Sensitivity analysis in linear programming: Just be careful!

In this paper we review the topic of sensitivity analysis in linear programming. We describe the problems that may occur when using standard software and advocate a framework for performing complete sensitivity analysis. Three approaches can be incorporated within it: one using bases, an approach using the optimal partition and one using optimal values. We elucidate problems and solutions with an academic example and give results from an implementation of these approaches to a large practical linear programming model of an oil refinery. This shows that the approaches are viable and useful in practice.