Extensive Model and Matheuristic Algorithm for the Train Platforming Problem with Two-Train-Capacity Tracks: A Case Study of Prague Central Station

Abstract

This paper provides a deeper insight into the train platforming problem (TPP). Many studies have focused on different versions of train scheduling and routing problems, and most of them assume that the platform track’s capacity is one train. However, especially in busy and complex railway stations, most platform tracks are divided into two parts, allowing two trains to simultaneously share the same platform track for passenger boarding/alighting. This results in more efficient train assignment to the platform tracks. In addition, consideration of the track capacity makes the problem more difficult because directions of trains are problematic. Motivated by this challenge, we consider the TPP with two-train-capacity tracks. We first describe the problem in detail and then propose a mixed-integer programming model. The objective of the considered problem is to minimize the total weighted train delays, which are defined as the difference between the departure times calculated by the mathematical model (M1) and the scheduled departure times of the trains in the timetable. Because of the NP-hard nature of the problem, the proposed M1 may not find feasible solutions for large-size problems. Thus, a matheuristic algorithm (MA) is developed to solve large-size problems. We used randomly generated test problems to demonstrate the performance of the proposed M1 and MA. Experimental results showed that MA outperforms M1 in both solution quality and solution time. Additionally, a case study was conducted at the central station of Prague, Czechia.