Detecting irreducibly inconsistent systems in infeasible linear programmes using techniques from goal programming

This paper presents ideas from goal programming (GP) used as an accompaniment to linear programming (LP) for the analysis of LP infeasibility. A new algorithm for the detection of irreducibly inconsistent systems of constraints is presented using this approach. The structure necessary for implementing such a procedure into a commercial LP solver is outlined. Results for a selection of infeasible LP problems are given, and conclusions drawn.