Model-Free Assortment Pricing with Transaction Data

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See all articles by Ningyuan Chen

Ningyuan Chen

University of Toronto at Mississauga - Department of Management; University of Toronto - Rotman School of Management

Andre Augusto Cire

University of Toronto at Scarborough - Division of Management; University of Toronto - Operations Management

Ming Hu

University of Toronto - Rotman School of Management

Saman Lagzi

University of Toronto - Rotman School of Management

Date Written: January 3, 2021

Abstract

We study a problem in which a firm sets prices for products based on the transaction data, i.e., which product past customers chose from an assortment and what were the historical prices that they observed. Our approach does not impose a model on the distribution of the customers' valuations and only assumes, instead, that purchase choices satisfy incentive-compatible constraints. The individual valuation of each past customer can then be encoded as a polyhedral set, and our approach maximizes the worst-case revenue assuming that new customers' valuations are drawn from the empirical distribution implied by the collection of such polyhedra. We show that the optimal prices in this setting can be approximated at any arbitrary precision by solving a compact mixed-integer linear program. Moreover, we study special practical cases where the program can be solved efficiently, and design three approximation strategies that are of low computational complexity and interpretable. Comprehensive numerical studies based on synthetic and real data suggest that our pricing approach is uniquely beneficial when the historical data has a limited size or is susceptible to model misspecification.

Keywords: data-driven, incentive-compatible, robust optimization, product pricing; small data

Suggested Citation

Chen, Ningyuan and Cire, Andre Augusto and Hu, Ming and Lagzi, Saman, Model-Free Assortment Pricing with Transaction Data (January 3, 2021). Available at SSRN: https://ssrn.com/abstract=

Ningyuan Chen (Contact Author)

University of Toronto at Mississauga - Department of Management ( email )


Canada

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Andre Augusto Cire

University of Toronto at Scarborough - Division of Management ( email )

1265 Military Trial
Scarborough, Ontario M1C 1A4
Canada

University of Toronto - Operations Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Ming Hu

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada
416-946-5207 (Phone)

HOME PAGE: http://ming.hu

Saman Lagzi

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada

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