Modified Balanced Assignment Problem in Vector Case: System Construction Problem

We consider a combinatorial problem that arises from systems´ construction. Each system consists of many components, and every component has its own error expressed in a vector. It is required to make the combination that minimizes as small as possible the difference between the maximum error and the minimum one. It means the vector case´s balanced optimization problem. In this paper, we consider the case that each system consists of 2 components and the vector dimension is 2. We propose the approximation algorithm for quasi optimal solution with results of numerical experiments.