mziana nachkebia

A joint study with energy experts on some issues of energy control is presented. Practical implications are discussed based on real, existing data

The tasks of area (region) search and search by call, which depend on the nature of the information about the location of the search object, are discussed.

The problem of river runoff management is discussed in terms of queue and stock management theories. A mathematical model in the framework of the Markov decision process is established

One dynamic problem of mathematical economics is discussed, namely, competition with two suppliers and many small consumers (actually one consumer). The process is step-by-step - at each stage, producers bring a certain amount of products to the market from their limited resources, on which their profit depends. The total winnings are determined by the sum of the winnings in the stages. We describe the competition as a two-person multi-player game. Two approaches - antagonistic and cooperative - are discussed. In an antagonistic game, solutions are sought in pure strategies (the game is complete information); In the cooperative variant, Nash and Shapley solutions are sought. Numerical realization relies on mathematical and dynamic programming methods.

The dynamic task of a duopoly, i.e., a market served by two producers in stages, and the demand determined by many small or single consumers, is discussed. The product is uniform and the price is determined by the total quantity of goods imported at each stage.

The task is presented as a two-person game. This is a multiplayer game with full information. Solutions are sought in pure strategies. Two approaches - antagonistic and cooperative - are discussed. In the cooperative variant, Nash and Shapley solutions are sought. Calculations are based on dynamic programming method.

The process of spreading oil pollution in the seas and oceans, taking into account the wind factor, is discussed. The process is described as a random stochastic linear motion when the wind speed and direction are stochastic.

2 models of sea pollution are presented. One model is deterministic and is characterized by ordinary differential equations. The second model is stochastic. Formulas of pollution density and distribution under different conditions are obtained. Numerical solutions for specific examples are described.

"We consider a one-product market with infinitely divisible production and n participants, of which n-1 participant is a seller, and one n-th participant is a buyer. Each seller has xi (i=1,2,..., n-1) quantity production, the buyer's demand is Y. Y is the maximum quantity of products that the buyer can purchase.

The task is how to conduct the trade and how to distribute the profit between the parties. We present this task in the form of a cooperative game: we have a set of players I=(1,2,...,n), of which the nth player has a special priority, it is the main player. If the main player does not enter the coalition K, the profit of this coalition will be zero, and if he enters, then the profit of the coalition K will be determined in proportion to the purchased products.

We used Shapley's principle of "fair distribution" to solve the obtained cooperative game. In different cases, the components of the Shapley vector - payoff for each player are calculated.

A mathematical model of the long-term optimal functioning of the energy system of the region is proposed. A mathematical programming type model. The minimum total annual costs or the minimum weighted sum of electricity shortages were taken as optimality criteria.

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Doctoral Thesis Referee

Master Theses Supervisor

Doctoral Thesis Supervisor/Co-supervisor

Scientific editor of monographs in foreign languages

Scientific editor of a monograph in Georgian

Editor-in-Chief of a peer-reviewed or professional journal / proceedings

Review of a scientific professional journal / proceedings

Member of the editorial board of a peer-reviewed scientific or professional journal / proceedings

Participation in a project / grant funded by an international organization

Participation in a project / grant funded from the state budget

Patent authorship

Membership of the Georgian National Academy of Science or Georgian Academy of Agricultural Sciences

Membership of an international professional organization

Membership of the Conference Organizing / Program Committee

National Award / Sectoral Award, Order, Medal, etc.

Honorary title

Monograph

Handbook

Research articles in high impact factor and local Scientific Journals

Publication in Scientific Conference Proceedings Indexed in Web of Science and Scopus