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The multi-level lot sizing problem with flexible production sequences

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  • Joseph Begnaud
  • Saif Benjaafar
  • Lisa Miller

Abstract

This paper considers a multi-level/multi-machine lot sizing problem with flexible production sequences, where the quantity and combination of items required to produce another item need not be unique. The problem is formulated as a mixed-integer linear program and the notion of echelon inventory is used to construct a new class of valid inequalities, which are called echelon cuts. Numerical results show the computational power of the echelon cuts in a branch-and-cut algorithm. These inequalities are compared to known cutting planes from the literature and it is found that, in addition to being strong and valid for the flexible production case, echelon cuts are at least as strong as certain classes of known cuts in the restricted fixed production setting.

Suggested Citation

  • Joseph Begnaud & Saif Benjaafar & Lisa Miller, 2009. "The multi-level lot sizing problem with flexible production sequences," IISE Transactions, Taylor & Francis Journals, vol. 41(8), pages 702-715.
    • Handle: RePEc:taf:uiiexx:v:41:y:2009:i:8:p:702-715
    DOI: 10.1080/07408170902736697
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    Cited by:

    1. Wei, Mingyuan & Qi, Mingyao & Wu, Tao & Zhang, Canrong, 2019. "Distance and matching-induced search algorithm for the multi-level lot-sizing problem with substitutable bill of materials," European Journal of Operational Research, Elsevier, vol. 277(2), pages 521-541.
    2. Jing, Fuying & Chao, Xiangrui, 2022. "Forecast horizons for a two-echelon dynamic lot-sizing problem," Omega, Elsevier, vol. 110(C).
    3. Simon Thevenin & Yossiri Adulyasak & Jean-François Cordeau, 2022. "Stochastic Dual Dynamic Programming for Multiechelon Lot Sizing with Component Substitution," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3151-3169, November.

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