Barracks Repair Before the Monsoon
A barracks block housing two companies must be repaired before the monsoon, which is now forecast to break in 24 days. The engineering store reckons the job at 1,200 worker-days - the equivalent of 30 workers for 40 days at the sanctioned pace. Work begins with 30 workers and runs uninterrupted for the first 10 days. The weather office then revises its forecast: rain will halt outdoor work for 3 of the remaining days, leaving only 11 effective working days. The contractor can bring in at most 35 additional workers from a neighbouring project. The battalion has ₹2,00,000 available for acceleration, over and above the normal wage bill. Normal wages are ₹800 per worker-day on an eight-hour day, and overtime is paid at 1.5 times the hourly rate. A pre-fabricated toilet-and-bath module costing ₹1,20,000 could replace 150 worker-days of masonry work if ordered immediately.
1. Compute the work remaining after 10 days and the minimum workforce needed to finish on time with no overtime.
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Total work: 30 workers × 40 days = 1,200 worker-days.
Work done in the first 10 days: 30 × 10 = 300 worker-days.
Work remaining: 1,200 − 300 = 900 worker-days.
Effective days left: the original window had 14 days left (24 − 10); losing 3 to rain leaves 11 working days.
Minimum workforce: 900 ÷ 11 = 81.82, so 82 workers must be on site every effective day. Since workers are counted in whole persons and a partial day of work is not a partial worker, the figure must be rounded up: 81 workers would deliver 891 worker-days, leaving 9 worker-days undone.
Against availability: the battalion can reach 30 + 35 = 65 workers, which in 11 days delivers 65 × 11 = 715 worker-days. The gap is 900 − 715 = 185 worker-days, i.e. about 20.6% of the remaining work.
The plain conclusion: the forecast revision has made the no-overtime target arithmetically impossible with the labour actually available. Any plan must close a 185 worker-day gap by some combination of extra hours, outsourcing or design substitution.
2. Evaluate the option of maximum extra labour plus two hours of daily overtime: does it meet the deadline, and does it stay within ₹2,00,000?
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Labour. Maximum available: 30 + 35 = 65 workers over 11 days = 715 worker-days against a requirement of 900.
Overtime contribution. A two-hour extension on an eight-hour day adds 25% of a worker-day per worker per day: 65 × 11 × 0.25 = 178.75 worker-days. Total output = 715 + 178.75 = 893.75 worker-days against 900 required - a shortfall of about 6.25 worker-days, roughly half a day's work by the whole gang. So the option fails the deadline by a narrow but real margin; a plan that assumes it works is 6 worker-days short.
Cost. Hourly rate = ₹800 ÷ 8 = ₹100. Overtime rate = ₹100 × 1.5 = ₹150 per hour. Two hours per worker per day costs 65 × 11 × 2 × 150 = ₹2,14,500.
Verdict. The option fails twice over: it is about ₹14,500 over the ₹2,00,000 ceiling and still leaves the job unfinished. Extending overtime to three hours would close the labour gap (268 worker-days of extra output) but would cost roughly ₹3,21,750 - far outside the sanction. Pure overtime is therefore the weakest of the options available, and should not go to the Commandant as a proposal.
3. Recommend a workable plan and show the arithmetic that supports it.
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Recommended plan: substitute the prefabricated module, then use a short overtime tail.
Step 1 - Order the module. It costs ₹1,20,000 and removes 150 worker-days of masonry. Revised requirement in the 11 effective days: 900 − 150 = 750 worker-days. Balance of the acceleration fund: ₹2,00,000 − ₹1,20,000 = ₹80,000.
Step 2 - Workforce needed. 750 ÷ 11 = 68.18, so 69 workers would finish with no overtime. Only 65 are available, delivering 715 worker-days.
Step 3 - Close the residual gap of 35 worker-days with overtime. Spread over 65 workers and 11 days, that is 35 ÷ (65 × 11) = 0.049 of a worker-day per person per day, i.e. about 24 minutes of overtime daily - round up to 30 minutes for a practical order.
Step 4 - Cost check. 65 × 11 × 0.5 × ₹150 = ₹53,625. Total acceleration spend = 1,20,000 + 53,625 = ₹1,73,625, leaving ₹26,375 unspent within the ₹2,00,000 ceiling.
Why this plan and not the alternatives. It is the only combination that satisfies both the calendar and the budget: pure overtime breaches the cap and still falls short; hiring alone cannot exceed 65 workers; and the module converts site work into off-site manufacture, which is also the least weather-sensitive part of the plan - an advantage the other options lack. The residual ₹26,375 should be retained as contingency for a further rain day, since each lost day costs roughly 65 worker-days of output and would need about an hour of daily overtime to recover.
Action deadlines to state in the order: the module must be ordered the same day (lead time is the binding constraint), overtime sanction must issue before day 12, and progress must be re-measured at day 17 so that a second rain revision can be absorbed while work remains rather than after it is too late.