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Single-period cutting planes for inventory routing problems

Author

Listed:
  • AVELLA, Pasquale

    (Universita del Sannio, Italy)

  • BOCCIA, Maurizio

    (Universita del Sannio, Italy)

  • WOLSEY, Laurence A.

    (Université catholique de Louvain, CORE, Belgium)

Abstract

IRP involves the distribution of one or more products from a supplier to a set of clients over a discrete planning horizon. Each client has a known demand to be met in each period and can only hold a limited amount of stock. The product is shipped through a distribution network by one or more vehicles of limited capacity. The objective is to find replenishment decisions minimizing the sum of the storage and distribution costs. In this paper we present reformulations of IRP, under the Maximum Level replenishment policy, derived from a single-period substructure. We define a generic family of valid inequalities, and then introduce two specific subclasses for which the separation problem of generating violated inequalities can be solved effectively. A basic Branch-and-Cut algorithm has been implemented to demonstrate the strength of the single-period reformulations. Computational results are presented for the benchmark instances with 50 clients and three periods and 30 clients and six periods.

Suggested Citation

  • AVELLA, Pasquale & BOCCIA, Maurizio & WOLSEY, Laurence A., 2014. "Single-period cutting planes for inventory routing problems," LIDAM Discussion Papers CORE 2014055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2014055
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2014.html
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    References listed on IDEAS

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    3. Coelho, Leandro C. & Laporte, Gilbert, 2014. "Improved solutions for inventory-routing problems through valid inequalities and input ordering," International Journal of Production Economics, Elsevier, vol. 155(C), pages 391-397.
    4. Jean-Claude Picard & H. Donald Ratliff, 1973. "A Graph-Theoretic Equivalence for Integer Programs," Operations Research, INFORMS, vol. 21(1), pages 261-269, February.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    inventory routing; valid inequalities; cutting planes;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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