Efficient Frontier and Applications in Product Offering and Pricing

52 Pages Posted: 12 Apr 2022 Last revised: 16 May 2022

See all articles by Chenxu Ke

Chenxu Ke

Nanjing University - School of Business

Lijian Lu

HKUST Business School - ISOM Department

Ruxian Wang

Johns Hopkins University - Carey Business School

Date Written: April 11, 2022


Problem definition: The joint assortment and pricing problem is notoriously challenging, especially with a large problem size and various operational constraints arising from business practices. In this paper, we consider the joint product offering and pricing under the constrained logit choice models with product-differentiated price sensitivities in both static and dynamic settings.

Methodology/results: We develop an efficient methodology that applies efficient frontier and dimensional reduction that transforms the joint optimization into a single-variable one controlling the aggregate resource consumption rate. The efficient frontier is employed to transform the non-concave objective function equivalently into its concave counterpart. We show that the optimal prices of all the products are uniquely determined by a target adjusted markup. The mixed combinatorial optimization can be simplified by searching over efficient sets of polynomial size. For the dynamic joint product selection and pricing, we fully characterize the optimal policy that adopts a simple time-threshold structure that can be pre-computed. We also show the robustness of our methodology by extending the analysis to general settings and the nested logit model.

Managerial implications: The proposed methodology contributes to the increasingly popular topic in the retail management by significantly reducing the computational complexity of joint product selection and pricing. Our results on the impacts of the product set constraints and price bounds provide concrete guidance to practitioners on products offerings and prices in various business scenarios.

Keywords: Efficient Frontier; Efficient Set and Price; Assortment Planning; Pricing; Time-Threshold Policy

Suggested Citation

Ke, Chenxu and Lu, Lijian and Wang, Ruxian, Efficient Frontier and Applications in Product Offering and Pricing (April 11, 2022). HKUST Business School Research Paper No. 2022-056, Johns Hopkins Carey Business School Research Paper 22-09, Available at SSRN: https://ssrn.com/abstract=4080854 or http://dx.doi.org/10.2139/ssrn.4080854

Chenxu Ke

Nanjing University - School of Business ( email )

22 Hankou Road
Nanjing, Jiangsu 210093 210093

Lijian Lu (Contact Author)

HKUST Business School - ISOM Department ( email )

Clear Water Bay
Hong Kong

Ruxian Wang

Johns Hopkins University - Carey Business School ( email )

1625 Massachusetts Ave NW
Washington, DC 20036
United States

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