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Probabilistic Analyses and Practical Algorithms for Inventory-Routing Models

Author

Listed:
  • Lap Mui Ann Chan

    (Philips Laboratories, Briarcliff Manor, New York)

  • Awi Federgruen

    (Columbia University, New York)

  • David Simchi-Levi

    (Northwestern University, Evanston, Illinois)

Abstract

We consider a distribution system consisting of a single warehouse and many geographically dispersed retailers. Each retailer faces demands for a single item which arise at a deterministic, retailer specific rate. The retailers' stock is replenished by a fleet of vehicles of limited capacity, departing and returning to the warehouse and combining deliveries into efficient routes. The cost of any given route consists of a fixed component and a component which is proportional with the total distance driven. Inventory costs are proportional with the stock levels. The objective is to identify a combined inventory policy and a routing strategy minimizing system-wide infinite horizon costs. We characterize the asymptotic effectiveness of the class of so-called Fixed Partition policies and those employing Zero Inventory Ordering. We provide worst case as well as probabilistic bounds under a variety of probabilistic assumptions. This insight is used to construct a very effective algorithm resulting in a Fixed Partition policy which is asymptotically optimal within its class. Computational results show that the algorithm is very effective on a set of randomly generated problems.

Suggested Citation

  • Lap Mui Ann Chan & Awi Federgruen & David Simchi-Levi, 1998. "Probabilistic Analyses and Practical Algorithms for Inventory-Routing Models," Operations Research, INFORMS, vol. 46(1), pages 96-106, February.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:1:p:96-106
    DOI: 10.1287/opre.46.1.96
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    References listed on IDEAS

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    1. Awi Federgruen & Yu-Sheng Zheng, 1992. "The Joint Replenishment Problem with General Joint Cost Structures," Operations Research, INFORMS, vol. 40(2), pages 384-403, April.
    2. C. R. Carr & C. W. Howe, 1962. "Optimal Service Policies and Finite Time Horizons," Management Science, INFORMS, vol. 9(1), pages 126-140, October.
    3. Julien Bramel & David Simchi-Levi, 1995. "A Location Based Heuristic for General Routing Problems," Operations Research, INFORMS, vol. 43(4), pages 649-660, August.
    4. A. Federgruen & M. Queyranne & Yu-Sheng Zheng, 1992. "Simple Power-of-Two Policies are Close to Optimal in a General Class of Production/Distribution Networks with General Joint Setup Costs," Mathematics of Operations Research, INFORMS, vol. 17(4), pages 951-963, November.
    5. Guillermo Gallego & David Simchi-Levi, 1990. "On the Effectiveness of Direct Shipping Strategy for the One-Warehouse Multi-Retailer R-Systems," Management Science, INFORMS, vol. 36(2), pages 240-243, February.
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