Dynamic Pricing (and Assortment) under a Static Calendar

Management Science

71 Pages Posted: 26 Oct 2018 Last revised: 23 Nov 2020

See all articles by Will Ma

Will Ma

Columbia University - Columbia Business School, Decision Risk and Operations

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Jinglong Zhao

Boston University - Questrom School of Business

Date Written: October 2, 2018

Abstract

This work is motivated by our collaboration with a large consumer packaged goods (CPG) company. We have found that while the company appreciates the advantages of dynamic pricing, they deem it operationally much easier to plan out a static price calendar in advance.

We investigate the efficacy of static control policies for revenue management problems whose optimal solution is inherently dynamic. In these problems, a firm has limited inventory to sell over a finite time horizon, over which heterogeneous customers stochastically arrive. We consider both pricing and assortment controls, and derive simple static policies in the form of a price calendar or a planned sequence of assortments, respectively. In the assortment planning problem, we also differentiate between the static vs. dynamic substitution models of customer demand. We show that our policies are within 1-1/e (approximately 0.63) of the optimum under stationary (IID) demand, and 1/2 of the optimum under non-stationary demand, with both guarantees approaching 1 if the starting inventories are large.

We adapt the technique of prophet inequalities from optimal stopping theory to pricing and assortment problems, and our results are relative to the linear programming relaxation. Under the special case of IID single-item pricing, our results improve the understanding of irregular and discrete demand curves, by showing that a static calendar can be (1-1/e)-approximate if the prices are sorted high-to-low.

Finally, we demonstrate on both data from the CPG company and synthetic data from the literature that our simple price and assortment calendars are effective.

Keywords: revenue management, dynamic pricing, dynamic assortment

Suggested Citation

Ma, Will and Simchi-Levi, David and Zhao, Jinglong, Dynamic Pricing (and Assortment) under a Static Calendar (October 2, 2018). Management Science, Available at SSRN: https://ssrn.com/abstract=3251015 or http://dx.doi.org/10.2139/ssrn.3251015

Will Ma

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

New York, NY
United States

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering ( email )

MA
United States

Jinglong Zhao (Contact Author)

Boston University - Questrom School of Business ( email )

595 Commonwealth Avenue
Boston, MA MA 02215
United States

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