A SET COVERING APPROACH TOINFEASIBILITY ANALYSIS OF LINEARPROGRAMMING PROBLEMS AND RELATEDISSUESbyMark Richard

With the increased sophistication of both computers and optimization software, linear programming problems of a size inconceivable to solve only a few years ago are now readily accessible. As model size and complexity increase, the issue of feasibility becomes a major issue in model development. This thesis explores the analysis of linear programming in-feasibility through the use of Irreducible Infeasible Subsystems, or I ISs. In particular, we develop a constraint generation algorithm for identifying the minimum weight I IS cover, which isolates a minimal weight set of constraints whose removal from the system yields a feasible system. It has been shown that this set covering problem has a very special structure. We also explore the facial structure of the set covering polyhedra and provide a generalization to a class of covering problems. The link between this problem and the linear discriminant problem is also explored. This abstract accurately represents the content of the candidate's thesis. I recommend its publication.