A Novel Dynamic Programming Approach to the Train Marshalling Problem

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.

Reconfiguring Shortest Paths in Graphs

“…Thus, our algorithm for permutation graphs is more efficient than our algorithm for circle graphs. In fact, permutation graphs themselves model a problem similar to container stowage called the train marshalling problem (Dahlhaus et al 2000;Jaehn, Rieder, and Wiehl 2015;Rinaldi and Rizzi 2017;Dörpinghaus and Schrader 2018;Falsafain and Tamannaei 2020). Both permutation graphs and circle graphs also have applications in memory allocation for system programs (Even and Itai 1971;Even, Pnueli, and Lempel 1972).…”

Train management in freight shunting yards: Formalisation and literature review

“…An improved DP algorithm is proposed in ref. [22] that directly solves the optimisation problem instead of its decision version, with a worst‐case time complexity of $$O(nt2^t)$$. This is achieved by grouping together subinstances that have the same optimal solution on the one hand, and by using the memorisation technique on the other, i.e.…”

Reconfiguring Shortest Paths in Graphs

“…We solve SPR for circle graphs by solving SPR for a subclass of circle graphs known as permutation graphs, and then generalizing our solution to circle graphs. In fact, permutation graphs themselves model a problem that is very much similar to container stowage called the train marshalling problem [Dahlhaus et al, 2000, Rinaldi and Rizzi, 2017, Falsafain and Tamannaei, 2020.…”