# A Novel Dynamic Programming Approach to the Train Marshalling Problem

## TL;DR

This paper introduces a new dynamic programming algorithm for the Train Marshalling Problem, significantly improving computational efficiency over existing methods and effectively reordering railcars with fewer classification tracks.

## Contribution

The paper presents a novel exact DP algorithm for TMP with lower worst-case complexity and better practical performance than existing algorithms.

## Key findings

- The new DP algorithm reduces computational complexity.
- Experimental results show improved performance over existing algorithms.
- The approach effectively minimizes the number of classification tracks needed.

## Abstract

Train marshalling is the process of reordering the railcars of a train in such a way that the railcars with the same destination appear consecutively in the final, reassembled train. The process takes place in the shunting yard by means of a number of classification tracks. In the Train Marshalling Problem (TMP), the objective is to perform this rearrangement of the railcars with the use of as few classification tracks as possible. The problem has been shown to be NP-hard, and several exact and approximation algorithms have been developed for it. In this paper, we propose a novel exact dynamic programming (DP) algorithm for the TMP. The worst-case time complexity of this algorithm (which is exponential in the number of destinations and linear in the number of railcars) is lower than that of the best presently available algorithm for the problem, which is an inclusion-exclusion-based DP algorithm. In practice, the proposed algorithm can provide a substantially improved performance compared to its inclusion-exclusion-based counterpart, as demonstrated by the experimental results.