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Fast Approximation Algorithms for the One-Warehouse Multi-Retailer Problem Under General Cost Structures and Capacity Constraints

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  • Jean-Philippe Gayon

    (University Grenoble Alpes, CNRS, G-SCOP, 38000 Grenoble, France)

  • Guillaume Massonnet

    (Laboratoire LS2N, IMT-Atlantique, 44300 Nantes, France)

  • Christophe Rapine

    (Université de Lorraine, laboratoire LGIPM, Île du Saulcy, 57045 Metz Cedex 01, France)

  • Gautier Stauffer

    (University Grenoble Alpes, CNRS, G-SCOP, 38000 Grenoble, France)

Abstract

We consider a well-studied multi-echelon (deterministic) inventory control problem, known in the literature as the one-warehouse multi-retailer (OWMR) problem. We propose a simple and fast 2-approximation algorithm for this NP-hard problem, by recombining the solutions of single-echelon relaxations at the warehouse and at the retailers. We then show that our approach remains valid under quite general assumptions on the cost structures and under capacity constraints at some retailers. In particular, we present the first approximation algorithms for the OWMR problem with nonlinear holding costs, truckload discount on procurement costs, or with capacity constraints at some retailers. In all cases, the procedure is purely combinatorial and can be implemented to run in low polynomial time.

Suggested Citation

  • Jean-Philippe Gayon & Guillaume Massonnet & Christophe Rapine & Gautier Stauffer, 2017. "Fast Approximation Algorithms for the One-Warehouse Multi-Retailer Problem Under General Cost Structures and Capacity Constraints," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 854-875, August.
    • Handle: RePEc:inm:ormoor:v:42:y:2017:i:3:p:854-875
    DOI: 10.1287/moor.2016.0830
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    References listed on IDEAS

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    Cited by:

    1. Gautier Stauffer, 2018. "Approximation algorithms for k-echelon extensions of the one warehouse multi-retailer problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 445-473, December.

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