Type of Publication: Article in Journal

Approximately Optimal Solutions for Nonlinear Dynamic Pricing in the Presence of Multiunit Demand

Author(s):

Schur, R.

Publication Date:

2024

Location(s):

Universität Duisburg-Essen

Language:

Englisch

Fulltext:

Approximately Optimal Solutions for Nonlinear Dynamic Pricing in the Presence of Multiunit Demand (749 KB)

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Abstract

We consider a dynamic pricing setting where a firm sells a perishable product over a finite selling horizon. Different from the standard setting, the firm faces multiunit demand and can separately quote a price for every batch size. Customers differ in their attraction to the product and their preference regarding the batch size. These two attributes are depicted by a random variable each and are the basis for the calculation of customers’ willingness-to-pay. The resulting customer choice model is very challenging to work with and we put some effort into reducing its complexity. We develop optimality conditions for the stage-wise optimization problem. As finding the optimal solution in every state is non-trivial, we resort to formulating a fluid approximation model. With a simplifying assumption, we can solve this approximation and subsequently verify that this assumption indeed holds for the optimal solution. The resulting static pricing policy is approximately optimal in our dynamic setting. However, instead of applying this static policy, we use it to ensure approximate optimality of the three novel heuristics we developed in this paper. We test all heuristics in a simulation study against an upper bound and analyze patterns in the corresponding policies to gain managerial insights. For example, we find that a piecewise linear pricing structure performs very well and might be an easy-to-communicate alternative to full nonlinearity.