室友之間的共享雜貨費用按特定消費比例和出勤率進行分配

如果這個問題出現在錯誤的部分，我深表歉意。

我和我的幾個室友（共 5 人）分擔雜貨費用。我們將購買記錄在 Excel 表中，並為每個成員指定單個項目的消費比例。

例如。

- Roommate A doesn't consume Milk and Jam, but consumes Bread equally and Butter most, so
   1. Milk = 0%
   2. Jam = 0%
   3. Bread = 20% (total expense for Bread equally divided between 5)
   4. Butter = 50% (total expense for Butter as per consumption ratio)
- Roommate B doesn't consume Milk, but consumes Jam and Bread equally and Butter more, so
   1. Milk = 0%
   2. Jam = 25% (total expense for Jam equally divided between 4)
   3. Bread = 20% (total expense for Bread equally divided between 5)
   4. Butter = 30% (total expense for Butter divided as per consumption ratio)
- Roommate C doesn't consume Butter but consumes Milk, Jam and Bread equally, so
   1. Milk = 50% (total expense for Milk equally divided between 2)
   2. Jam = 25% (total expense for Jam equally divided between 4)
   3. Bread = 20% (total expense for Bread equally divided between 5)
   4. Butter = 0%
- Roommate D doesn't consume Milk, but consumes Jam and Bread equally and Butter less, so
   1. Milk = 0%
   2. Jam = 25% (total expense for Jam divided by 4)
   3. Bread = 20% (total expense for Bread divided by 5)
   4. Butter = 10% (total expense for Butter divide as per consumption ratio)
- Roommate E consumes Milk, Jam and Bread equally and Butter less, so
   1. Milk = 50% (total expense for Milk equally divided between 2)
   2. Jam = 25% (total expense for Jam divided by 4)
   3. Bread = 20% (total expense for Bread divided by 5)
   4. Butter = 10% (total expense for Butter divided as per consumption ratio)

計算單個成員到此階段的份額相對容易，但如果考慮持續時間，特別是當某些成員可能不會在整個持續時間內出現時，計算是

例如。

Considering 100 days of calculation period, 

- Roommate A was present only for 20 days
- Roommate B was present only for 80 days
- Roommate C was present only for 90 days
- Roommate D was present for the entire 100 days
- Roommate # was present only for 70 days

因此，我只能計算下面列出的前兩種情況，但不能計算最準確的第三種情況。

1. 只根據消費比例分享
2. 僅根據出席情況分享
3. 根據消費比例和出勤率分享

我真的很努力想出公式的邏輯，我確信這是一種相當常見的計算方法，但我無法理解它（我什至不知道正確的數學術語這種類型的計算）。

如果有人幫助我，我會很高興。

提前致謝。

這個問題的解決方案有點像在曲線上分級。用消費比率乘以出勤率（也是一個比率，100天）來計算每個人欠多少錢。這會讓你很短。然後將一個類別中的所有份額加在一起，確定達到該類別實際成本所需的百分比增加，並將所有份額增加該百分比。

Example, for butter:

- Roommate A, 50% butter,  20 days.
- Roommate B, 30% butter,  80 days.
- Roommate C,  0% butter,  90 days.
- Roommate D, 10% butter, 100 days.
- Roommate E, 10% butter,  70 days.

Say you spend $100 on butter.
Step 1:

- Roommate A, 50% of  20% of $100 is $10
- Roommate B, 30% of  80% of $100 is $24
- Roommate C,  0% of  90% of $100 is  $0
- Roommate D, 10% of 100% of $100 is $10
- Roommate E, 10% of  70% of $100 is  $7

Now, that all adds up to $51.
To get to $100, you need to multiply $51 by approx 196%.
So, you multiply each of those shares by 1.96:

- Roommate A, $19.60
- Roommate B, $47.04
- Roommate C, $ 0.00
- Roommate D, $19.60
- Roommate E, $13.72
- Total:      $99.96 (four cents got lost due to rounding)

引用自：https://money.stackexchange.com/questions/36752