Interaction theory [new paradigm] for solving the assignment problem

The Assignment Problem is very interesting to be researched because it is simple but wide in the applications. Hungarian Method, developed by Harold Kuhn in 1955, is one of the most popular algorithms to solve the assignment problem since it is easy and practical. However, its easiness is restricting the form of iteration process which is quite complicated. A research about the effective and efficient new algorithm is needed. In this paper, we introduce a new concept for solving the assignment problem. The Interaction Theory has been developed since 1966. We developed the coefficient interaction formula and succeeded to be implemented to solving the hard problems in the exact way and giving more alternative optimal solutions with the same value. The algorithm is introduced in this paper along with several applications; including problem with more than one solution, unbalanced problem, and problem with incomplete data. The Interaction Theory gives a new hope as a new paradigm. The algorithm is simple yet effective and efficient to solve all kinds of assignment problems such as unbalanced assignment problem, and minimize and maximize objective. Moreover, the algorithm sometimes produces more than one optimal solution.