Resource allocation in hierarchical transport systems with interval optimal criterias

Abstract

Resource allocation in hierarchical transport systems with interval optimal criterias

Prilutskii M.H, Kolosovskaia U.S.

Incoming article date: 16.09.2015

In the paper we consider the multi-criteria resource allocation problem in hierarchical transport systems with interval optimal criteria. We build a general mathematical model with multi-criteria optimization problems. The optimal criteria are given in the form of piecewise constant functions. The problems are solved by searching for “optimal nodes” in multidimensional multi-valued cube. Every node of a cube defines own system of linear algebraic bilateral transport-type inequalities. By defining the order of criteria, the multi-criteria problem is reduced to single-criteria problem. This problem is solved on various subsets of the cube’s nodes. Solution is based on sequential checks of the compatibility of the system that defines resource allocation restrictions. If the system of the restrictions is given in the form of an oriented tree, checking the compatibility of the system is made with “modified boundaries” method. For the general case, we propose to use a generalization of the Agmon-Motzkin relaxation method of orthogonal projections. We considered a scheduling task for an enterprise as an example of applied problem.

Keywords: hierarchical transport system, resource allocation problem, multuindex system of linear algebraic inequalities, multicriteria optimization, multidimensional multivalued cube