Integrated demand-side management and timetabling for an urban rail transit line: A Benders decomposition approach

TL;DR

This paper presents a Benders decomposition approach to optimize demand-side management and train scheduling in urban rail transit, reducing passenger waiting times and balancing operational costs through integrated strategies.

Contribution

It introduces a novel mathematical framework combining demand management, timetabling, and trip-shifting, with an efficient Benders decomposition algorithm for urban rail systems.

Findings

Outperforms commercial solvers in computational efficiency.

Effectively reduces passenger waiting times and station overcrowding.

Ensures service fairness across stations.

Abstract

The intelligent upgrading of metropolitan rail transit systems has made it feasible to implement demand-side management policies that integrate multiple operational strategies in practical operations. However, the tight interdependence between supply and demand necessitates a coordinated approach combining demand-side management policies and supply-side resource allocations to enhance the urban rail transit ecosystem. In this study, we propose a mathematical and computational framework that optimizes train timetables, passenger flow control strategies, and trip-shifting plans through the pricing policy. Our framework incorporates an emerging trip-booking approach that transforms waiting at the stations into waiting at home, thereby mitigating station overcrowding. Additionally, it ensures service fairness by maintaining an equitable likelihood of delays across different stations. We formulate the problem as an integer linear programming model, aiming to minimize passengers' waiting time and government subsidies required to offset revenue losses from fare discounts used to encourage trip shifting. To improve the computational efficiency, we develop a Benders decomposition-based algorithm within the branch-and-cut method, which decomposes the model into train timetabling with partial passenger assignment and passenger flow control subproblems. We propose valid inequalities based on our model's properties to strengthen the linear relaxation bounds at each node of the branch-and-bound tree. Computational results from proof-of-concept and real-world case studies on the Beijing metro show that our solution method outperforms commercial solvers in terms of computational efficiency.