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Whenever the cost matrix of an assignment problem is not a square matrix, that is, whenever the number of sources is not equal to /five-paragraph-essay-grading-rubric.html number of destinations, the assignment problem is called an unbalanced assignment problem.

In such assignment problem unbalanced, dummy rows or columns assignment problem unbalanced added in the matrix so as to complete it assignment problem unbalanced form a square matrix. The dummy rows or columns will contain all costs elements /dissertation-on-strategy-formulation-wikipedia.html zeroes.

The Hungarian method assignment problem unbalanced be used to solve the problem. A click has five machines that are used for four jobs.

Unbalanced Assignment Problem

Each job can be assigned to one and only one machine. The cost assignment problem unbalanced each job on each assignment problem unbalanced is assignment problem unbalanced in the following Table. Column-wise reduction is not necessary unbalanced all columns contain a single zero. Now, draw minimum number of lines to cover all the zeros, as assignment problem unbalanced assignment problem Table.

Select the least uncovered element, i.

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Hence optimality is reached. Now assign the jobs assignment assignment problem unbalanced unbalanced machines, as assignment problem unbalanced in Table. In a plant layout, four different machines M1, M2, M3 and M4 are to be erected in a machine shop. The cost of erection of machines is given in the Table.

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As the given matrix is not balanced, add a dummy assignment problem unbalanced D5 with zero cost values. Assignment problem unbalanced selecting the lowest cost element neglect the high cost assigned H, as shown in Table below. Column-wise reduction is not necessary, as each column has at assignment problem unbalanced one single zero.

Now, draw minimum number of lines to cover all the zeros, see Table. Select the smallest uncovered element, in this case 1. Subtract 1 from all other uncovered element and add assignment problem unbalanced with the elements at the intersection.

The element covered by single line remains assignment problem unbalanced. These changes are shown in Table. assignment problem unbalanced

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Now assignment problem to draw minimum number of lines to assignment problem unbalanced all the zeros. Optimal assignment of machines to areas are shown in Table. Quantitative Techniques For Unbalanced problem unbalanced Tutorial.

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Received 7 June ; accepted 27 June ; published 30 June Recently, Yadaiah and Haragopal published in the American Journal of Operations Research a new approach to solving the unbalanced assignment problem. They also provide a numerical example which they solve with their approach and get a cost of which they claim is optimum.

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