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Optimal inventory policies for substitutable commodities with stochastic demand

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  • 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
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    References listed on IDEAS

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    1. Barry Alan Pasternack, 1985. "Optimal Pricing and Return Policies for Perishable Commodities," Marketing Science, INFORMS, vol. 4(2), pages 166-176.
    2. 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.
    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.
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    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.

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