IDI-75 - AN OPTIMAL ONES ASSIGNMENT METHOD FOR SOLVING UNBALANCED ASSIGNMENT PROBLEMS

Abstract

In this article, a new technique namely IDI-75 (named to commemorate the 75th Independence Day of India), which is a simplified form of the existing Ones Assignment Method (OAM) of solving assignment problems, finds the optimal solution to a given unbalanced assignment problem (UAP). In the OAM, it is required to convert the given UAP into a balanced one by introducing one dummy row or column with 1 unit of effectiveness in each cell. But, the IDI-75 technique can be applied directly on the given UAP without converting it into a balanced one. The technique requires only row minimum division operation or only column minimum division operation depending on the size of rows and columns in order to have at least one 1-entry in each of the required number of rows and/or columns only. The assignments are made on the appropriate 1-entry cells of reduced ratio of costs matrix. To test the validity and effectiveness of the IDI-75 technique, 20 benchmark instances with different sizes from the literatures have been tested. Simulation results authenticate that the technique IDI-75 is the best one which produces optimal solution to all 20 instances. Therefore, it is clever to apply the IDI-75 technique to solve the UAPs as it is very simple, easy to understand, easy to apply and consume less time in comparison to the existing OAM.