A study of the problem of optimal management of discrete product inventory in the stochastic regeneration model with continuous consumption and random delivery delay

30 Jan 2020  ·  Shnurkov P. V., Vakhtanov N. A. ·

The paper considers the optimal control problem of inventory of a discrete product in regeneration scheme with a Poisson flow of customer requirements. In the system deferred demand is allowed, the volume of which is limited by a given value... The control parameter is the level of the stock, at which achievement it is necessary to make an order for replenishment. The indicator of management effectiveness is the average specific profit received in one regeneration period. The optimal control problem is solved on the basis of the statement about the extremum of a fractional-linear integral functional on the set of discrete probability distributions. The significant content of the work is the derivation of analytical representations for the mathematical expectation of the increment of the functional of profit obtained during the regeneration period. The obtained analytical representations enable us to explicitly determine the stationary cost indicator of control efficiency, which was introduced in the first part of the research. Thus, it becomes possible to numerically solve the optimal control problem of inventory in the model under consideration. read more

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Optimization and Control