Overtime, Extra Hands or a Missed Date: Sizing a Fabrication Recovery Plan
A workshop has accepted a fabrication order on a fixed delivery date. The approved plan was 24 workers, 30 working days, 8 hours a day. Work started on time, but on the morning of day 13 the contractor pulled out 6 workers for another site and they will not return; the remaining 18 stay on the job. Days 1 to 12 are already booked as complete, and 16 full working days are left. The delivery date cannot move. Workshop rules allow a maximum of 9 hours on the shop floor per worker per day (8 normal plus 1 overtime hour), and the safety officer will not relax this. Overtime is paid at 1.5 times the normal hourly rate; a normal 8-hour day costs Rs 600. Extra workers can be hired from the same contractor at Rs 600 a day with no delay. The accountant wants the cheapest rule-compliant way to finish on time, plus the percentage cost overrun against the original plan.
1. How much work remains after day 12, and can the 18 remaining workers finish it within the 16 days left while respecting the 9-hour cap? Show the arithmetic.
Read the worked answer
Measure work in worker-hours, because that is what both the plan and the rule are expressed in.
- Planned total: 24 workers x 30 days x 8 h = 5,760 worker-hours
- Completed by day 12: 24 x 12 x 8 = 2,304 worker-hours
- Remaining: 5,760 - 2,304 = 3,456 worker-hours
Now test the 18 survivors at the legal maximum:
- Capacity: 18 x 16 days x 9 h = 2,592 worker-hours
- Shortfall: 3,456 - 2,592 = 864 worker-hours
The overtime route alone fails. To finish with 18 workers you would need 3,456 / (18 x 16) = 12 h per day, i.e. 4 overtime hours daily, which is four times the permitted one hour. So the answer to the question is: no, not with 18 workers.
Extra hands needed at 9 h/day: 864 / (16 x 9) = 6 workers. That brings the crew back to 24, and 24 x 16 x 9 = 3,456, an exact match with no slack - any further absenteeism or a machine breakdown will immediately push the date.
2. Compare the two recovery options on cost and compliance, and state which one the accountant should approve.
Read the worked answer
Normal hourly rate = 600 / 8 = Rs 75/h; overtime rate = 75 x 1.5 = Rs 112.50/h.
Option A - 18 workers on 12-hour days (not permissible):
- Normal pay: 18 x 16 x 8 x 75 = Rs 1,72,800
- Overtime: 18 x 16 x 4 x 112.50 = Rs 1,29,600
- Total = Rs 3,02,400
This is also the cheaper-looking option, which is exactly the trap: it breaches the 9-hour limit the safety officer has refused to relax, so it is not a valid choice at all.
Option B - hire 6 workers and run 24 workers on 9-hour days (permissible):
- Normal pay: 24 x 16 x 8 x 75 = Rs 2,30,400
- Overtime: 24 x 16 x 1 x 112.50 = Rs 43,200
- Total = Rs 2,73,600
Option B is both legal and Rs 28,800 cheaper than the stretched-shift plan, because one overtime hour spread over a larger crew costs less than four overtime hours over a smaller crew. Recommendation: sanction the 6 extra workers and one controlled overtime hour per day, and monitor daily output against the 3,456 worker-hour target, since the schedule has zero float.
3. What is the percentage cost overrun of the recommended plan against the original approved plan?
Read the worked answer
Original approved cost = 24 x 30 x 8 x 75 = Rs 4,32,000.
Actual spend = what was already paid for days 1-12 plus the cost of the recovery plan:
- Days 1-12 (24 workers, 8 h): 24 x 12 x 8 x 75 = Rs 1,72,800
- Recovery, days 13-28 (Option B): Rs 2,73,600
- Total = Rs 1,72,800 + Rs 2,73,600 = Rs 4,46,400
Overrun = 4,46,400 - 4,32,000 = Rs 14,400
Percentage overrun = (14,400 / 4,32,000) x 100 = 3.33%.
Note why the overrun is small even though the crew size is restored: the 6 withdrawn workers were absent for 12 of the 30 planned days, so the lost base cost partly offsets the overtime and the newly hired hands. A 3.33% overrun is defensible in a contract review, provided the withdrawal of labour is documented as a client/contractor-side variation rather than a workshop failure.