IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v38y1991i2p221-240.html
   My bibliography  Save this article

Optimal inventory policies for substitutable commodities with stochastic demand

Author

Listed:
  • Barry A. Pasternack
  • Zvi Drezner

Abstract

In this article we consider a stochastic model for two products which have a single‐period inventory structure and which can be used as substitutes for each other should the need arise. Substitution will occur with probability one, but at perhaps a different revenue level. We prove that the expected profit function is concave, allowing us to find optimal stocking levels for the two products. We compare optimum inventory levels for the case of single substitution with that where there is no substitution. It is demonstrated for the case of single substitution that total optimum order quantities can actually increase or decrease with the substitution revenue.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:2:p:221-240
    DOI: 10.1002/1520-6750(199104)38:23.0.CO;2-7
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199104)38:23.0.CO;2-7
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(199104)38:23.0.CO;2-7?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. Bryan L. Deuermeyer, 1980. "A single period model for a multiproduct perishable inventory system with economic substitution," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 27(2), pages 177-185, June.
    2. Barry Alan Pasternack, 1985. "Optimal Pricing and Return Policies for Perishable Commodities," Marketing Science, INFORMS, vol. 4(2), pages 166-176.
    3. Mahmut Parlar, 1988. "Game theoretic analysis of the substitutable product inventory problem with random demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(3), pages 397-409, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yehuda Bassok & Ravi Anupindi & Ram Akella, 1999. "Single-Period Multiproduct Inventory Models with Substitution," Operations Research, INFORMS, vol. 47(4), pages 632-642, August.
    2. Yalçın Akçay & Yunke Li & Harihara Prasad Natarajan, 2020. "Category Inventory Planning With Service Level Requirements and Dynamic Substitutions," Production and Operations Management, Production and Operations Management Society, vol. 29(11), pages 2553-2578, November.
    3. 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.
    4. Ata Allah Taleizadeh & Masoumeh Sadat Babaei & Shib Sankar Sana & Biswajit Sarkar, 2019. "Pricing Decision within an Inventory Model for Complementary and Substitutable Products," Mathematics, MDPI, vol. 7(7), pages 1-22, June.
    5. Narendra Agrawal & Stephen A. Smith, 2003. "Optimal retail assortments for substitutable items purchased in sets," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 793-822, October.
    6. Vashkar Ghosh & Anand Paul & Lingjiong Zhu, 2022. "Stocking Under Random Demand and Product Variety: Exact Models and Heuristics," Production and Operations Management, Production and Operations Management Society, vol. 31(3), pages 1006-1032, March.
    7. Robert A. Shumsky & Fuqiang Zhang, 2009. "Dynamic Capacity Management with Substitution," Operations Research, INFORMS, vol. 57(3), pages 671-684, June.
    8. Silbermayr, Lena & Waitz, Martin, 2024. "Omni-channel inventory management of perishable products under transshipment and substitution," International Journal of Production Economics, Elsevier, vol. 267(C).
    9. Jian Zhang & Shuang He & Juliang Zhang & T. C. Edwin Cheng, 2020. "Purchase and retrieval competition for seasonal produce," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(3), pages 161-184, April.
    10. Siddharth Mahajan & Garrett van Ryzin, 2001. "Stocking Retail Assortments Under Dynamic Consumer Substitution," Operations Research, INFORMS, vol. 49(3), pages 334-351, June.
    11. Yue Dai & Xiuli Chao & Shu-Cherng Fang & Henry Nuttle, 2005. "Game Theoretic Analysis of a Distribution System with Customer Market Search," Annals of Operations Research, Springer, vol. 135(1), pages 223-228, March.
    12. Qi Feng & Chengzhang Li & Mengshi Lu & Jeyaveerasingam George Shanthikumar, 2022. "Dynamic Substitution for Selling Multiple Products under Supply and Demand Uncertainties," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1645-1662, April.
    13. Hu, Benyong & Xu, Dong & Meng, Chao, 2017. "Inconsistency of a retailer's optimal policies and channel performance under revenue sharing contracts," International Journal of Production Economics, Elsevier, vol. 183(PA), pages 53-65.
    14. Youyi Feng & Jianjun Xu & Shaohui Zheng, 2019. "Technical Note—Dynamic Optimal Policy for an Inventory System of Two Substitutable Products with Positive Replenishment Lead Times," Operations Research, INFORMS, vol. 67(4), pages 1027-1034, July.
    15. 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).
    16. Ahmed Senoussi & Youcef Boutarfa & Nadjib Brahimi & Tarik Aouam, 2024. "Sustainable Hybrid Manufacturing and Refurbishing Systems with Substitution," Sustainability, MDPI, vol. 16(17), pages 1-33, August.
    17. Serguei Netessine & Gregory Dobson & Robert A. Shumsky, 2002. "Flexible Service Capacity: Optimal Investment and the Impact of Demand Correlation," Operations Research, INFORMS, vol. 50(2), pages 375-388, April.
    18. Ying Rong & Ying‐Ju Chen & Zuo‐Jun Max Shen, 2015. "The impact of demand uncertainty on product line design under endogenous substitution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(2), pages 143-157, March.
    19. Yale T. Herer & Ayelet Rashit, 1999. "Lateral stock transshipments in a two‐location inventory system with fixed and joint replenishment costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 525-547, August.
    20. Alavi Fard, Farzad & He, Jian & Ivanov, Dmitry & Jie, Ferry, 2019. "A utility adjusted newsvendor model with stochastic demand," International Journal of Production Economics, Elsevier, vol. 211(C), pages 154-165.
    21. 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.
    22. Yueshan Yu & Xin Chen & Fuqiang Zhang, 2015. "Dynamic Capacity Management with General Upgrading," Operations Research, INFORMS, vol. 63(6), pages 1372-1389, December.
    23. Yale T. Herer & Michal Tzur, 2001. "The dynamic transshipment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(5), pages 386-408, August.
    24. 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.

    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. Ravi Anupindi & Yehuda Bassok, 1999. "Centralization of Stocks: Retailers vs. Manufacturer," Management Science, INFORMS, vol. 45(2), pages 178-191, February.
    2. Fernando Bernstein & Awi Federgruen, 2005. "Decentralized Supply Chains with Competing Retailers Under Demand Uncertainty," Management Science, INFORMS, vol. 51(1), pages 18-29, January.
    3. Sting, Fabian J. & Huchzermeier, Arnd, 2010. "Ensuring responsive capacity: How to contract with backup suppliers," European Journal of Operational Research, Elsevier, vol. 207(2), pages 725-735, December.
    4. Gérard P. Cachon & Martin A. Lariviere, 2005. "Supply Chain Coordination with Revenue-Sharing Contracts: Strengths and Limitations," Management Science, INFORMS, vol. 51(1), pages 30-44, January.
    5. Birendra K. Mishra & Srinivasan Raghunathan, 2004. "Retailer- vs. Vendor-Managed Inventory and Brand Competition," Management Science, INFORMS, vol. 50(4), pages 445-457, April.
    6. Che-Tsung Tung & Kuo-Hsien Wang & Yu-Je Lee, 2014. "A Model and its Solution Method for a Two-Item Newsvendor Supply Chain with Return Policy and Demand Leakage," International Journal of Academic Research in Accounting, Finance and Management Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Accounting, Finance and Management Sciences, vol. 4(1), pages 397-408, January.
    7. Gérard P. Cachon & Paul H. Zipkin, 1999. "Competitive and Cooperative Inventory Policies in a Two-Stage Supply Chain," Management Science, INFORMS, vol. 45(7), pages 936-953, July.
    8. Rodney P. Parker & Roman Kapuściński, 2011. "Managing a Noncooperative Supply Chain with Limited Capacity," Operations Research, INFORMS, vol. 59(4), pages 866-881, August.
    9. Leng, Mingming & Zhu, An, 2009. "Side-payment contracts in two-person nonzero-sum supply chain games: Review, discussion and applications," European Journal of Operational Research, Elsevier, vol. 196(2), pages 600-618, July.
    10. Fang, Yaner & Shou, Biying, 2015. "Managing supply uncertainty under supply chain Cournot competition," European Journal of Operational Research, Elsevier, vol. 243(1), pages 156-176.
    11. Seifert, Ralf W. & Thonemann, Ulrich W. & Sieke, Marcel A., 2006. "Integrating direct and indirect sales channels under decentralized decision-making," International Journal of Production Economics, Elsevier, vol. 103(1), pages 209-229, September.
    12. Kuo-Hsien Wang & Yu-Je Lee & Che-Tsung Tung, 2013. "Optimal Prices and Inventories Decisions on Returns Policy with Practical Examples Thorough a Stackelberg Game," International Journal of Academic Research in Accounting, Finance and Management Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Accounting, Finance and Management Sciences, vol. 3(2), pages 66-77, April.
    13. Lauren Skinner Beitelspacher & Thomas L. Baker & Adam Rapp & Dhruv Grewal, 2018. "Understanding the long-term implications of retailer returns in business-to-business relationships," Journal of the Academy of Marketing Science, Springer, vol. 46(2), pages 252-272, March.
    14. Parlar, Mahmut & Weng, Z. Kevin, 2006. "Coordinating pricing and production decisions in the presence of price competition," European Journal of Operational Research, Elsevier, vol. 170(1), pages 211-227, April.
    15. Nils Rudi & Sandeep Kapur & David F. Pyke, 2001. "A Two-Location Inventory Model with Transshipment and Local Decision Making," Management Science, INFORMS, vol. 47(12), pages 1668-1680, December.
    16. Jan A. Van Mieghem & Nils Rudi, 2002. "Newsvendor Networks: Inventory Management and Capacity Investment with Discretionary Activities," Manufacturing & Service Operations Management, INFORMS, vol. 4(4), pages 313-335, August.
    17. Dasci, A. & Karakul, M., 2009. "Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly," European Journal of Operational Research, Elsevier, vol. 197(3), pages 945-968, September.
    18. Cao, Zong-Hong & Zhou, Yong-Wu & Zhao, Ju & Li, Chang-Wen, 2015. "Entry mode selection and its impact on an incumbent supply chain coordination," Journal of Retailing and Consumer Services, Elsevier, vol. 26(C), pages 1-13.
    19. Vishal Gaur & Young-Hoon Park, 2007. "Asymmetric Consumer Learning and Inventory Competition," Management Science, INFORMS, vol. 53(2), pages 227-240, February.
    20. Geng, Qin & Mallik, Suman, 2007. "Inventory competition and allocation in a multi-channel distribution system," European Journal of Operational Research, Elsevier, vol. 182(2), pages 704-729, October.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:38:y:1991:i:2:p:221-240. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.