The difference between the managerial and mathematical interpretation of sensitivity analysis results in linear programming

This paper shows that managerial questions are not answered satisfactorily with the mathematical interpretation of sensitivity analysis when the solution of a linear programming model is degenerate. Most of the commercially available software packages provide sensitivity results about the optimality of a basis and not about the optimality of the values of the decision variables. The misunderstanding of the shadow price and the validity range information provided by a simplex based computer program may lead to a wrong decision with considerable financial losses and strategic consequences. The paper classifies the most important types of sensitivity information, graphically illustrates degeneracy, and demonstrates its effect on sensitivity analysis. A production planning example is provided to show the possibility of faulty production management decisions when sensitivity results are not understood correctly. Finally the recommendations for the users of linear programming models and for software developers are provided.