Capacity Alignment Planning for a Coal Chain: A Case Study

We study a capacity alignment planning problem for a coal chain. Given a set of train operators, a set of train paths and a terminal comprising of a dump station and a set of routes from the dump station to the stockyard, we seek a feasible assignment of train operators to train paths, to time slots at the dump station, and to routes. The assignment must maximize the number of system paths in the resulting schedule and the schedule should perform well with respect to various performance criteria. We model the problem as a mixed-integer conic program (MICP) with multiple objectives which we solve using a hierarchical optimization procedure. In each stage of this procedure, we solve a single objective MICP. Depending upon whether we evaluate the associated performance criteria under a 2- or 1-norm, we reformulate the MICP as either a mixed-integer second-order cone program or as a mixed-integer linear program, respectively, and can streamline the hierarchical optimization procedure by exploiting properties of the model or observed behaviour on practical instances. We compare the performance of the procedure under the different norms on a real instance of the problem and find that the quality of the solutions found by the faster 1-norm procedure compares well to the solution found under the 2-norm.