Sensitivity Analysis of the Replacement Problem

Abstract

The replacement problem can be modeled as a finite, irreducible, homogeneous Markov Chain. In our proposal we modeled the problem using a Markov decision process and then, the instance is optimized using linear programming. Our goal is to analyze the sensitivity and robustness of the optimal solution across the perturbation of the optimal basis (B) obtained from the simplex algorithm. The perturbation (?B ) can be approximated by a given matrix H such that ?B = kB + H. Some algebraic relations between the optimal solution and the solution of the perturbed instance are obtained.