Старший преподаватель кафедры естественнонаучных дисциплин Рубанов Игорь Владимирович принял успешное участие в международной конференции "Logistics Analytics 2018"
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A system including O(n2) difference inequalities and box constraints for n variables is studied. This system, denoted as DBM, is a simplified model for determining feasible start times of vehicles, for example, airplanes, which follow fixed intersecting routes with given speeds and they have to keep a given safety distance from each other. The system can be solved by the Fourier – Motzkin method and by a reduction to the shortest path problem in a specially designed network with possible negative cycles. In the corresponding solution, a feasible interval (f-interval) for one variable can be determined such that the DMB system has a solution for any value of this variable from the f-interval. We consider a situation, in which a feasible solution of the DBM system is given, and one variable of this solution changes its value within its f-interval. In order to find values of the other variables such that the whole solution remains feasible, we suggest three algorithms: modifications of the Fourier-Motzkin method and the Dijkstra’s algorithm, both having O(n2) running time, and a simple O(n) algorithm.