The basic train makeup problem in shunting yards

In shunting yards, railcars of incoming trains are uncoupled and reassembled to outbound trains. This time-critical process that employs a complex system of switches, hump hills, and classification tracks requires plenty interdependent decision problems to be solved. An elementary decision task among these is the train makeup problem, which assigns railcars of inbound freight trains to outbound trains, such that the priority values of the selected cuts of railcars are maximized and given train capacities are observed. This assignment decision is further complicated by the fact that railcars cannot facultatively be selected, but the buildup sequences of incoming trains need to be considered. This work introduces and discusses the basic train makeup problem, analyses its complexity status and develops suited exact and heuristic solution procedures that are tested in a comprehensive computational study.