RESOURCE DISTRIBUTION PROBLEM

Abstract

In various subject areas, the problem of such a distribution of the resources of a controlled system between individual elements (objects) is relevant, which ensures the most efficient functioning of the system in given circumstances. The problem of distribution of the given global resource is considered at restrictions from below, applied on partial resources. It is shown, that the problem consists in construction of adequate criterion function for optimization of process of distribution of resources in conditions of their limitation. The objective function is a scalar convolution of the partial resource vector. Requirements for the objective function: it must penalize partial resources for dangerously approaching its limits and be differentiable in its arguments. In the problem under consideration, partial resources have a dual nature. On the one hand, they can be considered as independent variables, arguments for the optimization of the objective function. On the other hand, it is logical for each of the objects to strive to maximize its partial resource, to go as far as possible from a dangerous limitation in order to increase the efficiency of its functioning. From this point of view, resources can be considered as particular criteria for the quality of the functioning of the corresponding objects. These criteria are subject to maximization, they are limited from below, non-negative and contradictory (an increase in one resource is possible only at the expense of a decrease in others). For the decision of a considered problem the approach of multicriteria optimization with use of the nonlinear trade-off scheme is undertaken. The proposed approach is recommended for a compromise-optimal allocation of resources in a wide range of practical problems. The illustrating example is given.