A self-validating method for solving linear programming problems with interval input data

A Self-Validating Method for Solving Linear Programming Problems with Interval input Data. Linear programming problems are very important in many practical applications. They are usually solved by the simplex method. The computational results are, in general, good approximations to the solution of the problem. However, in some cases the computed approximation may be wrong due to round-off and cancellation errors. In practice it occurs frequently that the input data of a linear programming problem are not known exactly but are afflicted with tolerances. In this case it has to be precisely defined what a “solution” to such a problem is. A sensitivity or postoptimality analysis is necessary. In the following a method for linear programming problems with interval input data is described which computes guaranteed lower and upper bounds for all optimal vertices and the optimal value. The method controls rigorously all round-off errors and gives an automatic sensitivity analysis. As an example a diet problem is treated to demonstrate how the method in principle works. © Springer-Verlag/Wien 1988