Algorithms and complexity results for the single-cut routing problem in a rail yard

Abstract

Rail yards are facilities that play a critical role in the freight rail transportation system. A number of essential rail yard functions require moving connected “cuts” of rail cars through the rail yard from one position to another. In a congested rail yard, it is therefore of interest to identify a shortest route for such a move. With this motivation, we contribute theory and algorithms for the Single-Cut Routing Problem (SCRP) in a rail yard. Two key features distinguish SCRP from a traditional shortest path problem: (i) the entity occupies space on the network; and (ii) track geometry further restricts route selection. To establish the difficulty of solving SCRP in general, we prove NP-completeness of a related problem that seeks to determine whether there is space in the rail yard network to position the entity in a given direction relative to a given anchor node. However, we then demonstrate this problem becomes polynomially solvable—and therefore, SCRP becomes polynomially solvable, too—for “Bounded Cycle Length” (BCL) yard networks. We formalize the resulting two-stage algorithm for BCL yard networks and validate our algorithm on a rail yard data set provided by the class I railroad CSX Transportation.