Advances in Assignment Problem and comparison of algorithms

Assignment Problem (AP) was well studied in the past 50 years, and is of great value in operations research and engineering. The Hungarian Method is one of the effective algorithms for the assignment problem. Although the assignment problem is well studied and a variety of algorithms are proposed, the efficiencies of the algorithms are never completely compared in the literature. In this paper, we summarize the properties of the assignment problem, and then survey its research history, add two new algorithms to existing classification, and compare the performances of these two algorithms with that of the Hungarian Method. The computational results show that the Hungarian method can solve larger balanced assignment problems in engineering and is more efficient than the two algorithms involved, and the bidding algorithm is superior to solve unbalanced assignment problems.