Solving sorting of rolling stock problems utilizing pseudochain structures in graphs

Rearranging cars of an incoming train in a hump yard is a widely discussed topic. Sorting of Rolling Stock Problems can be described in several scenarios and with several constrains. We focus on the train marshalling problem where the incoming cars of a train are distributed to a certain number of sorting tracks. When pulled out again to build the outgoing train, cars sharing the same destination should appear consecutively. The goal is to minimize the number of sorting tracks. We suggest a graph-theoretic approach for this NP-complete problem. The idea is to partition an associated directed graph into what we call pseudochains of minimum length. We describe a greedy-type heuristic to solve the partitioning problem which, on random instances, performs better than the known heuristics for the train marshalling problem. In addition we discuss the TMP with b-bounded sorting tracks.