Sensivity analysis of the replacement problem capítulo: ingeniería y gestión de sistemas

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) which is obtained from the simplex algorithm in order to comprehend how the optimal solution changes with a slight change in the transition probabilities matrix . The perturbation (B~) can be approximated by a given matrix H such thatHkBB+=~. Some algebraic relations between the optimal solution (*B) and the solution of the perturbed instance (*B) are obtained, this is our approach, to establish some perturbation bounds through theorems and propositions.