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CMA Final · Strategic Cost Management · Assignment

A workshop has 4 machines and 3 jobs, and each job needs exactly one machine. The cost of doing each job on each machine is known. Which step correctly prepares this unbalanced assignment problem for the Hungarian method?

Add a dummy job with zero cost against every machine, giving a square 4 × 4 matrix. The machine assigned to the dummy simply stays idle. Zero costs keep the real optimum unaffected, whereas large costs or deleting a machine would distort the result.

  1. AAdd one dummy job (column) with zero cost for every machine, so the matrix becomes 4 × 4Correct
  2. BAdd one dummy job with a very large cost for every machine, so the matrix becomes 4 × 4
  3. CDelete the machine with the highest average cost and solve the remaining 3 × 3 matrix
  4. DAdd one dummy job whose cost equals the highest cost in the matrix for every machine

Explanation

An unbalanced problem is balanced by adding dummy rows or columns. The dummy carries zero cost because it is not a real activity, so the machine that gets it stays idle. A large or maximum cost would distort the optimal choice. Deleting a machine arbitrarily may discard the true optimum.

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