Other Model Analyses
The various algorithms for analyzing infeasibility turn out to be useful in analyzing other types of models and modeling problems. This chapter describes three such examples.
It is well known that if the primal form of a linear program is unbounded, then the dual form is infeasible (see e.g. Winston and Venkataramanan (2003)). For this reason, if an LP is found to be unbounded then an infeasibility analysis of the dual provides insight into the reason for the unboundedness. This is exactly the approach taken in the LINDO software (Schrage 1997) to return a minimal unbounded set of variables. At least one of the variables in this set must be finitely bounded to eliminate the unboundedness in the model. The thought process for the analyst is similar to the process for analyzing infeasibility: there may be other minimal unbounded sets of variables that must be found and fixed one by one in order to eliminate all unboundedness in the model. It is also possible to find a minimal set of variables to restrict so that all unboundedness is removed (similar to an IIS set cover). Since unboundedness difficulties are usually caused by missing constraints or bounds, the usefulness of this approach lies in providing clues as to where constraints have been omitted.
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