Model-Free Assortment Pricing with Transaction Data

Forthcoming in Management Science

62 Pages Posted: 18 Feb 2021 Last revised: 16 May 2022

See all articles by Ningyuan Chen

Ningyuan Chen

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

Wilfrid Laurier University - Lazaridis School of Business & Economics

Date Written: January 3, 2021

Abstract

We study the problem when 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 study the single-product case analytically and relate it to the traditional model-based approach. Moreover, we show that the optimal prices in the general case can be approximated at any arbitrary precision by solving a compact mixed-integer linear program. We also design three approximation strategies that are of low computational complexity and interpretable. In particular, the cut-off pricing heuristic has a competent provable performance guarantee. 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). Forthcoming in Management Science, Available at SSRN: https://ssrn.com/abstract=3759397 or http://dx.doi.org/10.2139/ssrn.3759397

Ningyuan Chen (Contact Author)

University of Toronto - Rotman School of Management ( email )

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

Wilfrid Laurier University - Lazaridis School of Business & Economics ( email )

Waterloo, Ontario N2L 3C5
Canada

HOME PAGE: http://samanlagzi.com

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
478
Abstract Views
4,217
Rank
96,790
PlumX Metrics