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Multi-item lot-sizing with a joint set-up cost

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  • ANILY, Shoshana
  • TZUR, Michal
  • WOLSEY, Laurence A.

Abstract

We consider a multi-item lot-sizing problem in which there are demands, and unit production and storage costs. In addition production of any mix of items is measured in batches of fixed size, and there is a fixed set-up cost per batch in each period. Suppose that the unit production costs are constant over time, the storage costs are nonnegative, and for any two items the one that has a higher storage cost in one period has a higher storage cost in every period. Then we show that there is a linear program with O(mTexp.2) constraints and variables that solves the multi-item lot-sizing problem, thereby establishing that it is polynomially solvable, wheremis the number of items and T the number of time periods. This generalizes an earlier result of Anily and Tzur who presented a O(mTexp.m+5) dynamic programming algorithm for essentially the same problem. Under additional conditions, a similar linear programming result is shown to hold in the presence of backlogging when the batch size is arbitrarily large. Brief computational results on two instances with varying batch sizes are presented and discussed.

Suggested Citation

  • ANILY, Shoshana & TZUR, Michal & WOLSEY, Laurence A., 2005. "Multi-item lot-sizing with a joint set-up cost," LIDAM Discussion Papers CORE 2005070, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2005070
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2005.html
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    References listed on IDEAS

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    1. Shoshana Anily & Michal Tzur, 2005. "Shipping Multiple Items by Capacitated Vehicles: An Optimal Dynamic Programming Approach," Transportation Science, INFORMS, vol. 39(2), pages 233-248, May.
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    Cited by:

    1. Retsef Levi & Andrea Lodi & Maxim Sviridenko, 2008. "Approximation Algorithms for the Capacitated Multi-Item Lot-Sizing Problem via Flow-Cover Inequalities," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 461-474, May.

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