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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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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Hemant K. Bhargava, 2012. "Retailer-Driven Product Bundling in a Distribution Channel," Marketing Science, INFORMS, vol. 31(6), pages 1014-1021, November.
    3. Chakravarty, A. & Mild, A. & Taudes, A., 2013. "Bundling decisions in supply chains," European Journal of Operational Research, Elsevier, vol. 231(3), pages 617-630.
    4. repec:eee:joreco:v:35:y:2017:i:c:p:106-117 is not listed on IDEAS
    5. 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.
    6. 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.
    7. Cataldo, Alejandro & Ferrer, Juan–Carlos, 2017. "Optimal pricing and composition of multiple bundles: A two-step approach," European Journal of Operational Research, Elsevier, vol. 259(2), pages 766-777.

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