A complex of mathematical models for prevention of catastrophes in warehouses of queueing-inventory systems

20.02.2025 /

One of the important scientific results obtained in 2024 in the Institute of Control Systems (ICS) of the Ministry of Science and Education of the Republic of Azerbaijan in the field of theoretical and applied control problems is the result obtained by the corresponding member of ANAS, Prof. Agasi Malikov and researcher Laman Poladova in their works on "Development mathematical models for calculation and optimization of quality indicators of stocks with the purpose of their increase taking into account the possibility of catastrophes in warehouses of queueing-inventory systems”.

Queueing-inventory systems (QIS) are systems in which, in addition to a free server, certain resources (stocks) are required to service incoming orders. Thus, at the end of the service, an incoming order leaves the the system with certain stocks. Such systems are common in real life. life. All material supply systems, logistics networks, human organ transplants, trading systems, etc. transplantation of human organs, trading systems, etc. are queueing-inventory systems.

The construction of adequate mathematical models of these systems is an important problem for their effective organization and management. In recent years a considerable amount of scientific work has been carried out in this direction. The known mathematical models take into account various specific properties of QIS. However, the known models do not take into account the possibility of catastrophes occurring in QIS warehouses. It is known that in real systems, including in the power supply systems, catastrophes occur, although rarely, and these factors seriously affect their operation. In the above-mentioned mathematical models, the mathematical models of QIS are built taking into account catastrophes. This, in turn, allows to increase the adequacy of models and, as a consequence, to increase the efficiency of decisions made on their basis.