ILOG CPLEX 11.0 User's Manual

24Preprocessing and FeasibilityILOG CPLEX preprocessing may declare a model infeasible before the selectedoptimization algorithm begins. This early declaration saves considerable execution time inmost cases. When this declaration is the outcome of preprocessing, it is important tounderstand that there are two classes of reductions performed by the preprocessor.Reductions that are independent of the objective function are called primal reductions; thosethat are independent of the righthand side (RHS) of the constraints are called dualreductions. Preprocessing operates on the assumption that the model being solved isexpected by the user to be feasible and that a finite optimal solution exists. If this assumptionis false, then the model is either infeasible or no bounded optimal solutions exist; that is, it isunbounded. Since primal reductions are independent of the objective function, they cannotdetect unboundedness, they can detect only infeasibility. Similarly, dual reductions candetect only unboundedness.Thus, to aid analysis of an infeasible or unbounded declaration by the preprocessor, aparameter is provided that the user can set, so that the optimization can be rerun to makesure that the results reported by the preprocessor can be interpreted. If a model is declared bythe preprocessor to be infeasible or unbounded and the user believes that it might beinfeasible, the parameter Reduce can be set to 1 by the user, and the preprocessor will onlyperform primal reductions. If the preprocessor still finds inconsistency in the model, it willbe declared by the preprocessor to be infeasible, instead of infeasible or unbounded.Similarly, setting the parameter to 2 means that if the preprocessor detects unboundedness inthe model, it will be declared unambiguously to be unbounded.ILOG CPLEX 11.0 — USER’ S MANUAL 385