Complaint Resolution Across Three District Offices
A regional service standard requires complaints to be resolved within 20 working days and reopened complaints to be re-examined within 10 days. The table shows four quarters of data for three district offices. 'Received' counts complaints opened in the quarter; 'resolved' counts complaints closed in the quarter, including some received earlier; 'reopened' counts resolutions later reopened; 'average days' is the mean calendar days to close complaints in that quarter. Office C has half the staffing of A and B.
| Office | Quarter | Received | Resolved | Reopened | Average days |
|---|---|---|---|---|---|
| A | Q1 | 400 | 320 | 28 | 18 |
| A | Q2 | 520 | 470 | 22 | 15 |
| A | Q3 | 610 | 585 | 19 | 14 |
| A | Q4 | 480 | 462 | 15 | 12 |
| B | Q1 | 300 | 255 | 40 | 25 |
| B | Q2 | 340 | 306 | 36 | 23 |
| B | Q3 | 310 | 295 | 28 | 19 |
| B | Q4 | 360 | 349 | 22 | 17 |
| C | Q1 | 210 | 200 | 10 | 9 |
| C | Q2 | 190 | 183 | 8 | 8 |
| C | Q3 | 240 | 229 | 9 | 11 |
| C | Q4 | 260 | 251 | 7 | 10 |
1. Calculate the annual resolution rate (resolved ÷ received) and reopened rate (reopened ÷ resolved) for each office. Which office shows the strongest improvement, and on which measure?
Read the worked answer
Totals:
- A: received 2,010; resolved 1,837; reopened 84. Resolution rate = 1,837 ÷ 2,010 = 91.4%. Reopened rate = 84 ÷ 1,837 = 4.6%.
- B: received 1,310; resolved 1,205; reopened 126. Resolution rate = 1,205 ÷ 1,310 = 92.0%. Reopened rate = 126 ÷ 1,205 = 10.5%.
- C: received 900; resolved 863; reopened 34. Resolution rate = 863 ÷ 900 = 95.9%. Reopened rate = 34 ÷ 863 = 3.9%.
The strongest improvement depends on the measure. A improved its quarterly resolution rate from 320 ÷ 400 = 80.0% in Q1 to 462 ÷ 480 = 96.3% in Q4, a 16.3-point gain. B improved from 85.0% to 96.9%, an 11.9-point gain, but cut its reopened rate from 15.7% to 6.3%, the largest fall. C was consistently strong but its average days rose from 9 to 10 in Q3 and Q4. On resolution rate the answer is A; on reopened rate it is B.
2. The director has two additional quality-review staff. Using the data, recommend where to deploy them and state two limitations of the data.
Read the worked answer
Deploy one to B and one to A, with B as first priority. B has 126 reopenings, 51.6% of all reopenings (126 ÷ 244), and a 10.5% reopened rate, nearly three times C's 3.9%. A has 84 reopenings but the largest volume (2,010 received) and the weakest single quarter (80.0% resolution in Q1). C is smaller, already strong, and has half the staff; a reviewer there would have less marginal effect.
Limitations: first, 'resolved' includes complaints received earlier, so the annual resolution rate is not a true cohort rate; a backlog carry-over can flatter or distort a quarter. Second, averages hide the tail of very old complaints, and a reopening may reflect a different issue rather than poor original handling. Staffing and complaint mix also differ. The deployment should be revisited after a cohort-based audit.