Quantity Premiums and Discounts in Dynamic Pricing

Yuri Levin (), Mikhail Nediak () and Andrei Bazhanov
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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

Operations Research, 2014, vol. 62, issue 4, 846-863

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.

Keywords: dynamic pricing; batched demand; stochastic orders; dynamic programming applications (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (5)

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