Abstract:
A mathematical model of stock change is described for the case of centralized source allocation, probabilistic nature of supplies and demands represented as a discrete Markov chain with a finite number of states. The paths of random processes and expressions of mean components of losses during the functioning of the system are shown to be function of deterministic vectors of initial stocks and funds allotted for the resources. Statements and mathematical models are given for various problems of selecting the optimal initial stocks and funds so to minimize the mean total losses due to shortage and idling of resources. Branch-and-bound solution algorithms are developed.
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