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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.

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  • 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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    4. 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.
    5. 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.
    6. Gökgür, Burak & Karabatı, Selçuk, 2019. "Dynamic and targeted bundle pricing of two independently valued products," European Journal of Operational Research, Elsevier, vol. 279(1), pages 184-198.
    7. Chakravarty, A. & Mild, A. & Taudes, A., 2013. "Bundling decisions in supply chains," European Journal of Operational Research, Elsevier, vol. 231(3), pages 617-630.
    8. Pan, Fei & Pan, Shenle & Zhou, Wei & Fan, Tijun, 2022. "Perishable product bundling with logistics uncertainty: Solution based on physical internet," International Journal of Production Economics, Elsevier, vol. 244(C).
    9. Doha, Ahmed & Ghasemaghaei, Maryam & Hassanein, Khaled, 2017. "Social bundling: A novel method to enhance consumers’ intention to purchase online bundles," Journal of Retailing and Consumer Services, Elsevier, vol. 35(C), pages 106-117.
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