A Reward Functional to Solve the Replacement Problem

Abstract

The replacement problem can be modeled as a finite, irreducible, homogeneous Markov Chain. In our proposal the pro- blem was modeled using a Markov decision process and then, the instance was optimized using dynamic programming. We proposed a new functional that includes a reward functional, that can be more helpful in processing industries be- cause it considerate instances like incomes, maintenance costs, fixed costs to replace equipment, purchase price and salvage values; and this functional can be solved with dynamic programming and used to make effective decisions. Two theorems are proved related with this new functional. A numerical example is presented in order to demonstrate the utility of this proposal.