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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.31 no.3 Antofagasta set. 2012

http://dx.doi.org/10.4067/S0716-09172012000300003 

Proyecciones Journal of Mathematics Vol. 31, No 3, pp. 219-233, September 2012. Universidad Católica del Norte Antofagasta - Chile

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

Rocio Ilhuicatzi-Roldan

Benemérita Universidad Autonoma de Puebla, Mexico

Hugo Cruz-Suarez

Benemerita Universidad Autonoma de Puebla, Mexico


ABSTRACT

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.

Keywords : Mathematical programming, Optimal stochastic control, Dynamic programming, Markov decision processes.


REFERENCES

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

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

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

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

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

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

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

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

[9] Sheti S. P., Sorger G., Zhou X. Y.; Stability of Real-Time Lot-Scheduling and Machine Replacement Policies with Quality Levels, IEEE Transactions on Automatic Control, Vol. 45, No. 11, 2000.         [ Links ]

 

Maria del Rocio Ilhuicatzi Roldán

Facultad de Ciencias FIsico-Matematicas Benemerita Universidad Autónoma de Puebla Mexico

e-mail: rroldan@alumnos.fcfm.buap.mx and

 

Hugo Cruz Suarez

Facultad de Ciencias FIsico-Matematicas Benemerita Universidad Autonoma de Puebla Mexico

e-mail: hcs@fcfm.buap.mx

Received : May 2011. Accepted : May 2012