Modified Hungarian method for unbalanced assignment problem with multiple jobs

摘要

The existing Hungarian method for solving unbalanced assignment problems is based on the assumptions to assign some jobs to dummy or pseudo machines, those jobs assigned to dummy machines are actually left without execution. In real world situations one may be interested to execute all the jobs on actual machines. This purpose can be served by assigning multiple jobs to a single machine. The present paper proposes a Modified Hungarian Method for solving unbalanced assignment problems which gives the optimal policy of assignment of jobs to machines. A stepwise algorithm of proposed method is presented and the developed algorithm is also coded in Java SE 11. A numerical example is taken to demonstrate the performance and efficiency of the proposed method. The obtained result is then compared with several existing methods to show the superiority of our algorithm.