A new technique for modifying the Hungarian method

Abstract

The classical method (the Hungarian method) aims to find the optimal solution for the assignment problems (AP). In this work, we introduced a new modification to the Hungarian method to solve (AP). First, we have to subtract the least element in each row from all elements of that row, every row and column must contain at least a zero and extends the least number of lines on the zeros. If the number of matrix rows (or columns) is equivalent to the number of extended lines, then we reach to the optimal solution, if it is not equal, then subtract the least uncovered element from all the elements in the matrix except the zeros until the number of rows (or columns) is equal to extend lines, then determine the cells that give optimal solution. By comparing with the Hungarian method, the results are equal, moreover, the new technique surpasses the Hungarian method with ease and simplicity steps, and it reaches the optimal solution faster and with less steps.