In the petrochemical industry, we have been required to optimize a production schedule for the efficient management. Determining how to provide naphtha to the petrochemical plant is one of the most crucial problems in the optimization of such production scheduling. Typically, purchased naphtha, which is provided from the sea berth, is first stored temporarily in storage tanks, and after that, is provided to the plant, according to a predetermined production schedule. Then we are required to find pairwise disjoint routes between the sea berth and a tank, between two distinct tanks, or between a tank and the plant. In this paper, we formulate the problem of finding routes in a tank network as a problem of computing disjoint paths in a graph, and propose an algorithm for enumerating all sets of disjoint paths based on the graph theory. Our algorithm first constructs a tree-shaped data structure for each pair of prescribed vertices which represents all paths between the pair of vertices, and then computes disjoint paths efficiently by traversing the tree-shaped data structures. We also evaluate the practical performance of our algorithm by conducting a computational experiment based on the case in Showa Denko K.K.
