Evaluation of Finding an Optimal Interval Solution for Interval Assignment Problems

The assignment problem (AP) is a distinct form of a transportation problem where the key objective is to find an assignment schedule in a job where n jobs are assigned to n workers and each worker accepts exactly just one job so that the entire assignment cost must be minimum. In the existing method throughout the entire procedure they applied Hungarian method based on the computation of intervals. A new approach namely, center point method is proposed to solve an optimal interval assignment cost for fully interval assignment problems (FIAP). In the proposed method, the given FIAP is decomposed into a crisp assignment problem (AP) with the help of midpoint technique, solving it with the existing technique and by using its optimal solutions; an optimal interval assignment cost to the given FIAP is obtained. Comparison of intervals and partial ordering techniques were not used and there is no restriction on the elements of coefficient interval matrix in the proposed method. The proposed method is easier and also, simply because of the linear programming techniques. Using numerical examples the above method is illustrated.