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Stationary Policies in Multiechelon Inventory Systems with Deterministic Demand and Backlogging

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  • Fangruo Chen

    (Columbia University, New York, New York)

Abstract

A stationary policy conducts replenishment activities—the placement and fulfillment of orders—in a stationary fashion. That is, each facility receives a constant batch (facility specific) in equal time intervals (facility specific) under a stationary policy. Although the advantages of stationary policies are clear (i.e., smooth operations), they represent a restriction in policy selection. This paper investigates how costly this restriction can be. For two multiechelon systems (serial and distribution) with deterministic demand and backlogging, we show that stationary policies are 70%-effective. This bound is tight in the sense that an example exists where the bound is reached. On the other hand, the average effectiveness of stationary policies is very high. In a set of 1,000 randomly generated numerical examples, we observed that the average effectiveness was 99%, and the standard deviation was 1.5%. The numerical examples also suggest that the performance of stationary policies deteriorates in systems where the setup cost decreases dramatically from an upstream stage to a downstream stage. Finally, a key building block of the above results is the existing lower bounds on the average costs of all feasible policies in the above systems. We provide a simpler derivation of these bounds.

Suggested Citation

  • Fangruo Chen, 1998. "Stationary Policies in Multiechelon Inventory Systems with Deterministic Demand and Backlogging," Operations Research, INFORMS, vol. 46(3-supplem), pages 26-34, June.
  • Handle: RePEc:inm:oropre:v:46:y:1998:i:3-supplement-3:p:s26-s34
    DOI: 10.1287/opre.46.3.S26
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    References listed on IDEAS

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    1. Joseph S. B. Mitchell, 1987. "98%-Effective Lot-Sizing for One-Warehouse, Multi-Retailer Inventory Systems with Backlogging," Operations Research, INFORMS, vol. 35(3), pages 399-404, June.
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    Cited by:

    1. Boissiere, J. & Frein, Y. & Rapine, C., 2008. "Optimal stationary policies in a 3-stage serial production-distribution logistic chain facing constant and continuous demand," European Journal of Operational Research, Elsevier, vol. 186(2), pages 608-619, April.
    2. Kevin H. Shang & Sean X. Zhou, 2010. "Optimal and Heuristic Echelon ( r, nQ, T ) Policies in Serial Inventory Systems with Fixed Costs," Operations Research, INFORMS, vol. 58(2), pages 414-427, April.
    3. Giannoccaro, Ilaria & Pontrandolfo, Pierpaolo & Scozzi, Barbara, 2003. "A fuzzy echelon approach for inventory management in supply chains," European Journal of Operational Research, Elsevier, vol. 149(1), pages 185-196, August.
    4. Kevin H. Shang, 2008. "Note: A Simple Heuristic for Serial Inventory Systems with Fixed Order Costs," Operations Research, INFORMS, vol. 56(4), pages 1039-1043, August.
    5. P. Majumder & U. K. Bera & M. Maiti, 2020. "An EPQ model of substitutable products under trade credit policy with stock dependent and random substitution," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1205-1243, December.
    6. Marcos Singer & Patricio Donoso & José Noguer, 2005. "Optimal Planning of a Multi-Station System with Sojourn Time Constraints," Annals of Operations Research, Springer, vol. 138(1), pages 203-222, September.
    7. Fangruo Chen, 1999. "94%-Effective Policies for a Two-Stage Serial Inventory System with Stochastic Demand," Management Science, INFORMS, vol. 45(12), pages 1679-1696, December.
    8. Fangruo Chen, 1998. "Echelon Reorder Points, Installation Reorder Points, and the Value of Centralized Demand Information," Management Science, INFORMS, vol. 44(12-Part-2), pages 221-234, December.
    9. Fangruo Chen, 2000. "Effectiveness of (R, Q) policies in one‐warehouse multiretailer systems with deterministic demand and backlogging," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(5), pages 422-439, August.
    10. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.

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