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

In a 4x4 assignment problem, the first step of the Hungarian method is row reduction. What is done in this step?

In row reduction, the smallest element of each row is subtracted from every element in that row. This creates at least one zero in every row without changing the optimal assignment, and column reduction and zero-covering follow.

  1. AThe largest element of each row is subtracted from every element of that row
  2. BThe smallest element of each row is subtracted from every element of that rowCorrect
  3. CThe smallest element of the whole matrix is added to every cell
  4. DEach row is divided by its smallest element

Explanation

Row reduction subtracts each row's minimum from all elements in that row, creating at least one zero per row. Subtracting the largest would give negative values, which is the maximisation-style error. Column reduction follows afterwards.

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