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

In the Hungarian method for a balanced minimisation assignment problem, what is the first step applied to the cost matrix?

The first step is row reduction: subtract the smallest element of each row from every element in that row. This creates at least one zero per row. Column reduction then follows, before zeros are covered with lines.

  1. ASubtract the smallest element of each row from every element of that rowCorrect
  2. BAdd the largest element of each column to every element of that column
  3. CDraw lines through the largest elements of the matrix
  4. DConvert every cost to a profit by subtracting from the largest cost

Explanation

The Hungarian method begins with row reduction: the smallest entry in each row is subtracted from all entries of that row. Column reduction follows, and zeros are then covered with the minimum number of lines. Converting costs by subtracting from the largest element is used only for maximisation problems.

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