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Deterministic hierarchical substitution inventory models

Author

Listed:
  • H Gurnani

    (The Hong Kong University of Science and Technology)

  • Z Drezner

    (California State, University)

Abstract

In this paper, we consider a deterministic nested substitution problem where there are multiple products which can be substituted one for the other, if necessary, at a certain cost. We consider the case when there are n products, and product j can substitute products j + 1,…,n at certain costs. The trade-off is the cost of storing products (for example, customised products) at a higher inventory holding stage versus the cost of transferring downwards from a lower inventory holding cost (generic product) stage. The standard approach to solving the problem yields an intractable formulation, but by reformulating the problem to determine the optimal run-out times, we are able to determine the optimal order and substitution quantities. Numerical examples showing the effect of various system parameters on the optimal order and substitution policy are also presented.

Suggested Citation

  • H Gurnani & Z Drezner, 2000. "Deterministic hierarchical substitution inventory models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(1), pages 129-133, January.
    • Handle: RePEc:pal:jorsoc:v:51:y:2000:i:1:d:10.1057_palgrave.jors.2600843
    DOI: 10.1057/palgrave.jors.2600843
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    Citations

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    Cited by:

    1. Betts, John M. & Johnston, Robert B., 2005. "Just-in-time component replenishment decisions for assemble-to-order manufacturing under capital constraint and stochastic demand," International Journal of Production Economics, Elsevier, vol. 95(1), pages 51-70, January.
    2. Vinod Kumar Mishra & Kripa Shanker, 2017. "Optimal ordering quantities for substitutable items under joint replenishment with cost of substitution," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(1), pages 77-104.
    3. Shin, Hojung & Park, Soohoon & Lee, Euncheol & Benton, W.C., 2015. "A classification of the literature on the planning of substitutable products," European Journal of Operational Research, Elsevier, vol. 246(3), pages 686-699.
    4. Pentico, David W., 2008. "The assortment problem: A survey," European Journal of Operational Research, Elsevier, vol. 190(2), pages 295-309, October.
    5. Mokhtari, Hadi, 2018. "Economic order quantity for joint complementary and substitutable items," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 154(C), pages 34-47.
    6. Teunter, Ruud H. & Kuipers, Stefan, 2022. "Inventory control with demand substitution: new insights from a two-product Economic Order Quantity analysis," Omega, Elsevier, vol. 113(C).
    7. Eksler, Leonid & Aviram, Roei & Elalouf, Amir & Kamble, Aakash, 2018. "An EOQ model for multiple products with varying degrees of substitutability," Economics Discussion Papers 2018-77, Kiel Institute for the World Economy (IfW Kiel).
    8. Milind Dawande & Srinagesh Gavirneni & Yinping Mu & Suresh Sethi & Chelliah Sriskandarajah, 2010. "On the Interaction Between Demand Substitution and Production Changeovers," Manufacturing & Service Operations Management, INFORMS, vol. 12(4), pages 682-691, September.
    9. Yancong Zhou & Junqing Sun, 2013. "Inventory Decisions in a Product-Updated System with Component Substitution and Product Substitution," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-9, March.

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