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Optimal bundle formation and pricing of two products with limited stock

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  • Gürlera, Ülkü
  • Öztop, Salih
  • Sen, Alper

Abstract

In this study, we consider the stochastic modeling of a retail firm that sells two types of perishable products in a single period not only as independent items but also as a bundle. Our emphasis is on understanding the bundling practices on the inventory and pricing decisions of the firm. One of the issues we address is to decide on the number of bundles to be formed from the initial product inventory levels and the price of the bundle to maximize the expected profit. Product demands follow a Poisson Process with a price dependent rate. Customer reservation prices are assumed to have a joint distribution. We study the impact of reservation price distributions, initial inventory levels, product prices, demand arrival rates and cost of bundling. We observe that the expected profit decreases as the correlation between the reservation prices of two products increases. With negative correlation, bundling cost has a significant impact on the number of bundles formed. When the product prices are low, the retailer sells individual products as well as the bundle (mixed bundling), when they are high, the retailer sells only bundles (pure bundling). The expected profit and the number of bundles offered decrease as the variance of the reservation price distribution increases. For high starting inventory levels, the retailer reduces bundle price and offers more bundles. The number of bundle sales decreases and the number of individual product sales increases when the arrival rate increases since the need for bundling decreases. Impacts of substitutability and complementarity of products are also investigated. The retailer forms more bundles, or charges higher prices for the bundle or both as the products become more complementary and less substitutable.

Suggested Citation

  • Gürlera, Ülkü & Öztop, Salih & Sen, Alper, 2009. "Optimal bundle formation and pricing of two products with limited stock," International Journal of Production Economics, Elsevier, vol. 118(2), pages 442-462, April.
    • Handle: RePEc:eee:proeco:v:118:y:2009:i:2:p:442-462
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    1. Long, John B, Jr, 1984. "Comments on "Gaussian Demand and Commodity Bundling."," The Journal of Business, University of Chicago Press, vol. 57(1), pages 235-246, January.
    2. Jeuland, Abel, 1984. "Comments on "Gaussian Demand and Commodity Bundling."," The Journal of Business, University of Chicago Press, vol. 57(1), pages 231-234, January.
    3. Ward Hanson & R. Kipp Martin, 1990. "Optimal Bundle Pricing," Management Science, INFORMS, vol. 36(2), pages 155-174, February.
    4. Guillermo Gallego & Garrett van Ryzin, 1997. "A Multiproduct Dynamic Pricing Problem and Its Applications to Network Yield Management," Operations Research, INFORMS, vol. 45(1), pages 24-41, February.
    5. Schmalensee, Richard, 1984. "Gaussian Demand and Commodity Bundling," The Journal of Business, University of Chicago Press, vol. 57(1), pages 211-230, January.
    6. Tuomas Sandholm & David Levine & Michael Concordia & Paul Martyn & Rick Hughes & Jim Jacobs & Dennis Begg, 2006. "Changing the Game in Strategic Sourcing at Procter & Gamble: Expressive Competition Enabled by Optimization," Interfaces, INFORMS, vol. 36(1), pages 55-68, February.
    7. R. Venkatesh & Wagner Kamakura, 2003. "Optimal Bundling and Pricing under a Monopoly: Contrasting Complements and Substitutes from Independently Valued Products," The Journal of Business, University of Chicago Press, vol. 76(2), pages 211-232, April.
    8. R. Preston McAfee & John McMillan & Michael D. Whinston, 1989. "Multiproduct Monopoly, Commodity Bundling, and Correlation of Values," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(2), pages 371-383.
    9. Karakul, M., 2008. "Joint pricing and procurement of fashion products in the existence of clearance markets," International Journal of Production Economics, Elsevier, vol. 114(2), pages 487-506, August.
    10. Salinger, Michael A, 1995. "A Graphical Analysis of Bundling," The Journal of Business, University of Chicago Press, vol. 68(1), pages 85-98, January.
    11. Kamel Jedidi & Z. John Zhang, 2002. "Augmenting Conjoint Analysis to Estimate Consumer Reservation Price," Management Science, INFORMS, vol. 48(10), pages 1350-1368, October.
    12. Carbajo, Jose & de Meza, David & Seidmann, Daniel J, 1990. "A Strategic Motivation for Commodity Bundling," Journal of Industrial Economics, Wiley Blackwell, vol. 38(3), pages 283-298, March.
    13. Choi, Tsan-Ming, 2007. "Pre-season stocking and pricing decisions for fashion retailers with multiple information updating," International Journal of Production Economics, Elsevier, vol. 106(1), pages 146-170, March.
    14. Ricardo Ernst & Panagiotis Kouvelis, 1999. "The Effects of Selling Packaged Goods on Inventory Decisions," Management Science, INFORMS, vol. 45(8), pages 1142-1155, August.
    15. Yannis Bakos & Erik Brynjolfsson, 1999. "Bundling Information Goods: Pricing, Profits, and Efficiency," Management Science, INFORMS, vol. 45(12), pages 1613-1630, December.
    16. William James Adams & Janet L. Yellen, 1976. "Commodity Bundling and the Burden of Monopoly," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(3), pages 475-498.
    17. Wedad Elmaghraby & P{i}nar Keskinocak, 2003. "Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions," Management Science, INFORMS, vol. 49(10), pages 1287-1309, October.
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    8. Li, Minqiang & Feng, Haiyang & Chen, Fuzan & Kou, Jisong, 2013. "Numerical investigation on mixed bundling and pricing of information products," International Journal of Production Economics, Elsevier, vol. 144(2), pages 560-571.
    9. 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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    11. Raghu Nandan Giri & Shyamal Kumar Mondal & Manoranjan Maiti, 2020. "Bundle pricing strategies for two complementary products with different channel powers," Annals of Operations Research, Springer, vol. 287(2), pages 701-725, April.

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