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M. Abbad, J. Filar and T. R. Bielecki, “Algorithms for Singularly Perturbed Markov Chain,” Proceedings of the 29th IEEE Conference, Honolulu, 5-7 December 1990, pp. 1402-1407.

has been cited by the following article:

• TITLE: A Reward Functional to Solve the Replacement Problem

  AUTHORS: Eva Selene Hernández Gress, Oscar Montaño Arango, José Ramón Corona Armenta, Antonio Oswaldo Ortega Reyes

  KEYWORDS: Markov Chains; Dynamic Programming; Replacement Problem

  JOURNAL NAME: Intelligent Control and Automation, Vol.3 No.4, November 28, 2012

  ABSTRACT: The replacement problem can be modeled as a finite, irreducible, homogeneous Markov Chain. In our proposal the problem 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 because 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.