AN ACHIEVEMENT RATE APPROACH TO LINEAR-PROGRAMMING PROBLEMS WITH AN INTERVAL OBJECTIVE FUNCTION

In this paper, we focus on a treatment of a linear programming problem with an interval objective function. From the viewpoint of the achiev ement rate, a new solution concept, the maximin achievement rate solut ion, is proposed. Nice properties of this solution are shown: a maximi n achievement rate solution is necessarily optimal when a necessarily optimal solution exists, and if not, then it is still a possibly optim al solution. An algorithm for a maximin achievement rate solution is p roposed based on a relaxation procedure together with a simplex method . A numerical example is given to demonstrate the proposed solution al gorithm.