Improving classic hungarian algorithm considering uncertainty by applying for grey numbers

The Hungarian Algorithm is the most famous method for solving Linear Assignment Problems (LAP). Linear Assignment Method (LAM), as an application of LAP, is among the most popular approaches for solving Multi Criteria Decision Making (MCDM) problems. LAM assigns a priority to each alternative based on a Decision Matrix (DM). The elements of the DM are often deterministic in MCDM. However, in the real world, the value of the elements of the DM might not be specified precisely. Hence, using interval grey numbers as the value of the DM to consider the uncertainty is reasonable. In this research, for providing a real circumstance, the classic Hungarian algorithm has been extended by using the concept of grey preference degree as the Grey Hungarian Algorithm (GHA) to solve LAM under uncertainty. To verify the proposed GHA, a real case for ranking several items of mining machinery warehouse from Sarcheshmeh Copper Complex has been solved by the GHA. Also, the same case study has been prioritized by two other methods: Grey TOPSIS and Grey VIKOR. The results of all mentioned approaches are identical, showing the validity of the proposed GHA developed in this research.