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

Three operators P, Q and R are to be assigned to three machines (one each). The cost matrix in ₹ is: P: 4, 6, 8; Q: 6, 8, 10; R: 5, 7, 9 (machines 1, 2, 3). How many different complete assignments give the minimum total cost?

Six assignments are optimal. Each cost equals a row amount plus a column amount, so any one-to-one assignment totals ₹21. Since all six possible permutations have the same total, every one of them is a minimum-cost solution, giving multiple optimal solutions.

  1. A1
  2. B2
  3. C3
  4. D6Correct

Explanation

Each entry equals a row value (4, 6, 5) plus a column value (0, 2, 4). Every complete assignment therefore costs 15 + 6 = ₹21. All six permutations tie at the minimum, so there are six optimal solutions. Picking only the diagonal and stopping would miss the alternative optima.

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