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A solution approach to the inventory routing problem in a three-level distribution system

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  • Li, Jianxiang
  • Chu, Feng
  • Chen, Haoxun

Abstract

We consider the infinite horizon inventory routing problem in a three-level distribution system with a vendor, a warehouse and multiple geographically dispersed retailers. In this problem, each retailer faces a demand at a deterministic, retailer-specific rate for a single product. The demand of each retailer is replenished either from the vendor through the warehouse or directly from the vendor. Inventories are kept at both the retailers and the warehouse. The objective is to determine a combined transportation (routing) and inventory strategy minimizing a long-run average system-wide cost while meeting the demand of each retailer without shortage. We present a decomposition solution approach based on a fixed partition policy where the retailers are partitioned into disjoint and collectively exhaustive sets and each set of retailers is served on a separate route. Given a fixed partition, the original problem is decomposed into three sub-problems. Efficient algorithms are developed for the sub-problems by exploring important properties of their optimal solutions. A genetic algorithm is proposed to find a near-optimal fixed partition for the problem. Computational results show the performance of the solution approach.

Suggested Citation

  • Li, Jianxiang & Chu, Feng & Chen, Haoxun, 2011. "A solution approach to the inventory routing problem in a three-level distribution system," European Journal of Operational Research, Elsevier, vol. 210(3), pages 736-744, May.
    • Handle: RePEc:eee:ejores:v:210:y:2011:i:3:p:736-744
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    3. Ali Diabat & Claudia Archetti & Waleed Najy, 2021. "The Fixed-Partition Policy Inventory Routing Problem," Transportation Science, INFORMS, vol. 55(2), pages 353-370, March.
    4. Li, Kunpeng & Chen, Bin & Sivakumar, Appa Iyer & Wu, Yong, 2014. "An inventory–routing problem with the objective of travel time minimization," European Journal of Operational Research, Elsevier, vol. 236(3), pages 936-945.
    5. Emre Çankaya & Ali Ekici & Okan Örsan Özener, 2019. "Humanitarian relief supplies distribution: an application of inventory routing problem," Annals of Operations Research, Springer, vol. 283(1), pages 119-141, December.
    6. Ali Ekici & Okan Örsan Özener, 2020. "Inventory routing for the last mile delivery of humanitarian relief supplies," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(3), pages 621-660, September.
    7. Ivanov, Dmitry & Pavlov, Alexander & Sokolov, Boris, 2014. "Optimal distribution (re)planning in a centralized multi-stage supply network under conditions of the ripple effect and structure dynamics," European Journal of Operational Research, Elsevier, vol. 237(2), pages 758-770.
    8. Ali Ekici & Okan Örsan Özener & Gültekin Kuyzu, 2015. "Cyclic Delivery Schedules for an Inventory Routing Problem," Transportation Science, INFORMS, vol. 49(4), pages 817-829, November.

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