An Efficient Algorithm for Dynamic Pricing Using a Graphical Representation

40 Pages Posted: 1 May 2016 Last revised: 16 Apr 2018

See all articles by Maxime Cohen

Maxime Cohen

New York University (NYU) - Leonard N. Stern School of Business

Swati Gupta

Massachusetts Institute of Technology (MIT), Students

Jeremy Kalas

Massachusetts Institute of Technology (MIT)

Georgia Perakis

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Date Written: April 28, 2016

Abstract

We study a multi-period, multi-item pricing problem faced by a retailer. The objective is to maximize the total profit by choosing optimal prices. This problem is faced by many retailers (e.g., supermarkets) who need to set the prices for multiple items at the beginning of the selling season. Data is used to estimate demand, and then pricing decisions need to be set in tractable way, while satisfying several important business rules. The strength of our work lies in the graphical reformulation we introduce, which allows us to use ideas from combinatorial optimization. In contrast with some previous work, we do not impose assumptions on the structure of the demand function. The complexity of our method depends linearly on the number of time periods but is exponential in the model memory (number of past prices that affect current demand) and in the number of items. Consequently, for problems with large memory, we show that the profit maximization problem is NP-hard by presenting a reduction from the Traveling Salesman Problem. We introduce the discrete reference price model which is a discretized version of the commonly used reference price model, accounting for an exponential smoothed contribution of all past prices. This discrete model allows us to capture the fact that customers do not form reference prices with infinite precision. For this model, we show that the problem can be solved efficiently with low runtimes. We then approximate several common demand functions by using the discrete reference price model. Next, we extend the reference price model to handle cross-item effects among multiple items using the notion of a virtual reference price. To allow the scalability of our approach, we cluster the different items into blocks and show how to incorporate global business constraints which are important and challenging in practice. Finally, we apply our solution approach using demand models calibrated with supermarket data and show that we can solve realistic size instances in a few minutes.

Keywords: Retail Pricing, Layered Graph, Reference Price Model, Multi-item Pricing

Suggested Citation

Cohen, Maxime and Gupta, Swati and Kalas, Jeremy and Perakis, Georgia, An Efficient Algorithm for Dynamic Pricing Using a Graphical Representation (April 28, 2016). Available at SSRN: https://ssrn.com/abstract=2772231 or http://dx.doi.org/10.2139/ssrn.2772231

Maxime Cohen (Contact Author)

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

Swati Gupta

Massachusetts Institute of Technology (MIT), Students ( email )

Cambridge, MA
United States

Jeremy Kalas

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Georgia Perakis

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

100 Main Street
E62-565
Cambridge, MA 02142
United States

Register to save articles to
your library

Register

Paper statistics

Downloads
196
rank
148,080
Abstract Views
814
PlumX Metrics