A multiobjective interval goal programming method using penalty function

This article demonstrates how the penalty function can efficiently be used for solving multiobjective linear programming problem with interval valued objective functions. In the proposed approach, first the target intervals are obtained for the defined objectives. Then, using interval arithmetic and the concept of interval goal programming (IGP) the interval goals are transformed into crisp goals. In the process of solution, the goal achievement function is constructed as a convex combination of the sum of total penalty and the maximum penalty associated with unwanted deviations of the respective goals. Numerical examples are provided to illustrate the proposed approach.