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.