Chernenko O. Properties of Mathematical Models of Problems with Linear-fractional Function on Arrangements and Methods of their Decision

Properties of mathematical models of Euclidean combinatorial optimization problems with linear-fractional criterion function on arrangements are investigated. Mathematical models of applied problems of such type are constructed. Properties of a polyhedron in a problem with linear conditional function, to which the problem with linear-fractional criterion function on arrangements is reduced, are formulated and proved. Superfluous restrictions in system of linear inequalities of this polyhedron are revealed and its nonreducible system of restrictions is received. The analytical method of the decision of unconditional problems on set of arrangements with linear-fractional criterion function is proved. The method of construction of lexicographic equivalence is advanced. The algorithm of the decision of conditional problems on arrangements with linear-fractional criterion function is stated for the first time. Estimations are made. Practical efficiency of algorithm is investigated on the basis of the lead numerical experiments.