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Backorders optimization in a one‐warehouse N‐identical retailer distribution system

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  • Ralph D. Badinelli
  • Leroy B. Schwarz

Abstract

This article examines the allocation of safety stock between sectors in a one‐warehouse N‐retailer distribution system which follows a (Q,R) inventory replenishment policy. In particular, the so‐called „portfolio”︁ motive for holding warehouse safety‐stock inventory is investigated. Two optimization problems involving the tradeoff between average system inventory investment and customer service, i.e., customer backorders, are considered and shown to be equivalent to a simpler optimization problem involving the tradeoff between customer service and system safety stock. Equivalence implies that the set of optimal policies for the simpler optimization problem provides all of the optimal policies for the more complex ones. This equivalence result is applied to the Deuermeyer and Schwarz (DS) model of the distribution system under study. Bounds on the set of optimal policies are provided. A heuristic for minimizing expected backorders with respect to a constraint on average system on‐hand inventory is introduced, and empirical tests described. The heuristic, which prescribes little warehouse on‐hand inventory, appears to be near optimal for the DS model. A simulation study supports this „near‐zero”︁ inventory prescription for the warehouse.

Suggested Citation

  • Ralph D. Badinelli & Leroy B. Schwarz, 1988. "Backorders optimization in a one‐warehouse N‐identical retailer distribution system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 427-440, October.
    • Handle: RePEc:wly:navres:v:35:y:1988:i:5:p:427-440
    DOI: 10.1002/1520-6750(198810)35:53.0.CO;2-U
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    References listed on IDEAS

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    1. 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.
    2. Panayotis Afentakis & Bezalel Gavish & Uday Karmarkar, 1984. "Computationally Efficient Optimal Solutions to the Lot-Sizing Problem in Multistage Assembly Systems," Management Science, INFORMS, vol. 30(2), pages 222-239, February.
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    Cited by:

    1. Ki Ling Cheung & Warren H. Hausman, 2000. "An Exact Performance Evaluation for the Supplier in a Two-Echelon Inventory System," Operations Research, INFORMS, vol. 48(4), pages 646-653, August.

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