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Adaptive control of a production-inventory system

Published online by Cambridge University Press:  14 July 2016

Bharat T. Doshi
Bharat T. Doshi*
Affiliation:
Bell Laboratories
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Abstract

We study a production-inventory system in which input is deterministic, and its rate is the controlled parameter. The output is a compound Poisson process with exponential jump-size distribution. The parameters of the output process are unknown. The following adaptive policy is used: At each time t the unknown parameters are estimated by maximum likelihood method and the input rate which would be optimal if these were the true values of the parameter is used. The issues investigated are (1) the convergence of maximum likelihood estimates to the true value, and (2) the asymptotic properties of the cost under the adaptive policy.

Keywords

PRODUCTION-INVENTORY SYSTEMADAPTIVE CONTROLAVERAGE COSTCONVERGENCE OF MLEASYMPTOTIC PROPERTIES OF TOTAL COST

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 204 - 215
Copyright
Copyright © Applied Probability Trust 

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References

[1] Akritas, M. G. (1979) Asymptotic theory for estimating the parameters of a Levy process. Technical Report No. 11, MIT.Google Scholar
[2] Doshi, B. T. (1976) Continuous-time control of Markov processes on an arbitrary state space-average return criterion. Stoch. Proc. Appl. 4, 55–77.CrossRefGoogle Scholar
[3] Doshi, B. T. (1976) Optimal dynamic selection of production rate in a production-inventory system. Technical Report, Rutgers University.Google Scholar
[4] Doshi, B. T. (1978) Optimal control of the service rate in an M/G/1 queueing system. Adv. Appl. Prob. 10, 682–701.Google Scholar
[5] Doshi, B. T. and Shreve, S. (1980) Strong consistency of a modified maximum likelihood estimator for controlled Markov chains. J. Appl. Prob. 17, 726–734.CrossRefGoogle Scholar
[6] Dufková, V. (1977) On controlled one-dimensional diffusion processes with unknown parameter. Adv. Appl. Prob. 9, 105–124.CrossRefGoogle Scholar
[7] Feigin, P. D. (1976) Maximum likelihood estimation for continuous-time stochastic processes. Adv. Appl. Prob. 8, 712–736.Google Scholar
[8] Mandl, P. (1974) Estimation and control in Markov chains. Adv. Appl. Prob. 6, 40–60.Google Scholar
[9] Mandl, P. (1973) On the adaptive control of finite state Markov processes. Z. Wahrscheinlichkeitsth. 27, 263–276.Google Scholar
[10] Mitchell, B. (1973) Optimal service-rate selection in an M/G/1 queue. SIAM J. Appl. Math. 24, 19–35.Google Scholar