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Efficient FORTRAN implementations for the case of complete and sparse matrices are given.An assignment problem can be easily solved by applying Hungarian method which consists of two phases. Wiley Online Library requires cookies for authentication and use of other site features; therefore, cookies must be enabled to browse the site.
Select the smallest element of the whole matrix, which is NOT COVERED by lines.
Subtract this smallest element with all other remaining elements that are NOT COVERED by lines and add the element at the intersection of lines.
The row wise reduced matrix is shown in table below.
Reduce the new matrix given in the following table by selecting the smallest value in each column and subtract from other values in that corresponding column.
We combine the above two objectives into one term: the total cost, a sum of the total dock operational cost and the penalty cost for all the unfulfilled shipments.
The problem is then formulated as an Integer Programming (IP) model.
Repeat the process until all the assignments have been made.
Write down the assignment results and find the minimum cost/time.
Take the smallest element of the matrix that is not covered by single line, which is 3. Now, draw minimum number of lines to cover all the zeros and check for optimality. Select a row that has a single zero and assign by squaring it.
Subtract 3 from all other values that are not covered and add 3 at the intersection of lines. Here in table minimum number of lines drawn is 4 which are equal to the order of matrix. Strike off remaining zeros if any in that row or column.