IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v47y1999i4p632-642.html
   My bibliography  Save this article

Single-Period Multiproduct Inventory Models with Substitution

Author

Listed:
  • Yehuda Bassok

    (Department of Management Sciences, School of Business Administration, University of Washington, Seattle, Washington 98195)

  • Ravi Anupindi

    (J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60208)

  • Ram Akella

    (Department of Engineering Economic Systems, Stanford University, Stanford, California 94305)

Abstract

We study a single period multiproduct inventory problem with substitution and proportional costs and revenues. We consider N products and N demand classes with full downward substitution, i.e., excess demand for class i can be satisfied using product j for i ≥ j . We first discuss a two-stage profit maximization formulation for the multiproduct substitution problem. We show that a greedy allocation policy is optimal. We use this to write the expected profits and its first partials explicitly. This in turn enables us to prove additional properties of the profit function and several interesting properties of the optimal solution. In a limited computational study using two products, we illustrate the benefits of solving for the optimal quantities when substitution is considered at the ordering stage over similar computations without considering substitution while ordering. Specifically, we show that the benefits are higher with high demand variability, low substitution cost, low profit margins (or low price to cost ratio), high salvage values, and similarity of products in terms of prices and costs.

Suggested Citation

  • Yehuda Bassok & Ravi Anupindi & Ram Akella, 1999. "Single-Period Multiproduct Inventory Models with Substitution," Operations Research, INFORMS, vol. 47(4), pages 632-642, August.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:4:p:632-642
    DOI: 10.1287/opre.47.4.632
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.47.4.632
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.47.4.632?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Barry A. Pasternack & Zvi Drezner, 1991. "Optimal inventory policies for substitutable commodities with stochastic demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 221-240, April.
    2. Arthur F. Veinott, Jr., 1965. "Optimal Policy for a Multi-Product, Dynamic, Nonstationary Inventory Problem," Management Science, INFORMS, vol. 12(3), pages 206-222, November.
    3. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    4. Awi Federgruen & Paul Zipkin, 1984. "Approximations of Dynamic, Multilocation Production and Inventory Problems," Management Science, INFORMS, vol. 30(1), pages 69-84, January.
    5. Edward Ignall & Arthur F. Veinott, Jr., 1969. "Optimality of Myopic Inventory Policies for Several Substitute Products," Management Science, INFORMS, vol. 15(5), pages 284-304, January.
    6. G. R. Bitran & S. Dasu, 1992. "Ordering Policies in an environment of Stochastic Yields and Substitutable Demands," Operations Research, INFORMS, vol. 40(5), pages 999-1017, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Anantaram Balakrishnan & Joseph Geunes, 2000. "Requirements Planning with Substitutions: Exploiting Bill-of-Materials Flexibility in Production Planning," Manufacturing & Service Operations Management, INFORMS, vol. 2(2), pages 166-185, January.
    2. Siddharth Mahajan & Garrett van Ryzin, 2001. "Stocking Retail Assortments Under Dynamic Consumer Substitution," Operations Research, INFORMS, vol. 49(3), pages 334-351, June.
    3. Iida, Tetsuo, 2001. "The infinite horizon non-stationary stochastic multi-echelon inventory problem and near-myopic policies," European Journal of Operational Research, Elsevier, vol. 134(3), pages 525-539, November.
    4. Yossi Aviv & Awi Federgruen, 2001. "Design for Postponement: A Comprehensive Characterization of Its Benefits Under Unknown Demand Distributions," Operations Research, INFORMS, vol. 49(4), pages 578-598, August.
    5. Yale T. Herer & Michal Tzur, 2001. "The dynamic transshipment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(5), pages 386-408, August.
    6. Hariga, Moncer A., 2010. "A single-item continuous review inventory problem with space restriction," International Journal of Production Economics, Elsevier, vol. 128(1), pages 153-158, November.
    7. Han, Guanghua & Dong, Ming & Liu, Shaoxuan, 2014. "Yield and allocation management in a continuous make-to-stock system with demand upgrade substitution," International Journal of Production Economics, Elsevier, vol. 156(C), pages 124-131.
    8. Harvey M. Wagner, 2002. "And Then There Were None," Operations Research, INFORMS, vol. 50(1), pages 217-226, February.
    9. Chou, Mabel & Sim, Chee-Khian & Yuan, Xue-Ming, 2013. "Optimal policies for inventory systems with two types of product sharing common hardware platforms: Single period and finite horizon," European Journal of Operational Research, Elsevier, vol. 224(2), pages 283-292.
    10. Wang, Yunzeng, 2001. "The optimality of myopic stocking policies for systems with decreasing purchasing prices," European Journal of Operational Research, Elsevier, vol. 133(1), pages 153-159, August.
    11. Choi, Sungyong & Ruszczynski, Andrzej, 2011. "A multi-product risk-averse newsvendor with exponential utility function," European Journal of Operational Research, Elsevier, vol. 214(1), pages 78-84, October.
    12. Boutarfa, Y. & Senoussi, A. & Brahimi, N. & Aouam, T., 2024. "Integration and substitution in hybrid manufacturing and refurbishing systems," International Journal of Production Economics, Elsevier, vol. 274(C).
    13. Chao, Gary H., 2013. "Production and availability policies through the Markov Decision Process and myopic methods for contractual and selective orders," European Journal of Operational Research, Elsevier, vol. 225(3), pages 383-392.
    14. Xin, Linwei & Goldberg, David A., 2021. "Time (in)consistency of multistage distributionally robust inventory models with moment constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1127-1141.
    15. Geunes, Joseph P. & Ramasesh, Ranga V. & Hayya, Jack C., 2001. "Adapting the newsvendor model for infinite-horizon inventory systems," International Journal of Production Economics, Elsevier, vol. 72(3), pages 237-250, August.
    16. Retsef Levi & Martin Pál & Robin O. Roundy & David B. Shmoys, 2007. "Approximation Algorithms for Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 284-302, May.
    17. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
    18. Agrawal, Sunil & Sengupta, Raghu Nandan & Shanker, Kripa, 2009. "Impact of information sharing and lead time on bullwhip effect and on-hand inventory," European Journal of Operational Research, Elsevier, vol. 192(2), pages 576-593, January.
    19. Retsef Levi & Robin O. Roundy & David B. Shmoys & Van Anh Truong, 2008. "Approximation Algorithms for Capacitated Stochastic Inventory Control Models," Operations Research, INFORMS, vol. 56(5), pages 1184-1199, October.
    20. Arthur Hsu & Yehuda Bassok, 1999. "Random Yield and Random Demand in a Production System with Downward Substitution," Operations Research, INFORMS, vol. 47(2), pages 277-290, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:47:y:1999:i:4:p:632-642. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.