Digitisation Deadline: Overtime or Rent Another Scanner
A records team must digitise 250,000 pages within 20 working days. Two scanners are available: Scanner A runs at 1,000 pages per hour and Scanner B at 750 pages per hour, each needing one operator. Operators are productive for 7 hours of a 7.5-hour day. Quality checks find that 8% of scanned pages must be rescanned on the same machine, consuming the same throughput. The team has two operators and no spare staff. Procurement offers two options: one extra hour of overtime per operator at £38, or a third scanner with its own operator for the 20 days at £400 a day, adding 900 pages per hour. The team leader must choose the cheapest option that reliably clears the deadline.
1. Does current capacity meet the deadline? Quantify the gap.
Read the worked answer
Gross output per day: (1,000 + 750) × 7 = 12,250 pages.
Rework means 8% of scanning effort is repeated, so good pages = 12,250 × 0.92 = 11,270 per day.
Over 20 days: 225,400 pages - a shortfall of 250,000 − 225,400 = 24,600 pages (9.8%).
Required net rate: 250,000 ÷ 20 = 12,500 pages/day. Required gross rate: 12,500 ÷ 0.92 = 13,587 pages/day.
Gap = 13,587 − 12,250 = 1,337 gross pages per day, about 0.8 hours of combined machine time. The baseline clearly fails.
2. Compare the overtime option with the rented third scanner on cost per additional net page.
Read the worked answer
Overtime on both machines, one hour: gross 12,250 + 1,750 = 14,000/day; net 14,000 × 0.92 = 12,880/day; total 257,600 - clears the target by 7,600 pages (3.0%). Cost = 2 × £38 × 20 = £1,520.
One hour on Scanner A alone: 13,250 gross → 12,190 net → 243,800, still short, so both operators are needed.
Third scanner: 900 × 7 = 6,300 gross/day = 5,796 net/day = 115,920 pages over the run, total 341,320 - about 91,000 pages of paid-for idle capacity. Cost = £400 × 20 = £8,000.
Cost per extra net page: overtime £1,520 ÷ 32,200 = £0.047; rented scanner £8,000 ÷ 115,920 = £0.069. Overtime is cheaper and sufficient.
3. The 8% rework figure is an assumption. At what point does your recommendation fail, and what would you do about it?
Read the worked answer
Break-even: 12,500 ÷ 14,000 = 0.8929, so the overtime plan fails once rework reaches about 10.7%.
At 10% rework: 14,000 × 0.90 = 12,600/day = 252,000, clearing by only 2,000 pages (0.8%). At 11%: 12,460/day = 249,200 - misses.
The whole plan therefore rests on the 8% assumption. Protect it: authorise the overtime but measure rework on the first 20,000 pages. If the observed rate exceeds 10%, add a second overtime hour, which raises gross to 15,750/day and covers rework up to 12,500 ÷ 15,750 = 20.6%, for £3,040 total - still well under the £8,000 scanner.