Annals of Operations Research

, Volume 254, Issue 1–2, pp 131–164 | Cite as

Multiproduct price optimization under the multilevel nested logit model

  • Hai JiangEmail author
  • Rui Chen
  • He Sun
Original Paper


We study the multiproduct price optimization problem under the multilevel nested logit model, which includes the multinomial logit and the two-level nested logit models as special cases. When the price sensitivities are identical within each primary nest, that is, within each nest at level 1, we prove that the profit function is concave with respect to the market share variables. We proceed to show that the markup, defined as price minus cost, is constant across products within each primary nest, and that the adjusted markup, defined as price minus cost minus the reciprocal of the product between the scale parameter of the root nest and the price-sensitivity parameter of the primary nest, is constant across primary nests at optimality. This allows us to reduce the multidimensional pricing problem to an equivalent single-variable maximization problem involving a unimodal function. Based on these findings, we investigate the oligopolistic game and characterize the Nash equilibrium. We also develop a dimension reduction technique which can simplify price optimization problems with flexible price-sensitivity structures.


Differentiated products Multiproduct pricing Multilevel nested logit Oligopolistic competition 



The authors are very grateful to the anonymous referees whose thoughtful comments and constructive suggestions have allowed them to improve the quality of this paper. This research is supported by the Natural Science Foundation of China [Grant 71622006] and the Center for Data-Centric Management in the Department of Industrial Engineering at Tsinghua University.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Industrial EngineeringTsinghua UniversityBeijingChina

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