Optimal replacement in a system of n-machines with random horizon

  • Rocío Ilhuicatzi-Roldan Benemerita Universidad Autónoma de Puebla.
  • Hugo Cruz Benemerita Universidad Autónoma de Puebla.
Palabras clave: Mathematical programming, optimal stochastic control, dynamic programming, Markov decision processes, programación matemática, control estocástico óptimo, programación dinámica, procesos de decisión de Markov.


This paper considers a system consisting of independently operating n-machines, which follows a deterioration processes with an associated cost function. It is assumed that the system is observed at discrete time and the objective function is the total expected cost. Also, it is considered that the horizon of the problem is random. For this problem, a replacement optimal policy that minimize the operation cost of the system is provided. Besides, a numerical example through a program in Matlab is presented.

Biografía del autor

Rocío Ilhuicatzi-Roldan, Benemerita Universidad Autónoma de Puebla.
Facultad de Ciencias Físico-Matemáticas.
Hugo Cruz, Benemerita Universidad Autónoma de Puebla.
Facultad de Ciencias Físico-Matemáticas.


[1] Bertsekas D.; Programming and Optimal Control, Athena Scientific, Massacchusetts, 1987.

[2] Childress S., Durango-Cohen P.; On Parallel Machine Replacement Problems with General Replacement Functions and Stochastic Deterioration, Vol. 52, Naval Research Logistics, 2005.

[3] Hernandez-Lerma O., Lasserre J. B.; Discrete-Time Markov Control Processes: Basic Optimality Criteria, Springer-Verlag, New York, 1996.

[4] Iida T., Mori M.; Markov Decision Processes with Random Horizon, Journal of the Operations Research, Vol. 39, No. 4, 1996.

[5] Levhari D., Mirman L. J.; Savings and Consumption with an Uncertain Horizon, Journal of Political Economy, Vol. 85, No. 2, 1977.

[6] Nair S. K., Hopp W. J.; A model for equipment replacement due to technological obsolescence, European Journal of Operational Research, Vol. 63, 1992.

[7] Powell W. B.; Approximate Dynamic Programming: Solving the Curses of Dimensionality, John Wiley & Sons, New Jersey, 2007.

[8] Puterman M. L.; Markov Decision Process: Discrete Stochastic Dynamic Programming, John Wiley & Sons, New York, 1994.

[9] Sheti S. P., Sorger G., Zhou X. Y.; Stability of Real-Time LotScheduling and Machine Replacement Policies with Quality Levels, IEEE Transactions on Automatic Control, Vol. 45, No. 11, 2000.
Cómo citar
Ilhuicatzi-Roldan, R., & Cruz, H. (2012). Optimal replacement in a system of n-machines with random horizon. Proyecciones. Revista De Matemática, 31(3), 219-233. https://doi.org/10.4067/S0716-09172012000300003