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Dynamic pricing of substitutable products with limited inventories under logit demand

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  • Minsuk Suh
  • Goker Aydin

Abstract

This article considers the dynamic pricing of two substitutable products over a predetermined, finite selling season. The initial inventory levels of the products are fixed exogenously and there are no replenishment opportunities during the season. It is assumed that each arriving customer chooses from available products based on the multinomial logit choice model, which captures the effect of prices on consumer choice. Every time a product runs out of stock, the set of choices shrinks, capturing the effect of stockouts on consumer choice. It is shown that, under the optimal pricing policy, the marginal value of an item is increasing in the remaining time and decreasing in its own stock level and the other product's stock level. Despite such non-surprising behavior on the part of marginal values, the optimal price itself is not simply monotonic in the remaining time or the other product's stock level. For example, a product's optimal price may increase if the remaining time decreases or if the total inventory grows. It is shown that such optimal behavior can be understood through alternative gauges such as the optimal price difference between the two products and the optimal purchase probabilities.

Suggested Citation

  • Minsuk Suh & Goker Aydin, 2011. "Dynamic pricing of substitutable products with limited inventories under logit demand," IISE Transactions, Taylor & Francis Journals, vol. 43(5), pages 323-331.
  • Handle: RePEc:taf:uiiexx:v:43:y:2011:i:5:p:323-331
    DOI: 10.1080/0740817X.2010.521803
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    Citations

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    Cited by:

    1. Xinan Yang & Arne K. Strauss & Christine S. M. Currie & Richard Eglese, 2016. "Choice-Based Demand Management and Vehicle Routing in E-Fulfillment," Transportation Science, INFORMS, vol. 50(2), pages 473-488, May.
    2. Fatemeh Nosrat & William L. Cooper & Zizhuo Wang, 2021. "Pricing for a product with network effects and mixed logit demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(2), pages 159-182, March.
    3. Farhad Etebari, 2020. "Pricing Competition Under Specific Discrete Choice Models," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(02), pages 1-14, March.
    4. Kuo, Chia-Wei & Huang, Kwei-Long, 2012. "Dynamic pricing of limited inventories for multi-generation products," European Journal of Operational Research, Elsevier, vol. 217(2), pages 394-403.
    5. Mahmoud Dehghan Nayeri & Amir-Nader Haghbin & Abdolkarim Mohammadi-Balani & Karim Bayat, 2020. "A multi-objective mean–variance mathematical programming approach to combined phase-out and clearance pricing strategy for seasonal products: case study of a Jeans retailer," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 19(3), pages 210-217, June.
    6. Chenhao Du & William L. Cooper & Zizhuo Wang, 2016. "Optimal Pricing for a Multinomial Logit Choice Model with Network Effects," Operations Research, INFORMS, vol. 64(2), pages 441-455, April.
    7. Lebedev, Denis & Goulart, Paul & Margellos, Kostas, 2021. "A dynamic programming framework for optimal delivery time slot pricing," European Journal of Operational Research, Elsevier, vol. 292(2), pages 456-468.
    8. Elçin Ergin & Mehmet Gümüş & Nathan Yang, 2022. "An Empirical Analysis of Intra‐Firm Product Substitutability in Fashion Retailing," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 607-621, February.
    9. Fang, Fei & Nguyen, Tri-Dung & Currie, Christine S.M., 2021. "Joint pricing and inventory decisions for substitutable and perishable products under demand uncertainty," European Journal of Operational Research, Elsevier, vol. 293(2), pages 594-602.
    10. Michael D. Wittman & Thomas Fiig & Peter P. Belobaba, 2018. "A dynamic pricing engine for multiple substitutable flights," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 17(6), pages 420-435, December.
    11. Ming Chen & Zhi-Long Chen, 2018. "Robust Dynamic Pricing with Two Substitutable Products," Manufacturing & Service Operations Management, INFORMS, vol. 20(2), pages 249-268, May.

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