How to Analyze the Results of Linear Programs—Part 4: Forcing Substructures

Often, solution values are forced by implication of some of the constraints. A forcing substructure is a portion of the linear program that forces some of the variables to have only one value in every feasible solution. In some cases, finding a forcing substructure reveals an error, and in other cases, it leads to a reduction of the linear program. Discovering and explaining forcing substructures are aspects of good model management. Besides its role when debugging a model, understanding forcing substructures deepens our understanding of the solution by revealing some activity levels that are determined by implications of the constraints, not by economic preference.