Optimizing the Worst Achievement Rate in Linear Programming Problems with an Interval Objective Function

Abstract

In this paper, a new solution concept for linear programming problem with an interval objective function is proposed based on the worst achievement rate. First, given coefficients of the objective function, the achievement rate for each feasible solution is defined. Using the achievement rate, the interval linear programming problem is formulated as an optimization problem of the worst achivement rate among the objective coefficients within given intervals. The optimization problem of the worst achievement rate is reduced to a min-max or max-min problem subject to separate constraints. It is shown that the solution optimizing the worst achievement rate has a desirable property. A solution algorithm based on the relaxation procedure and the simplex method is proposed to solve the optimization problem of the worst achievement rate. In order to illustrate the proposed solution algorithm, a numerical example is given.