Engine Scheduling by Column Generation

Abstract

This practically oriented thesis deals with the generation of short term schedules for switching engines at industrial in-plant railroads. The problem is related to the multiple-vehicle pickup and delivery problem with time windows. We consider combinatorial restrictions of the sequence of visited locations, introducing the concept of pattern concatenation. We show that the construction of schedules of minimal cost with respect to total travel time is NP-complete in the strong sense. Two models for the minimization problem are developed in this thesis. The first is an adaptation of a mixed integer program known from the literature. It is of polynomial size but the quality of its LP relaxation is provably poor. The second formulation is a set partitioning program where a variable corresponds to a feasible schedule for an engine, represented by the subset of visited requests. The number of variables is exponential in the size of the instance, and we propose to solve its LP relaxation by column generation. The pricing problem is a constrained shortest path problem and is proven to be NP-complete in the strong sense. A new lower bounding criterion is used to prune the search space of the princing dynamic programming algorithm. We extensively discuss our implementation and give computational results for practical problem instances. An investigation of the concept of patterns reveals its theoretical advantages as well. The large bibliography is intended to contribute in its own right and contains more than 100 references to column generation.