Goal-optimal Pareto solution of multiobjective linear programs and its computing with standard single objective LP software

Least squares goal programming on the balance set is used to determine the optimal balance point of a multiobjective linear program. Then, available linear system solvers or standard single objective LP software codes can be applied for computing goal-optimal Pareto solutions. The method is applicable for preferential relative cost arrangements (generally non-Pareto) and for use with a direct choice of gain/loss ratios for nonimprovable (Pareto) solutions. Only linear operations are used, and illustrative examples from the literature are considered. The results open new avenues in multicriteria decision making giving decision makers direct access to cost balance control and to the use of effective single objective LP software tools for multiobjective applications.