Feasibility in Transportation

In this paper we consider a new type of mixed integer programming problem: Transportation Network with Supply Eating Arcs. This problem arises from an application in intelligent telecommunications] networks, IN. It contains within its deenition many classical mixed integer programming problems. The problem is deened as a transportation network with an additional condition. For an arc to have positive ow, the node capacity of its originating node (i.e. a supply node) is decreased by a xed amount dependent on the arc. In studying this problem we are interested mainly in feasibility of such problems and focus our attention on this aspect here. We discuss why nding a feasible solution is diicult as well as various methods for nding one. In particular we describe a set of solutions (in terms of solution structure) which always contains a feasible solution, if one exists, and describe a method for nding a feasible solution based on enumerating this set. The main advantage of the solution procedure is that at no time do we need to explicitly solve an LP (or even a transportation problem).