Assignment Problem In Operational Research

Leave the elements covered by single line as it is. Take any row or column which has a single zero and assign by squaring it.Strike off the remaining zeros, if any, in that row and column (X).In column 1, the smallest value is 0, column 2 is 4, column 3 is 3 and column 4 is 0.

The objective is to find an optimal assignment of trucks that minimizes the operational cost of the cargo shipments and the total number of unfulfilled shipments.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.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.Repeat the process until all the assignments have been made.Write down the assignment results and find the minimum cost/time.In the first phase, row reductions and column reductions are carried out.In the second phase, the solution is optimized on iterative basis.In this OR-Wiki entry we're going to explain the Hungarian method with 3 examples.In the first example you'll find the optimal solution after a few steps with the help of the reduced matrix.

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