The complexity of the Timetable-Based Railway Network Design Problem

TL;DR

This paper introduces a robust, scenario-based approach to designing railway infrastructure that accounts for uncertain long-term timetables and capacity constraints, aiming to minimize expansion costs while ensuring operational flexibility.

Contribution

It formulates the railway network design as an NP-hard problem under uncertainty and proposes an integer linear programming model with scenario-based optimization.

Findings

The problem is NP-hard even on simple bipartite graphs.

Special cases of the problem are solvable more easily.

A scenario-based ILP model effectively balances expansion costs and timetable robustness.

Abstract

Because of the long planning periods and their long life cycle, railway infrastructure has to be outlined long ahead. At the present, the infrastructure is designed while only little about the intended operation is known. Hence, the timetable and the operation are adjusted to the infrastructure. Since space, time and money for extension measures of railway infrastructure are limited, each modification has to be done carefully and long lasting and should be appropriate for the future unknown demand. To take this into account, we present the robust network design problem for railway infrastructure under capacity constraints and uncertain timetables. Here, we plan the required expansion measures for an uncertain long-term timetable. We show that this problem is NP-hard even when restricted to bipartite graphs and very simple timetables and present easier solvable special cases. This problem corresponds to the fixed-charge network design problem where the expansion costs are minimized such that the timetable is conductible. We model this problem by an integer linear program using time expanded networks. To incorporate the uncertainty of the future timetable, we use a scenario-based approach. We define scenarios with individual departure and arrival times and optional trains. The network is then optimized such that a given percentage of the scenarios can be operated while minimizing the expansion costs and potential penalty costs for not scheduled optional trains.