinha & Andris A. Zoltners, 1979. "The Multiple-Choice Knapsack Problem," Operations Research, INFORMS, vol. 27(3), pages 503-515, June.
    3. Gaetan Belvaux & Laurence A. Wolsey, 2000. "bc --- prod: A Specialized Branch-and-Cut System for Lot-Sizing Problems," Management Science, INFORMS, vol. 46(5), pages 724-738, May.
    4. Alan S. Manne, 1958. "Programming of Economic Lot Sizes," Management Science, INFORMS, vol. 4(2), pages 115-135, January.
    5. Gary D. Eppen & R. Kipp Martin, 1987. "Solving Multi-Item Capacitated Lot-Sizing Problems Using Variable Redefinition," Operations Research, INFORMS, vol. 35(6), pages 832-848, December.
    6. BELVAUX, Gaëtan & WOLSEY, Laurence A., 2000. "bc-prod: A specialized branch-and-cut system for lot-sizing problems," LIDAM Reprints CORE 1455, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
    8. Pisinger, David, 1995. "A minimal algorithm for the multiple-choice knapsack problem," European Journal of Operational Research, Elsevier, vol. 83(2), pages 394-410, June.
    9. Bernard P. Dzielinski & Ralph E. Gomory, 1965. "Optimal Programming of Lot Sizes, Inventory and Labor Allocations," Management Science, INFORMS, vol. 11(9), pages 874-890, July.
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    Cited by:

    1. Glomb, Lukas & Liers, Frauke & Rösel, Florian, 2022. "A rolling-horizon approach for multi-period optimization," European Journal of Operational Research, Elsevier, vol. 300(1), pages 189-206.

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    More about this item

    Keywords

    Dantzig-Wolfe decomposition; Lagrange relaxation; capacitated lot sizing; lower bounds;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics

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