How to solve the assignment problem in networks?

The assignment problem in networks can be solved using the Hungarian algorithm.

The assignment problem in networks involves finding the optimal assignment of tasks to workers, where each worker can only perform one task and each task can only be performed by one worker. The Hungarian algorithm is a method for solving this problem.

The first step in using the Hungarian algorithm is to create a cost matrix, where each row represents a worker and each column represents a task. The entries in the matrix represent the cost of assigning a particular worker to a particular task. If a worker cannot perform a task, the cost is set to infinity.

The next step is to find the minimum cost in each row and subtract it from all the entries in that row. Then, find the minimum cost in each column and subtract it from all the entries in that column. This creates a new matrix with at least one zero in each row and column.

The next step is to find the optimal assignment by selecting zeros in the matrix in such a way that no row or column has more than one zero selected. If there are fewer zeros than there are rows or columns, additional zeros can be added by creating a minimum number of lines that cover all the zeros in the matrix.

Finally, the optimal assignment can be found by selecting the zeros that are covered by the minimum number of lines. The total cost of the optimal assignment is the sum of the entries in the original cost matrix that correspond to the selected zeros.

Overall, the Hungarian algorithm is an efficient and effective method for solving the assignment problem in networks.