This question's explanation and your answers so far.
あるサービスデスクでは，電子メールによる問合せに対応しており，受付担当者がメールの内容を確認し，回答担当者の割当てをしていた。このたび，割当て業務の効率化を目的に，自動割当てツールを導入した。自動割当てツールは，メールの内容を基に自動で回答担当者の割当てを行うが，割当てができないことや割当てミスをすることがあり，それらについては，人手で対応している。導入前及び導入半年後の状況が次のとき，割当ての時間はサービスデスク全体で何%削減できたか。ここで，割当ての時間の削減率（％）は小数第1位を四捨五入するものとする。
| 問合せ件数 | 割当ての時間 | |
|---|---|---|
| 導入前 | 1,000件/日 | 2分/件 |
| 導入半年後 | 1,000件/日 | |
| 自動割当てができた割合 | 90% | 0分/件 |
| うち，割当てミスの割合 | 5% | 4分/件 |
| 自動割当てができなかった割合 | 10% | 2分/件 |
This value comes from misreading the 5% of incorrect assignments as 5% of all 1,000 cases = 50 cases. Then 50×4 = 200 min and the non-auto-assigned 100×2 = 200 min give a total of 400 min, and the reduction rate (2,000 − 400) ÷ 2,000 = 80%. However, “of which” refers to 5% of the 900 cases that were auto-assigned = 45 cases, so this reading is wrong.
正解 Before introduction, the assignment time is 1,000 cases/day × 2 min/case = 2,000 min/day. Six months after introduction, out of all 1,000 cases, 90% (900 cases) were auto-assigned successfully at 0 min/case. Of those, 5% were incorrect assignments, i.e., 5% of the 900 cases = 45 cases, which are handled manually and take 4 min/case (45×4 = 180 min). The cases that could not be auto-assigned were 10% (100 cases), handled manually at 2 min/case (100×2 = 200 min). The remaining 855 cases that were correctly auto-assigned take 0 min. Therefore, the total after introduction is 180 + 200 = 380 min/day. The reduction rate is (2,000 − 380) ÷ 2,000 × 100 = 81%, so the correct answer is イ (81).
If the manual handling for incorrect assignments is counted at 2 min/case (the same as the non-auto-assigned cases) instead of the proper 4 min/case, underestimating the manual handling time, the total after introduction becomes about 300 min and the reduction rate becomes 85%. Incorrect assignments should be counted at 4 min/case, so this is an error caused by underestimation.
If the number of cases or minutes handled manually is counted even lower, the total after introduction becomes about 280 min and the reduction rate becomes 86%. Correctly adding the 45 incorrect-assignment cases × 4 min = 180 min and the 100 non-auto-assigned cases × 2 min = 200 min gives 380 min and 81%; 86% is an excessively high reduction rate resulting from undercounting the manual handling time, and is wrong.