Sensitivity Analysis of the Replacement Problem

Eva Selene Hernández Gress, Gilberto Pérez Lechuga, Neil Hernández Gress

Academic Area of Engineering, Autonomous University of Hidalgo, Pachuca, México.
Monterrey Institute of Technology-Mexico State Campus, Pachuca, México.

DOI: 10.4236/ica.2014.52006                

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 H such that . Some algebraic relations between the optimal solution and the perturbed instance are obtained and discussed.

 

Keywords

Replacement Policy, Markov Processes, Linear Programming

Conflicts of Interest

The authors declare no conflicts of interest.

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