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Two‐echelon distribution systems with random demands and storage constraints

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  • Awi Federgruen
  • C. Daniel Guetta
  • Garud Iyengar

Abstract

We consider a general two‐echelon distribution system consisting of a depot and multiple sales outlets, henceforth referred to as retailers, which face random demands for a given item. The replenishment process consists of two stages: the depot procures the item from an outside supplier, while the retailers' inventories are replenished by shipments from the depot. Both of the replenishment stages are associated with a given facility‐specific leadtime. The depot as well as the retailers faces a limited inventory capacity. Inventories are reviewed and orders are placed on a periodic basis. When a retailer runs out of stock, unmet demand is backlogged. We propose a new approach to the above class of dynamic programming models based on Lagrangian relaxation. Every choice of the vector of Lagrange multipliers generates a lower bound via the solution of a single dynamic program (DP) with a one‐dimensional state‐space. The best such bound is obtained by maximizing over the vector of multipliers. The strategy that is optimal for this (maximal) lower bound DP employs an (s, S) ordering policy (generally, with time‐dependent policy parameters). To arrive at an upper bound and an implementable heuristic, this (s, S) policy is paired with one of several possible allocation policies that allocate the system‐wide inventory across the different facilities. We report on an extensive numerical study with close to 14 000 instances which evaluates the accuracy of the lower bound and the optimality gap of the various heuristic policies. The study reveals that the lower bound and the heuristic strategy that is constructed on its basis perform exceedingly well, almost across the entire parameter spectrum, including instances where demands are rather volatile or the average cycle time between consecutive orders is relatively large. The exception arises when storage at the depot is as expensive as at the retailer level and the retailers have large storage capacities.

Suggested Citation

  • Awi Federgruen & C. Daniel Guetta & Garud Iyengar, 2018. "Two‐echelon distribution systems with random demands and storage constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 594-618, December.
    • Handle: RePEc:wly:navres:v:65:y:2018:i:8:p:594-618
    DOI: 10.1002/nav.21825
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    1. Ganesh Janakiraman & John A. Muckstadt, 2009. "A Decomposition Approach for a Class of Capacitated Serial Systems," Operations Research, INFORMS, vol. 57(6), pages 1384-1393, December.
    2. Paul H. Zipkin, 1980. "Simple Ranking Methods for Allocation of One Resource," Management Science, INFORMS, vol. 26(1), pages 34-43, January.
    3. Kunnumkal, Sumit & Topaloglu, Huseyin, 2011. "Linear programming based decomposition methods for inventory distribution systems," European Journal of Operational Research, Elsevier, vol. 211(2), pages 282-297, June.
    4. Johan Marklund & Kaj Rosling, 2012. "Lower Bounds and Heuristics for Supply Chain Stock Allocation," Operations Research, INFORMS, vol. 60(1), pages 92-105, February.
    5. Edward Ignall & Arthur F. Veinott, Jr., 1969. "Optimality of Myopic Inventory Policies for Several Substitute Products," Management Science, INFORMS, vol. 15(5), pages 284-304, January.
    6. Donald L. Iglehart, 1963. "Optimality of (s, S) Policies in the Infinite Horizon Dynamic Inventory Problem," Management Science, INFORMS, vol. 9(2), pages 259-267, January.
    7. Yu-Sheng Zheng & A. Federgruen, 1991. "Finding Optimal (s, S) Policies Is About As Simple As Evaluating a Single Policy," Operations Research, INFORMS, vol. 39(4), pages 654-665, August.
    8. Awi Federgruen & Paul Zipkin, 1984. "Approximations of Dynamic, Multilocation Production and Inventory Problems," Management Science, INFORMS, vol. 30(1), pages 69-84, January.
    9. Awi Federgruen & Paul Zipkin, 1984. "Allocation policies and cost approximations for multilocation inventory systems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(1), pages 97-129, March.
    10. Xiuli Chao & Sean X. Zhou, 2009. "Optimal Policy for a Multiechelon Inventory System with Batch Ordering and Fixed Replenishment Intervals," Operations Research, INFORMS, vol. 57(2), pages 377-390, April.
    11. Gabriel R. Bitran & Arnoldo C. Hax, 1981. "Disaggregation and Resource Allocation Using Convex Knapsack Problems with Bounded Variables," Management Science, INFORMS, vol. 27(4), pages 431-441, April.
    12. Awi Federgruen & Paul Zipkin, 1984. "Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model," Operations Research, INFORMS, vol. 32(4), pages 818-836, August.
    13. Guillermo Gallego & Özalp Özer & Paul Zipkin, 2007. "Bounds, Heuristics, and Approximations for Distribution Systems," Operations Research, INFORMS, vol. 55(3), pages 503-517, June.
    14. Awi Federgruen & Henri Groenevelt, 1986. "The Greedy Procedure for Resource Allocation Problems: Necessary and Sufficient Conditions for Optimality," Operations Research, INFORMS, vol. 34(6), pages 909-918, December.
    15. Sumit Kunnumkal & Huseyin Topaloglu, 2008. "A duality‐based relaxation and decomposition approach for inventory distribution systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(7), pages 612-631, October.
    16. Peter L. Jackson, 1988. "Stock Allocation in a Two-Echelon Distribution System Or "What to Do Until Your Ship Comes In"," Management Science, INFORMS, vol. 34(7), pages 880-895, July.
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