An Efficient Algorithm for Dynamic Pricing Using a Graphical Representation

42 Pages Posted: 1 May 2016 Last revised: 26 Mar 2020

See all articles by Maxime Cohen

Maxime Cohen

Desautels Faculty of Management, McGill University

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 dynamic pricing problem faced by a retailer. The objective is to maximize the total profit by choosing prices, while satisfying several business rules. The strength of our work lies in our graphical model reformulation, which allows us to use ideas from combinatorial optimization. We do not make any 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 memory of the model (number of past prices that affect current demand) and in the number of items. We prove that the profit maximization problem is NP-hard by showing an approximation preserving reduction from the weighted Max-3-SAT problem. We next introduce the discrete reference price model which is a discretized version of the reference price model, accounting for an exponentially smoothed contribution of all past prices. We show that our problem can be solved efficiently under this model. We then approximate common demand functions using the discrete reference price model. To handle cross-item effects among multiple items, we propose to use a virtual reference price that assigns a reference price for each category of items (as opposed to a reference price for each item). To enhance the tractability of our approach, we cluster items into blocks and show how to adapt our method to include business constraints across blocks. Finally, we apply our solution approach using demand models calibrated with supermarket data and validate its practical performance.

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)

Desautels Faculty of Management, McGill University ( email )

1001 Sherbrooke St. W
Montreal, Quebec H3A 1G5
Canada

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

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