FINDING POSTAL CARRIER WALK PATHS IN MIXED GRAPHS

The postman problem requires finding a lowest cost tour in a connected graph that traverses each edge at least once. In this paper we first give a brief survey of the literature on postman problems including, t he original Chinese postman problem on undirected graphs, the windy Ch inese postman problem on graphs where the cost of an are depends on th e direction the are is transversed, the directed postman problem on gr aphs with directed edges, and the mixed postman problem on graphs in w hich there are some directed and some undirected arcs. We show how the mixed postman problem can be solved as an integer program, using the formulation of Gendreau, Laporte and Zhao, by a new row addition branc h and bound algorithm, which is a modification of the column subtracti on algorithm for set partitioning problems of Harche and Thompson. Com putational experience shows that a ''slack variable'' heuristic is ver y effective in finding good solutions that are frequently optimal for these problems.