Assign-to-Seat: Dynamic Capacity Control for Selling High-Speed Train Tickets

Abstract

Problem definition: We consider a revenue management problem that arises from the selling of high-speed train tickets in China. Compared with traditional network revenue management problems, the new feature of our problem is the assign-to-seat restriction. That is, each request, if accepted, must be assigned instantly to a single seat throughout the whole journey, and later adjustment is not allowed. When making decisions, the seller needs to track not only the total seat capacity available, but also the status of each seat. Methodology/results: We build a modified network revenue management model for this problem. First, we study a static problem in which all requests are given. Although the problem is NP-hard in general, we identify conditions for solvability in polynomial time and propose efficient approximation algorithms for general cases. We then introduce a bid-price control policy based on a novel maximal sequence principle. This policy accommodates nonlinearity in bid prices and, as a result, yields a more accurate approximation of the value function than a traditional bid-price control policy does. Finally, we combine a dynamic view of the maximal sequence with the static solution of a primal problem to propose a “re-solving a dynamic primal” policy that can achieve uniformly bounded revenue loss under mild assumptions. Numerical experiments using both synthetic and real data document the advantage of our proposed policies on resource-allocation efficiency. Managerial implications: The results of this study reveal connections between our problem and traditional network revenue management problems. Particularly, we demonstrate that by adaptively using our proposed methods, the impact of the assign-to-seat restriction becomes limited both in theory and practice. Funding: S. Liu’s research is partly supported by the National Natural Science Foundation of China (NSFC) [Grant NSFC-72072117]. Z. Wang’s research is partly supported by the NSFC [Grant NSFC-72150002]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.1188 .