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A single‐period inventory placement problem for a serial supply chain

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  • Chia‐Shin Chung
  • James Flynn
  • Piotr Stalinski

Abstract

This article addresses the inventory placement problem in a serial supply chain facing a stochastic demand for a single planning period. All customer demand is served from stage 1, where the product is stored in its final form. If the demand exceeds the supply at stage 1, then stage 1 is resupplied from stocks held at the upstream stages 2 through N, where the product may be stored in finished form or as raw materials or subassemblies. All stocking decisions are made before the demand occurs. The demand is nonnegative and continuous with a known probability distribution, and the purchasing, holding, shipping, processing, and shortage costs are proportional. There are no fixed costs. All unsatisfied demand is lost. The objective is to select the stock quantities that should be placed different stages so as to maximize the expected profit. Under reasonable cost assumptions, this leads to a convex constrained optimization problem. We characterize the properties of the optimal solution and propose an effective algorithm for its computation. For the case of normal demands, the calculations can be done on a spreadsheet. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:506–517, 2001

Suggested Citation

  • Chia‐Shin Chung & James Flynn & Piotr Stalinski, 2001. "A single‐period inventory placement problem for a serial supply chain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(6), pages 506-517, September.
    • Handle: RePEc:wly:navres:v:48:y:2001:i:6:p:506-517
    DOI: 10.1002/nav.1032
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    References listed on IDEAS

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    1. Amit Eynan & Meir J. Rosenblatt, 1995. "Assemble to order and assemble in advance in a single‐period stochastic environment," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(5), pages 861-872, August.
    2. Hau L. Lee & Corey Billington, 1993. "Material Management in Decentralized Supply Chains," Operations Research, INFORMS, vol. 41(5), pages 835-847, October.
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    1. Ting-Chen Hu & Kuo-Chen Hung & Kuo-Lung Yang, 2019. "The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models," Mathematics, MDPI, vol. 7(5), pages 1-10, May.

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