Five days, 4,800 claim files
Your branch has 4,800 pending claim files to be data-entered before close of business on Friday. Work starts on Monday, there are five working days, and no weekend work is authorised. Each file carries an average of 30 fields, and a full-speed operator enters 900 fields an hour, which works out at 30 files an hour. After lunch, counter duty and other office work, the day gives six productive hours per person.
The team has five people: three full-speed operators and two trainees who work at 60 per cent of full speed. Overtime is permitted up to two hours per person per day and is paid at 250 per hour per person. Alternatively a temporary operator can be engaged at 1,500 per day at full speed, but needs half a day of induction and so cannot produce anything before Tuesday noon.
A sample check shows the error rate stays near 1.5 per cent up to six working hours and rises to about 2.5 per cent during overtime hours.
1. Does the existing team, working only normal hours, clear the backlog by Friday? Show your arithmetic.
Read the worked answer
Convert everyone to files per day. A full-speed operator does 30 files an hour × 6 hours = 180 files a day. A trainee works at 60 per cent, i.e. 18 files an hour × 6 hours = 108 files a day.
Daily team output = (3 × 180) + (2 × 108) = 540 + 216 = 756 files. Over five days: 756 × 5 = 3,780 files.
Required: 4,800. Shortfall = 4,800 − 3,780 = 1,020 files, which is a little over one and a third days of the whole team's output. So normal hours alone do not meet Friday's deadline, and the gap is far too large to be absorbed by a final push - roughly 1,020 ÷ 126 = 8.1 team-hours are needed, where 126 files an hour is the whole team's combined hourly rate (3 × 30 + 2 × 18).
2. Work out the cheapest plan that still finishes on time, and say what could go wrong with it.
Read the worked answer
Option A, overtime only. The team produces 126 files per team-hour. Overtime cap is 2 hours a day × 5 days = 10 team-hours = 1,260 files, which covers the 1,020 gap with a 240-file buffer. Cost = 5 people × 10 hours × 250 = 12,500.
Option B, one temporary plus limited overtime. The temp works Tuesday afternoon (3 hours after induction) plus three full days = 21 hours × 30 = 630 files, for 4 days' pay = 6,000. Remaining gap 1,020 − 630 = 390 files; at 126 files a team-hour that is about 3.1 hours, so 2 hours of team overtime on any two days (504 files) suffices. Cost = 20 person-hours × 250 = 5,000. Total 11,000.
Option B is about 1,500 cheaper and cuts overtime, hence errors, but it depends on the temp actually arriving Tuesday morning and on someone supervising the induction. If the induction slips by even half a day, the buffer disappears. Option A is costlier but wholly within the branch's control - that is the judgement call, and A is the safer choice if the temp's attendance is not confirmed in writing.
3. The branch manager says: "Just authorise overtime for everyone; errors can be rectified later." Assess that instruction.
Read the worked answer
The arithmetic supports the schedule but not the shrug about quality. If the 1,020 shortfall files are done in overtime at 2.5 per cent and the other 3,780 at 1.5 per cent, total errors are about 25.5 + 56.7 = 82 out of 4,800, i.e. roughly 1.7 per cent overall - barely above the normal rate. The rise is real but small, so refusing overtime on quality grounds alone would be an overreaction.
The weak part of the instruction is "rectified later". Claim files are money: a wrong account number or a transposed amount is not a spelling slip, and rectification after payment is far costlier than the overtime saved. The defensible version of the instruction is: authorise the overtime, but attach a condition - 100 per cent verification of amount, account number and insured person's name on all overtime-entered files, with a second person signing off. That keeps the Friday deadline, costs a few hours of checking, and confines the 2.5 per cent error exposure to fields where a mistake is cheap to fix.