Minimax regret solution to linear programming problems with an interval objective function

This paper deals with a linear programming problem with interval objective function coefficients. A new treatment of an interval objective function is presented by introducing the minimax regret criterion as used in decision theory. The properties of minimax regret solution and the relations with possibly and necessarily optimal solutions are investigated. Next, the minimax regret criterion is applied to the final determination of the solution when a reference solution set is given. A method of solution by a relaxation procedure is proposed. The solution is obtained by repetitional use of the simplex method. The minimax regret solution is obtained by the proposed solution method when the reference solution set is the set of possibly optimal solutions. In order to illustrate the proposed solution method, a numerical example is given.