Assortment Optimization and Pricing Under the Threshold-Based Choice Models

42 Pages Posted: 6 Nov 2020

See all articles by Xu Tian

Xu Tian

University of Science and Technology of China (USTC) - School of Management

Anran Li

LSE

Date Written: September 17, 2020

Abstract

In this paper, we study revenue maximization assortment and pricing problems under threshold-based choice models, where a product is placed in a consumer's consideration set if its utility to the consumer exceeds the utility of an outside option by a specified threshold. We discuss two such models: the relative utility and absolute utility threshold-based choice models. For both models, the best revenue-ordered assortment and same-price policy can not achieve the optimal profit for the assortment problem or the pricing problem. Further, the revenue-maximizing assortment problem is NP-complete or NP-hard. However, we show that a performance guarantee relative to the optimal policy can be found for each model: for the relative utility model, by employing the best revenue-ordered assortment and same-price policy; for the absolute utility model, via a dynamic-program-based algorithm and a same-price policy. Finally, we show that our algorithms can be asymptotically optimal if the search cost of consumers is sufficiently small.

Suggested Citation

Tian, Xu and Li, Anran, Assortment Optimization and Pricing Under the Threshold-Based Choice Models (September 17, 2020). Available at SSRN: https://ssrn.com/abstract=3694222 or http://dx.doi.org/10.2139/ssrn.3694222

Xu Tian (Contact Author)

University of Science and Technology of China (USTC) - School of Management ( email )

China

Anran Li

LSE ( email )

Houghton Street
London, WC2A 2AE
United Kingdom

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