TITLE:
Sensitivity Analysis of the Replacement Problem
AUTHORS:
Eva Selene Hernández Gress, Gilberto Pérez Lechuga, Neil Hernández Gress
KEYWORDS:
Replacement Policy, Markov Processes, Linear Programming
JOURNAL NAME:
Intelligent Control and Automation,
Vol.5 No.2,
May
8,
2014
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 obtained from the simplex algorithm. The
perturbation can be
approximated by a given matrix Hsuch
that . Some algebraic relations between the optimal
solution and the perturbed instance are obtained and discussed.