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Inventory/routing: Reduction from an annual to a short‐period problem

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  • Moshe Dror
  • Michael Ball

Abstract

The inventory‐routing problem is a distribution problem in which each customer maintains a local inventory of a product such as heating oil and consumes a certain amount of that product each day. Given a central supplier, the objective is to minimize the annual delivery costs while attempting to insure that no customer runs out of the commodity at any time. In this article we present a procedure for reducing the long‐term version of this problem to a single‐period problem, which can be attacked using standard routing algorithms. The reduction procedure involves the definition of single‐period costs that reflect long‐term costs, the definition of a safety stock level and a specification of the customer subset to be considered during a single period.

Suggested Citation

  • Moshe Dror & Michael Ball, 1987. "Inventory/routing: Reduction from an annual to a short‐period problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 891-905, December.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:6:p:891-905
    DOI: 10.1002/1520-6750(198712)34:63.0.CO;2-J
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    References listed on IDEAS

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    1. Tan, C.C.R. & Beasley, J.E., 1984. "A heuristic algorithm for the period vehicle routing problem," Omega, Elsevier, vol. 12(5), pages 497-504.
    2. Stewart, William R. & Golden, Bruce L., 1983. "Stochastic vehicle routing: A comprehensive approach," European Journal of Operational Research, Elsevier, vol. 14(4), pages 371-385, December.
    3. Walter J. Bell & Louis M. Dalberto & Marshall L. Fisher & Arnold J. Greenfield & R. Jaikumar & Pradeep Kedia & Robert G. Mack & Paul J. Prutzman, 1983. "Improving the Distribution of Industrial Gases with an On-Line Computerized Routing and Scheduling Optimizer," Interfaces, INFORMS, vol. 13(6), pages 4-23, December.
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    Cited by:

    1. Ann Melissa Campbell & Martin W. P. Savelsbergh, 2004. "A Decomposition Approach for the Inventory-Routing Problem," Transportation Science, INFORMS, vol. 38(4), pages 488-502, November.
    2. Jørgen Glomvik Rakke & Henrik Andersson & Marielle Christiansen & Guy Desaulniers, 2015. "A New Formulation Based on Customer Delivery Patterns for a Maritime Inventory Routing Problem," Transportation Science, INFORMS, vol. 49(2), pages 384-401, May.
    3. le Blanc, H.M. & Cruijssen, F. & Fleuren, H.A. & de Koster, M.B.M., 2006. "Factory gate pricing: An analysis of the Dutch retail distribution," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1950-1967, November.
    4. Anton J. Kleywegt & Vijay S. Nori & Martin W. P. Savelsbergh, 2004. "Dynamic Programming Approximations for a Stochastic Inventory Routing Problem," Transportation Science, INFORMS, vol. 38(1), pages 42-70, February.
    5. Anton J. Kleywegt & Vijay S. Nori & Martin W. P. Savelsbergh, 2002. "The Stochastic Inventory Routing Problem with Direct Deliveries," Transportation Science, INFORMS, vol. 36(1), pages 94-118, February.
    6. Ann Melissa Campbell & Martin Savelsbergh, 2004. "Efficient Insertion Heuristics for Vehicle Routing and Scheduling Problems," Transportation Science, INFORMS, vol. 38(3), pages 369-378, August.
    7. Luca Bertazzi & Giuseppe Paletta & M. Grazia Speranza, 2002. "Deterministic Order-Up-To Level Policies in an Inventory Routing Problem," Transportation Science, INFORMS, vol. 36(1), pages 119-132, February.
    8. Vishal Gaur & Marshall L. Fisher, 2004. "A Periodic Inventory Routing Problem at a Supermarket Chain," Operations Research, INFORMS, vol. 52(6), pages 813-822, December.
    9. Daniel Adelman, 2004. "A Price-Directed Approach to Stochastic Inventory/Routing," Operations Research, INFORMS, vol. 52(4), pages 499-514, August.
    10. Roberto Baldacci & Andrew Lim & Emiliano Traversi & Roberto Wolfler Calvo, 2020. "Optimal Solution of Vehicle Routing Problems with Fractional Objective Function," Transportation Science, INFORMS, vol. 54(2), pages 434-452, March.
    11. Oğuz Solyalı & Haldun Süral, 2011. "A Branch-and-Cut Algorithm Using a Strong Formulation and an A Priori Tour-Based Heuristic for an Inventory-Routing Problem," Transportation Science, INFORMS, vol. 45(3), pages 335-345, August.
    12. Jin-Hwa Song & Martin Savelsbergh, 2007. "Performance Measurement for Inventory Routing," Transportation Science, INFORMS, vol. 41(1), pages 44-54, February.
    13. Claudia Archetti & Luca Bertazzi & Gilbert Laporte & Maria Grazia Speranza, 2007. "A Branch-and-Cut Algorithm for a Vendor-Managed Inventory-Routing Problem," Transportation Science, INFORMS, vol. 41(3), pages 382-391, August.
    14. Yugang Yu & Chengbin Chu & Haoxun Chen & Feng Chu, 2012. "Large scale stochastic inventory routing problems with split delivery and service level constraints," Annals of Operations Research, Springer, vol. 197(1), pages 135-158, August.
    15. Jia Shu, 2010. "An Efficient Greedy Heuristic for Warehouse-Retailer Network Design Optimization," Transportation Science, INFORMS, vol. 44(2), pages 183-192, May.
    16. Lei Lei & Hua Zhong & W. Art Chaovalitwongse, 2009. "On the Integrated Production and Distribution Problem with Bidirectional Flows," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 585-598, November.
    17. Chung-Piaw Teo & Jia Shu, 2004. "Warehouse-Retailer Network Design Problem," Operations Research, INFORMS, vol. 52(3), pages 396-408, June.
    18. Ketzenberg, Michael E. & Metters, Richard D., 2020. "Adapting operations to new information technology: A failed “internet of things” application," Omega, Elsevier, vol. 92(C).
    19. Og̀uz Solyalı & Haldun Süral & Meltem Denizel, 2010. "The one‐warehouse multiretailer problem with an order‐up‐to level inventory policy," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(7), pages 653-666, October.
    20. Leandro C. Coelho & Jean-François Cordeau & Gilbert Laporte, 2014. "Thirty Years of Inventory Routing," Transportation Science, INFORMS, vol. 48(1), pages 1-19, February.

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