The Dynamic, Resource-constrained Shortest Path Problem on an Acyclic Graph with Application in Column Generation and a Literature Review on Sequence-dependent Scheduling

The Dynamic, Resource-Constrained Shortest-Path Problem on an Acyclic Graph with Application in Column Generation and a Literature Review on Sequence-Dependent Scheduling. (December 2005) Xiaoyan Zhu, B.En., Tsinghua University; M.S., MIT & Nanyang Technological University; M.S., Texas A&M University Chair of Advisory Committee: Dr. Wilbert E. Wilhelm This dissertation discusses two independent topics: a resource-constrained shortest-path problem (RCSP) and a literature review on scheduling problems involving sequence-dependent setup (SDS) times (costs). RCSP is often used as a subproblem in column generation because it can be used to solve many practical problems. This dissertation studies RCSP with multiple resource constraints on an acyclic graph, because many applications involve this configuration, especially in column genetation formulations. In particular, this research focuses on a dynamic RCSP since, as a subproblem in column generation, objective function coefficients are updated using new values of dual variables at each iteration. This dissertation proposes a pseudo-polynomial solution method for solving the dynamic RCSP by exploiting the special structure of an acyclic graph with the goal of effectively reoptimizing RCSP in the context of column generation. This method uses a one-time “preliminary” phase to transform RCSP into an unconstrained shortest path problem (SPP) and then solves the resulting SPP after new values of dual variables are used to update objective function coefficients (i.e., reduced costs) at each iteration. Network reduction techniques are considered to remove some nodes and/or arcs permanently in the