Analytical Study on Problem of the Optimal Control of the Inventory of a Continuous Product in a Regeneration Scheme

The aim of the thesis is to consider the model of stock management with the new factor introduced in it, its theoretical and analytical research and the way to solve the problem of management optimization. The solution method consists in proving the main statement about the representation of a stationary indicator in the form of a fractional-linear functional and finding its functions in an explicit form. Also, on the basis of the theorem on a linear fractional functional, an approach to solving the control problem is described. Also, the results of analytical and theoretical research are in the proofs of the lemma on the continuity of the profit function, the theorem on sufficient conditions for the continuity of the main function of the value functional and the theorem on the existence of a solution to optimal stock management using information from mathematical analysis and functional analysis. All evidence takes into account the emergence of a new factor. The model helps to simplify and competently plan the process of almost any trading and marketing system as a whole. The work contains 39 pages, 1 graphic illustration, as well as 11 used sources as basic materials.