Sensitivity analysis

Abstract

In many cases, after solving an LP problem with the simplex method, there is a change in the data of the LP problem. With sensitivity analysis, we can find if the input data of the LP problem can change without affecting the optimal solution. This chapter discusses how to deal with such changes efficiently. This topic is called sensitivity analysis. Sensitivity analysis is very useful in two situations: (i) when we wish to know how the solution will be affected if we perform a small change in the LP problem, and (ii) when we have already solved an LP problem and we also want to solve a second LP problem in which the data is only slightly different. Rather than restarting the simplex method from scratch for the modified LP problem, we want to solve the modified LP problem starting with the optimal basis of the original LP problem and perform only a few iterations to solve the modified LP problem (if necessary). We examine how the solution of an LP problem is affected when changes are made to the input data of the LP problem. Moreover, we examine changes in: (i) the cost vector, (ii) the right-hand side vector, and (iii) the coefficient of the constraints.