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

A firm has four workers W1 to W4 and three jobs J1 to J3, each job needing one worker and each worker doing at most one job. Costs (₹ thousand) for J1, J2, J3 are: W1: 8, 10, 12; W2: 9, 7, 11; W3: 10, 9, 6; W4: 7, 12, 9. Using a dummy job of zero cost, what is the minimum total cost and which worker stays unassigned?

The minimum cost is ₹20 thousand, with W1 left unassigned (matched to the dummy job). The assignment is W2 to J2 (7), W3 to J3 (6) and W4 to J1 (7). Leaving any other worker out costs ₹21, 23 or 24 thousand at best.

  1. A₹20 thousand; W1 unassignedCorrect
  2. B₹21 thousand; W4 unassigned
  3. C₹23 thousand; W2 unassigned
  4. D₹24 thousand; W3 unassigned

Explanation

Adding a dummy job of zero cost makes the problem 4×4. Best total if W1 is left out: W2-J2 7 + W3-J3 6 + W4-J1 7 = 20. Leaving out W2 gives a minimum of 23, W3 gives 24 and W4 gives 21 (8+7+6). So the minimum is 20 with W1 idle; ₹21 thousand is the best when W4 is left out.

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