Erwin Pesch, Alena Otto, Xiyu Li

• We propose a two-way bounded dynamic programming (TBDP) approach to deal with situations, when it takes a long time to evaluate the value function in the state graph of dynamic programming. TBDP provides sharp bounds early in the solution process and identifies critical subproblems, i.e., states and transition arcs, for which the value function has to be estimated.Based on the TBDP framework, we develop a heuristic and an exact algorithm for the static crane scheduling problem (SCSP). The SCSP refers to simultaneous yard partitioning into single-crane areas and job sequencing at railway container transshipment yards, where both rail-rail and rail-road transshipments are present and rail-rail moves are short. The designed exact solution algorithm solves instances of practically relevant size within acceptable time limits. The proposed heuristic finds optimal solutions in 90% of the cases. We recommend using the heuristic algorithm for planning very large transshipment yards, with more than five tracks and a large number of container moves per crane.