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  • A Study of the Problem of Continuous Product Stock Control in a Stochastic Model of Regeneration with Two Optimization Parameters

A Study of the Problem of Continuous Product Stock Control in a Stochastic Model of Regeneration with Two Optimization Parameters

Student: Adamova Ksenia

Supervisor: Peter V. Shnourkoff

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Mathematical Methods of Modelling and Computer Technologies (Master)

Year of Graduation: 2017

The present study aims to analyze several interconnected problems of optimal control of continuous product in regeneration circuit. In the beginning, the theory of unconditional extremum of linear fractional integral functional, which depends on the parameter, was proved. This theorem lays a basis for solving various optimal control problems, which contain several control parameters, including random and deterministic ones. In the following study, we analyzed the storage models of continuous product with two optimizing parameters. One of these parameters is a random time from replenishment until the next order. The other parameter is a maximum deterministic storage capacity (level of replenishment). We have understood the concept of permanent cost parameter for the management quality in the form of linear fractional integral functional, which depends on the parameter. The proven theorem is used to solve a problem of optimal management. In the conclusion, we conducted an analytical study of the main function of the linear fractional integral functional and understood the sufficient conditions for the given function to reach the global extremum. In accordance with the proven theorem, these conditions ensure the existence of the solution for the storage management.

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