Analysis of the problem of continuous-product inventory control under deterministic lead time

Consideration was given to the control of the continuous-product inventory in the storage system delivering to the end consumers. In the system, the product is replenished at a deterministic lead time of duration obeying the volume of order. The system behavior is described by a regenerative random or deterministic process. The general task of control lies in determining the optimal time to place the replenishment order. Functionals of the mean specific income and mean specific costs were constructed, and a theorem of solution existence and uniqueness was given. For several variants of the model, explicit solutions of the problem of control under different inter-parameters relations were obtained. A number of examples of particular economic systems obeying the model under study were discussed. A procedure for seeking numerical parameters of the optimal control was analyzed in detail.