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Inventory Control in Directed Networks: A Note on Linear Costs

Author

Listed:
  • Ganesh Janakiraman

    (IOMS-OM Group, Stern School of Business, New York University, 44 West Fourth Street, New York, New York 10012-1126)

  • John A. Muckstadt

    (School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853)

Abstract

We consider periodic review inventory control problems in directed networks, primary examples of which are distribution systems and assembly systems. External demand could occur at each node. When inventory is insufficient to meet requirements at a node, a portion of this demand is backordered and the remaining is lost. External demands, as well as lead times for inventory purchase, assembly, and transportation, are stochastic. In each period, linear sales revenues and the following costs, all linear, are charged at each node: (a) inventory purchase/assembly/transfer cost to receive inventory, (b) holding cost, (c) backorder cost, and (d) lost sales cost. When the objective function of interest is a discounted sum of profits over a finite planning horizon, it is shown that the sales prices and the inventory purchase/assembly/transfer cost parameters can be assumed to be zero without loss of generality. The result is proved for every realization of demands and lead times. Some extensions to these results are discussed. During this process, we also generalize the concept of echelon inventories to directed networks.

Suggested Citation

  • Ganesh Janakiraman & John A. Muckstadt, 2004. "Inventory Control in Directed Networks: A Note on Linear Costs," Operations Research, INFORMS, vol. 52(3), pages 491-495, June.
    • Handle: RePEc:inm:oropre:v:52:y:2004:i:3:p:491-495
    DOI: 10.1287/opre.1030.0103
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    Citations

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    Cited by:

    1. Jiahua Zhang & Shu-Cherng Fang & Yifan Xu, 2018. "Inventory centralization with risk-averse newsvendors," Annals of Operations Research, Springer, vol. 268(1), pages 215-237, September.
    2. Jinzhi Bu & Xiting Gong & Dacheng Yao, 2019. "Technical Note—Constant-Order Policies for Lost-Sales Inventory Models with Random Supply Functions: Asymptotics and Heuristic," Operations Research, INFORMS, vol. 68(4), pages 1063-1073, July.
    3. Marco Bijvank & Woonghee Tim Huh & Ganesh Janakiraman & Wanmo Kang, 2014. "Robustness of Order-Up-to Policies in Lost-Sales Inventory Systems," Operations Research, INFORMS, vol. 62(5), pages 1040-1047, October.
    4. Paul Zipkin, 2008. "Old and New Methods for Lost-Sales Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1256-1263, October.
    5. Saurabh Bansal & Mahesh Nagarajan, 2017. "Product Portfolio Management with Production Flexibility in Agribusiness," Operations Research, INFORMS, vol. 65(4), pages 914-930, August.
    6. Farvid, Mojtaba & Rosling, Kaj, 2014. "The discounted (R,Q) inventory model—The Shrewd Accountant's Heuristic," International Journal of Production Economics, Elsevier, vol. 149(C), pages 17-27.
    7. 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.
    8. Woonghee Tim Huh & Paat Rusmevichientong, 2009. "A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 103-123, February.
    9. Ganesh Janakiraman & Robin O. Roundy, 2004. "Lost-Sales Problems with Stochastic Lead Times: Convexity Results for Base-Stock Policies," Operations Research, INFORMS, vol. 52(5), pages 795-803, October.
    10. Wei Chen & Milind Dawande & Ganesh Janakiraman, 2014. "Fixed-Dimensional Stochastic Dynamic Programs: An Approximation Scheme and an Inventory Application," Operations Research, INFORMS, vol. 62(1), pages 81-103, February.

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