We consider a dynamic pricing problem in network revenue management in which customer behavior is predicted by a choice model, that is, the multinomial logit model. The problem, even in the static setting (i.e., customer demand remains unchanged over time), is highly nonconcave in prices. Existing studies mostly rely on the observation that the objective function is concave in terms of purchasing probabilities, implying that the static pricing problem with linear constraints on purchasing probabilities can be efficiently solved. However, this approach is limited in handling constraints on prices, noting that such constraints could be highly relevant in some real business considerations. To address this limitation, in this work, we consider a general pricing problem that involves constraints on both prices and purchasing probabilities. To tackle the nonconcavity challenge, we develop an approximation mechanism that allows solving the constrained static pricing problem through bisection and mixed-integer linear programming (MILP). We further extend the approximation method to the dynamic pricing context. Our approach involves a resource decomposition method to address the curse of dimensionality of the dynamic problem as well as an MILP approach to solving subproblems to near optimality. Numerical results based on generated instances of various sizes indicate the superiority of our approximation approach in both static and dynamic settings. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: S.-F. Cheng acknowledges funding support from the Singapore Ministry of Education Academic Research Fund Tier 1 Grant Grant 23-SIS-SMU-017. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0852 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0852 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
Shao et al. (Fri,) studied this question.