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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
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal International Journal of Production Economics.

    Volume (Year): 118 (2009)
    Issue (Month): 2 (April)
    Pages: 442-462

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    Handle: RePEc:eee:proeco:v:118:y:2009:i:2:p:442-462

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    Web page: http://www.elsevier.com/locate/ijpe

    Related research

    Keywords: Revenue management Pricing Product bundling;

    References

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    1. 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.
    2. Yannis Bakos & Erik Brynjolfsson, 1999. "Bundling Information Goods: Pricing, Profits, and Efficiency," Management Science, INFORMS, vol. 45(12), pages 1613-1630, December.
    3. 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 283-98, March.
    4. Ricardo Ernst & Panagiotis Kouvelis, 1999. "The Effects of Selling Packaged Goods on Inventory Decisions," Management Science, INFORMS, vol. 45(8), pages 1142-1155, August.
    5. 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.
    6. Ward Hanson & R. Kipp Martin, 1990. "Optimal Bundle Pricing," Management Science, INFORMS, vol. 36(2), pages 155-174, February.
    7. McAfee, R Preston & McMillan, John & Whinston, Michael D, 1989. "Multiproduct Monopoly, Commodity Bundling, and Correlation of Values," The Quarterly Journal of Economics, MIT Press, vol. 104(2), pages 371-83, May.
    8. 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.
    9. Schmalensee, Richard, 1984. "Gaussian Demand and Commodity Bundling," The Journal of Business, University of Chicago Press, vol. 57(1), pages S211-30, January.
    10. 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.
    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. Long, John B, Jr, 1984. "Comments on "Gaussian Demand and Commodity Bundling."," The Journal of Business, University of Chicago Press, vol. 57(1), pages S235-46, January.
    13. Salinger, Michael A, 1995. "A Graphical Analysis of Bundling," The Journal of Business, University of Chicago Press, vol. 68(1), pages 85-98, January.
    14. Adams, William James & Yellen, Janet L, 1976. "Commodity Bundling and the Burden of Monopoly," The Quarterly Journal of Economics, MIT Press, vol. 90(3), pages 475-98, August.
    15. Jeuland, Abel, 1984. "Comments on "Gaussian Demand and Commodity Bundling."," The Journal of Business, University of Chicago Press, vol. 57(1), pages S231-34, January.
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    Cited by:
    1. 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.
    2. Mayer, Stefan & Klein, Robert & Seiermann, Stephanie, 2013. "A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints," International Journal of Production Economics, Elsevier, vol. 145(2), pages 584-598.

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