Target Level Method in Linear Multi-Criterion Problems

We consider the target level method for solving linear multi-criterion maximization problems. The method finds an efficient (Pareto-optimal) vector estimate that is closest in the Chebyshev metric to the target level point specified by the decision maker. The proposed method describes (parametrizes and approximates) the efficient set. In the linear case the number of scalar optimization problems needed to describe the set of efficient vector estimates is substantially reduced. A formula is derived which, under certain conditions, can be used to compute efficient vector estimates without solving any optimization problems. An algorithm based on these results is proposed for two-criterion problems.