Global Solutions for a Nonconvex Nonconcave Rail Network Model

Abstract

This paper is concerned with developing long-range planning models of transportation systems to assist planners in assessing the impact of various levels of service in a transportation network. Railroad distribution networks are studied in particular, and emphasis is placed on the problem of determining optimal levels of service (improvements, degradations, abandonments) on each arc in the existing network. The problem is to optimally design a transportation system: the term “design” as used here, does not comprehend new networks, but more importantly, the optimization or “pruning” of existing transshipment networks. The model is formulated so that improvements to the shipping arcs are included as decision variables: The concave transshipment problem is extended to the case where coefficients of the shipping cost functions are treated as decision variables. Thus the model determines optimum movements of freight between nodes and optimum improvements/degradations to the network to minimize shipping costs plus maintenance costs on the shipping arcs. The result is a nonconvex, nonconcave transshipment problem which is then converted into a concave minimization problem for which global optimal solutions can be found. Several sample problems are solved.