Optimal Freight Train Classification using Column Generation

We consider planning of freight train classification at hump yards using integer programming. The problem involves the formation of departing freight trains from arriving trains subject to scheduling and capacity constraints. To increase yard capacity, we allow the temporary storage of early freight cars on specific mixed-usage tracks. The problem has previously been modeled using a direct integer programming model, but this approach did not yield lower bounds of sufficient quality to prove optimality. In this paper, we formulate a new extended integer programming model and design a column generation approach based on branch-and-price to solve problem instances of industrial size. We evaluate the method on historical data from the Hallsberg hump yard in Sweden, and compare the results with previous approaches. The new method managed to find optimal solutions in all of the 192 problem instances tried. Furthermore, no instance took more than 13 minutes to solve to optimality using fairly standard computer hardware.