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Quantity Premiums and Discounts in Dynamic Pricing

Author

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  • Yuri Levin

    (School of Business, Queen's University, Kingston, Ontario, K7L 3N6, Canada)

  • Mikhail Nediak

    (School of Business, Queen's University, Kingston, Ontario, K7L3N6, Canada)

  • Andrei Bazhanov

    (School of Business, Queen's University, Kingston, Ontario, K7L3N6, Canada)

Abstract

We consider a dynamic pricing problem for a monopolistic company selling a perishable product when customer demand is both uncertain and occurs in batches that must be fulfilled as a whole. The seller can price-discriminate between different sized batches by setting different unit prices. The problem is modeled as a stochastic optimal control problem to find an inventory-contingent dynamic pricing policy that maximizes the expected total revenues. We find the optimal pricing policy and prove several monotonicity results. First, we establish stochastic order conditions on the unit willingness-to-pay distributions that determine when quantity discounts or premiums take place for a batch purchase compared to a rapid sequence of purchases with the same total size. Second, we give sufficient conditions for prices to be monotonically decreasing or increasing in inventory. Third, we characterize the conditions for the perceived quantity discounts and premiums that result from comparing unit prices for different batch sizes under a particular inventory level.

Suggested Citation

  • Yuri Levin & Mikhail Nediak & Andrei Bazhanov, 2014. "Quantity Premiums and Discounts in Dynamic Pricing," Operations Research, INFORMS, vol. 62(4), pages 846-863, August.
    • Handle: RePEc:inm:oropre:v:62:y:2014:i:4:p:846-863
    DOI: 10.1287/opre.2014.1285
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    References listed on IDEAS

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    5. Khouja, Moutaz & Li, Yuefeng & Zhou, Jing, 2023. "Nonlinear pricing for yield management and countering strategic consumer behavior," European Journal of Operational Research, Elsevier, vol. 307(1), pages 212-232.

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