Dynamic programming and questions of solvability of route bottleneck problem with resource constraints

Abstract

The article deals with the problem of admissible routing for a system of cycles each of which contains exterior permutation and works connected with megalopolises (non-empty finite sets) visiting. In the initial setting, a resource constraint is given; this constraint should be fulfilled for every cycle under permutation. The solvability conditions in this problem are connected with the extremum of the auxiliary bottleneck routing problem without above-mentioned constraint, in which the apparatus of widely understood dynamic programming (DP) is used. A particular case of the setting is the known bottleneck courier problem which can be used (in particular) for routing a vehicle (airplane or helicopter) aiming to realize the given shipping system with a limited fuel reserve on each flight. An algorithm implemented on a personal computer is constructed.