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CMA Intermediate · Operations Management and Strategic Management · Job Evaluation, Job Allocation - Assignment

In a 4×4 minimisation assignment problem, after row and column reduction the zeros can be covered by only 3 lines. What should be done next?

Revise the matrix: subtract the smallest uncovered element from every uncovered element and add it to the elements lying at line intersections. Since 3 lines are fewer than the order 4, no optimal assignment is yet possible, so the test is repeated.

  1. AMake the assignment immediately on the zero cells, since an optimum exists
  2. BSubtract the smallest uncovered element from all uncovered elements and add it to elements at line intersectionsCorrect
  3. CAdd a dummy row to make the matrix 5×5
  4. DAdd the smallest uncovered element to all uncovered elements and subtract it from intersections

Explanation

An optimal assignment needs the minimum number of covering lines to equal the matrix order, here 4. As only 3 lines are used, the matrix must be revised: the smallest uncovered element is subtracted from uncovered cells and added to cells at intersections of lines; cells covered once remain unchanged. The zeros are then re-tested.

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