Linear Interval Tolerance Problem and Linear Programming Techniques

In this paper, we consider the linear interval tolerance problem, which consists of finding the largest interval vector included in (A], b]) = {x R ⁿ | A A], b b], Ax = b}. We describe two different polyhedrons that represent subsets of all possible interval vectors in (A], b]), and we provide a new definition of the optimality of an interval vector included in (A], b]). Finally, we show how the Simplex algorithm can be applied to find an optimal interval vector in (A], b]).