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Inventory decisions for substitutable products with stock-dependent demand

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  • Stavrulaki, Euthemia

Abstract

We study a retailer's inventory policy for two products. The products are substitutable and have inventory dependent demand, so a higher inventory level of a product increases its sales. We model the joint effect of demand stimulation and product substitution on inventory decisions by considering a single-period, stochastic demand setting. We provide the first order optimality conditions for the profit maximizing order quantities and interpret them using marginal analysis. We also consider two heuristic solutions that separately account for either demand stimulation or product substitution. Our numerical analysis reveals that the optimal policy by appropriately using sales information that quantifies substitution and demand stimulation can produce significantly higher profits. The profit benefits are lessened under certain circumstances, such as when the two products have similar critical fractile values, suggesting that in such instances the heuristics may be used effectively.

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  • Stavrulaki, Euthemia, 2011. "Inventory decisions for substitutable products with stock-dependent demand," International Journal of Production Economics, Elsevier, vol. 129(1), pages 65-78, January.
    • Handle: RePEc:eee:proeco:v:129:y:2011:i:1:p:65-78
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    1. Garrett van Ryzin & Siddharth Mahajan, 1999. "On the Relationship Between Inventory Costs and Variety Benefits in Retail Assortments," Management Science, INFORMS, vol. 45(11), pages 1496-1509, November.
    2. Alain Bultez & Philippe Naert, 1988. "SH.A.R.P.: Shelf Allocation for Retailers' Profit," Marketing Science, INFORMS, vol. 7(3), pages 211-231.
    3. Wang, Qinan & Parlar, Mahmut, 1994. "A three-person game theory model arising in stochastic inventory control theory," European Journal of Operational Research, Elsevier, vol. 76(1), pages 83-97, July.
    4. Mahesh Nagarajan & S. Rajagopalan, 2008. "Inventory Models for Substitutable Products: Optimal Policies and Heuristics," Management Science, INFORMS, vol. 54(8), pages 1453-1466, August.
    5. 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.
    6. Ernst, Ricardo & Kamrad, Bardia, 2006. "Estimating demand by using sales information: inaccuracies encountered," European Journal of Operational Research, Elsevier, vol. 174(2), pages 675-688, October.
    7. E Stavrulaki & D K H Fong & D K J Lin, 2003. "Two-resource stochastic capacity planning employing a Bayesian methodology," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(11), pages 1198-1208, November.
    8. 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.
    9. Urban, Timothy L., 1995. "Inventory models with the demand rate dependent on stock and shortage levels," International Journal of Production Economics, Elsevier, vol. 40(1), pages 21-28, June.
    10. James D. Dana, Jr. & Nicholas C. Petruzzi, 2001. "Note: The Newsvendor Model with Endogenous Demand," Management Science, INFORMS, vol. 47(11), pages 1488-1497, November.
    11. Khouja, Moutaz & Mehrez, Abraham & Rabinowitz, Gad, 1996. "A two-item newsboy problem with substitutability," International Journal of Production Economics, Elsevier, vol. 44(3), pages 267-275, July.
    12. Goh, Mark, 1992. "Some results for inventory models having inventory level dependent demand rate," International Journal of Production Economics, Elsevier, vol. 27(2), pages 155-160, May.
    13. Rajaram, Kumar & Tang, Christopher S., 2001. "The impact of product substitution on retail merchandising," European Journal of Operational Research, Elsevier, vol. 135(3), pages 582-601, December.
    14. Stephen A. Smith & Narendra Agrawal, 2000. "Management of Multi-Item Retail Inventory Systems with Demand Substitution," Operations Research, INFORMS, vol. 48(1), pages 50-64, February.
    15. Vishal Gaur & Dorothée Honhon, 2006. "Assortment Planning and Inventory Decisions Under a Locational Choice Model," Management Science, INFORMS, vol. 52(10), pages 1528-1543, October.
    16. Ricardo Ernst & Panagiotis Kouvelis, 1999. "The Effects of Selling Packaged Goods on Inventory Decisions," Management Science, INFORMS, vol. 45(8), pages 1142-1155, August.
    17. 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.
    18. Koschat, Martin A., 2008. "Store inventory can affect demand: Empirical evidence from magazine retailing," Journal of Retailing, Elsevier, vol. 84(2), pages 165-179.
    19. Siddharth Mahajan & Garrett van Ryzin, 2001. "Stocking Retail Assortments Under Dynamic Consumer Substitution," Operations Research, INFORMS, vol. 49(3), pages 334-351, June.
    20. Anantaram Balakrishnan & Michael S. Pangburn & Euthemia Stavrulaki, 2004. ""Stack Them High, Let 'em Fly": Lot-Sizing Policies When Inventories Stimulate Demand," Management Science, INFORMS, vol. 50(5), pages 630-644, May.
    21. Anantaram Balakrishnan & Michael S. Pangburn & Euthemia Stavrulaki, 2008. "Integrating the Promotional and Service Roles of Retail Inventories," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 218-235, July.
    22. Marcel Corstjens & Peter Doyle, 1981. "A Model for Optimizing Retail Space Allocations," Management Science, INFORMS, vol. 27(7), pages 822-833, July.
    23. 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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    10. P. Majumder & U. K. Bera & M. Maiti, 2020. "An EPQ model of substitutable products under trade credit policy with stock dependent and random substitution," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1205-1243, December.
    11. 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.
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    15. Jie Zhang & Weijun Xie & Subhash C. Sarin, 2021. "Multiproduct Newsvendor Problem with Customer-Driven Demand Substitution: A Stochastic Integer Program Perspective," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1229-1244, July.
    16. 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.
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    20. Wang, Fuqiang & Fang, Xiaoping & Chen, Xiaohong & Li, Xihua, 2016. "Impact of inventory inaccuracies on products with inventory-dependent demand," International Journal of Production Economics, Elsevier, vol. 177(C), pages 118-130.

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