On solving assignment type mixed integer linear programming problems within decision support systems

In this paper we discuss how assignment type mixed integer problems as they often occur in practical situations can be handled. It is shown that the linear programming relaxation of mixed integer problems of a certain type yields solutions with only a few non-unique assignments. We will give tight upperbounds for the number of non-unique assignments that result after solving the linear programming relaxation of the problem. Since the number of splitted assignments is small one can use a heuristic to reach a practically good and feasible assignment. The final part of the paper is devoted to deriving heuristics for generalized assignment type problems. These heuristics take the LP-relaxation solution as a startingspoint. Conditions are given which guarantee that the heuristics produce good feasible solutions. Key words: Mixed integer linear programming, assignment problems, location-allocation problems, distribution problems.