The Cut Search Algorithm with Arc Capacities and Lower Bounds

This paper presents a computational procedure for solving maximal flow problems in flow networks subject to positive upper bound or capacity constraints and lower bound restrictions that are equal to or greater than zero. This procedure, referred to as the cut search algorithm, locates directly the minimal cut in a flow network structure. The algorithm not only has demonstrated computational efficiency over the existing out-of-kilter procedure, but also it provides a direct solution routine for project time/cost tradeoff problems and other network cut based problem situations in which the restricting arcs of the network formulation must be located.