Efficient Frontier and Applications in Product Offering and Pricing

Chenxu Ke (), Lijian Lu () and Ruxian Wang ()
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Chenxu Ke: College of Business, Shanghai University of Finance and Economics, Shanghai 200433, China
Lijian Lu: School of Business and Management, Hong Kong University of Science and Technology, Hong Kong
Ruxian Wang: Johns Hopkins Carey Business School, Baltimore, Maryland 21202

Manufacturing & Service Operations Management, 2025, vol. 27, issue 2, 389-407

Abstract: Problem definition : The joint assortment and pricing problem is notoriously difficult to solve, especially for large-scale issues subject to various operational constraints arising from business practices. In this paper, we delve into the joint optimization challenge under constrained logit choice models, accounting for product-differentiated price sensitivities across static, randomized, and dynamic contexts. Methodology/results : We develop a unified optimization methodology that applies efficient frontier and dimensional reduction and transforms the joint optimization problem into a single-variable one with respect to the total choice probability. The efficient frontier is employed to transform the nonconcave objective function equivalently into its concave counterpart. We show that the optimal prices are uniquely determined by the common target adjusted markup. The complexity of the mixed combinatorial optimization problem can be reduced by searching over efficient sets of polynomial size. In the randomized assortment and pricing problem in which the product offer sets and prices follow certain distribution, we show that randomization has the potential to elevate the total revenue to the exact efficient frontier, a feat that the static problem may fail to achieve (with a given total choice probability). For dynamic joint product selection and pricing, we find that the optimal policy adopts a simple time-threshold structure that can be precomputed. Furthermore, we illustrate the robustness of our methodology by extending the analysis to a variety of general settings, including the nested logit model. Managerial implications : The proposed methodology contributes to the increasingly popular topic in retail management by significantly reducing the computational complexity of joint product offering and pricing under different constraints. Our results regarding the effects of product set constraints and price bounds provide valuable insights and guidance to practitioners on product offering and pricing in various business scenarios.

Keywords: efficient frontier; efficient set; efficient prices; assortment and pricing; threshold policy (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormsom:v:27:y:2025:i:2:p:389-407

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