Ustyan N. The combinatorial optimization problems of the game type

The mathematical models of the combinatorial optimization problems of the game type where one or both players have combinatorial restrictions which are determined by the permutations and arrangements are created and investigated. The properties of points of the permutation polyhedron are proved. The modification of Chernikova's method for finding the general formula of the solutions of the system of the linear inequalities which describes the permutation polyhedron with the additional linear inequalities is done. The graphical method for solving the combinatorial optimization problems of the game type with the some dimensions is created. The theorems about the equivalence of three models of the combinatorial optimization problems of the game type and two optimization problems are proved. Two methods for finding of the optimal strategy of the player which has the combinatorial restrictions which are determined by the permutations are created.