Geodesic
Analysis of a discrete semi-Markov model of continuous inventory control with periodic interruptions of consumption
Diskretnaya Matematika, Tome 26 (2014) no. 1, pp. 143-154

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We consider a discrete stochastic model of inventory control based on a controlled semi-Markov process. Probabilistic characteristics of the semi-Markov process are found along with characteristics of a stationary cost functional connected with this process. It is proved that an optimal policy of inventory control is a deterministic one. Explicit analitical representation of stationary functional characterising the control quality is obtained. An optimal control problem is reduced to the solution of an extremal problem for a multivariate function.
Keywords: inventory control, semi-Markov process, optimal control. 
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     author = {P. V. Shnurkov and A. V. Ivanov},
     title = {Analysis of a discrete {semi-Markov} model of continuous inventory control with periodic interruptions of consumption},
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     url = {http://geodesic.mathdoc.fr/item/DM_2014_26_1_a11/}
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P. V. Shnurkov; A. V. Ivanov. Analysis of a discrete semi-Markov model of continuous inventory control with periodic interruptions of consumption. Diskretnaya Matematika, Tome 26 (2014) no. 1, pp. 143-154. http://geodesic.mathdoc.fr/item/DM_2014_26_1_a11/