IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v129y2011i1p65-78.html
   My bibliography  Save this article

Inventory decisions for substitutable products with stock-dependent demand

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925-5273(10)00324-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Alain Bultez & Philippe Naert, 1988. "SH.A.R.P.: Shelf Allocation for Retailers' Profit," Marketing Science, INFORMS, vol. 7(3), pages 211-231.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Ricardo Ernst & Panagiotis Kouvelis, 1999. "The Effects of Selling Packaged Goods on Inventory Decisions," Management Science, INFORMS, vol. 45(8), pages 1142-1155, August.
    10. 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.
    11. Marcel Corstjens & Peter Doyle, 1981. "A Model for Optimizing Retail Space Allocations," Management Science, INFORMS, vol. 27(7), pages 822-833, July.
    12. 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.
    13. Mahesh Nagarajan & S. Rajagopalan, 2008. "Inventory Models for Substitutable Products: Optimal Policies and Heuristics," Management Science, INFORMS, vol. 54(8), pages 1453-1466, August.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Siddharth Mahajan & Garrett van Ryzin, 2001. "Stocking Retail Assortments Under Dynamic Consumer Substitution," Operations Research, INFORMS, vol. 49(3), pages 334-351, June.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Koschat, Martin A., 2008. "Store inventory can affect demand: Empirical evidence from magazine retailing," Journal of Retailing, Elsevier, vol. 84(2), pages 165-179.
    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. Mohammad Saffari, 2022. "Periodic inventory management when demand stochastically depends on shelf-stock," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1489-1501, December.
    2. Devangan, Lokendra & Amit, R.K. & Mehta, Peeyush & Swami, Sanjeev & Shanker, Kripa, 2013. "Individually rational buyback contracts with inventory level dependent demand," International Journal of Production Economics, Elsevier, vol. 142(2), pages 381-387.
    3. 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.
    4. 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.
    5. 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.
    6. Zhang, Jie & Xie, Weijun & Sarin, Subhash C., 2021. "Robust multi-product newsvendor model with uncertain demand and substitution," European Journal of Operational Research, Elsevier, vol. 293(1), pages 190-202.
    7. Youhua (Frank) Chen & Ye Lu & Minghui Xu, 2012. "Optimal inventory control policy for periodic‐review inventory systems with inventory‐level‐dependent demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(6), pages 430-440, September.
    8. Liu, Wei & Song, Shiji & Wu, Cheng, 2013. "Impact of loss aversion on the newsvendor game with product substitution," International Journal of Production Economics, Elsevier, vol. 141(1), pages 352-359.
    9. Lu, Fen & Xu, He & Chen, Pengyu & Zhu, Stuart X., 2018. "Joint pricing and production decisions with yield uncertainty and downconversion," International Journal of Production Economics, Elsevier, vol. 197(C), pages 52-62.
    10. Mou, Shandong & Robb, David J. & DeHoratius, Nicole, 2018. "Retail store operations: Literature review and research directions," European Journal of Operational Research, Elsevier, vol. 265(2), pages 399-422.
    11. Apostolos Burnetas & Odysseas Kanavetas, 2018. "Inventory policies for two products under Poisson demand: Interaction between demand substitution, limited storage capacity and replenishment time uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 676-698, December.
    12. Pan, Qin-hua & He, Xiuli & Skouri, Konstantina & Chen, Sheng-Chih & Teng, Jinn-Tsair, 2018. "An inventory replenishment system with two inventory-based substitutable products," International Journal of Production Economics, Elsevier, vol. 204(C), pages 135-147.
    13. 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.
    14. 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.
    15. 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.
    16. Zhao, Jing & Wei, Jie & Li, Yongjian, 2014. "Pricing decisions for substitutable products in a two-echelon supply chain with firms׳ different channel powers," International Journal of Production Economics, Elsevier, vol. 153(C), pages 243-252.
    17. 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.
    18. Wen, Xin & Choi, Tsan-Ming & Chung, Sai-Ho, 2019. "Fashion retail supply chain management: A review of operational models," International Journal of Production Economics, Elsevier, vol. 207(C), pages 34-55.
    19. Guchhait, Partha & Kumar Maiti, Manas & Maiti, Manoranjan, 2013. "Production-inventory models for a damageable item with variable demands and inventory costs in an imperfect production process," International Journal of Production Economics, Elsevier, vol. 144(1), pages 180-188.
    20. Menezes, Mozart B.C. & Pinto, Roberto, 2022. "Product proliferation, cannibalisation, and substitution: A first look into entailed risk and complexity," International Journal of Production Economics, Elsevier, vol. 243(C).

    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. 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.
    2. Mou, Shandong & Robb, David J. & DeHoratius, Nicole, 2018. "Retail store operations: Literature review and research directions," European Journal of Operational Research, Elsevier, vol. 265(2), pages 399-422.
    3. Pol Boada-Collado & Victor Martínez-de-Albéniz, 2020. "Estimating and Optimizing the Impact of Inventory on Consumer Choices in a Fashion Retail Setting," Manufacturing & Service Operations Management, INFORMS, vol. 22(3), pages 582-597, May.
    4. Zhang, Ren-Qian & Zhang, Lan-Kang & Zhou, Wen-Hui & Saigal, Romesh & Wang, Hui-Wen, 2014. "The multi-item newsvendor model with cross-selling and the solution when demand is jointly normally distributed," European Journal of Operational Research, Elsevier, vol. 236(1), pages 147-159.
    5. Transchel, Sandra, 2017. "Inventory management under price-based and stockout-based substitution," European Journal of Operational Research, Elsevier, vol. 262(3), pages 996-1008.
    6. 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.
    7. 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.
    8. Vaagen, Hajnalka & Wallace, Stein W. & Kaut, Michal, 2011. "Modelling consumer-directed substitution," International Journal of Production Economics, Elsevier, vol. 134(2), pages 388-397, December.
    9. Transchel, Sandra & Buisman, Marjolein E. & Haijema, Rene, 2022. "Joint assortment and inventory optimization for vertically differentiated products under consumer-driven substitution," European Journal of Operational Research, Elsevier, vol. 301(1), pages 163-179.
    10. Hübner, Alexander H. & Kuhn, Heinrich, 2012. "Retail category management: State-of-the-art review of quantitative research and software applications in assortment and shelf space management," Omega, Elsevier, vol. 40(2), pages 199-209, April.
    11. Yücel, Eda & Karaesmen, Fikri & Salman, F. Sibel & Türkay, Metin, 2009. "Optimizing product assortment under customer-driven demand substitution," European Journal of Operational Research, Elsevier, vol. 199(3), pages 759-768, December.
    12. 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.
    13. 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.
    14. Huang, Di & Zhou, Hong & Zhao, Qiu-Hong, 2011. "A competitive multiple-product newsboy problem with partial product substitution," Omega, Elsevier, vol. 39(3), pages 302-312, June.
    15. Stelios Tsafarakis & Charalampos Saridakis & Nikolaos Matsatsinis & George Baltas, 2016. "Private labels and retail assortment planning: a differential evolution approach," Annals of Operations Research, Springer, vol. 247(2), pages 677-692, December.
    16. Zhang, Wei & Rajaram, Kumar, 2017. "Managing limited retail space for basic products: Space sharing vs. space dedication," European Journal of Operational Research, Elsevier, vol. 263(3), pages 768-781.
    17. Yu, Yimin & Shou, Biying & Ni, Yaodong & Chen, Li, 2017. "Optimal production, pricing, and substitution policies in continuous review production-inventory systems," European Journal of Operational Research, Elsevier, vol. 260(2), pages 631-649.
    18. Li Chen & Erica L. Plambeck, 2008. "Dynamic Inventory Management with Learning About the Demand Distribution and Substitution Probability," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 236-256, May.
    19. Serguei Netessine & Nils Rudi, 2003. "Centralized and Competitive Inventory Models with Demand Substitution," Operations Research, INFORMS, vol. 51(2), pages 329-335, April.
    20. Brian Tomlin & Yimin Wang, 2008. "Pricing and Operational Recourse in Coproduction Systems," Management Science, INFORMS, vol. 54(3), pages 522-537, March.

    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:eee:proeco:v:129:y:2011:i:1:p:65-78. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijpe .

    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.