Solving a freight transport problem using facility location techniques

Use of consolidation terminals to transport products from various sources to various destinations can take advantage of economies of scale in transportation costs. Instead of making direct shipments, each source can ship in bulk to one or more consolidation terminals. There, shipments can be broken down, and material bound for the same destination can be combined. Such a freight transport problem (FTP) is considered. For each source-destination pair, it must be decided whether to ship the product directly or via a consolidation terminal. Shipping costs are piecewise linear concave functions of the volume shipped. Shipping via a terminal can also incur a linear inventory holding cost. A minimum cost pattern of direct and indirect (i.e., via a terminal) shipments is sought. This is a type of concave cost multiproduct network flow problem. This problem can be solved optimally if either the source-to-terminal or the terminal-to-destination shipping costs are linear. In this case, FTP decomposes into a set of concave cost facility location problems (CFLP). In more general cases, heuristic methods that solve sequences of linear problems can be used. Some computational results are presented.