Optimizing Fair Distribution of Pooled Funds among Debtors

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SUMMARY

The discussion focuses on optimizing the distribution of pooled funds among debtors when the total amount owed exceeds the available funds. The proposed method involves calculating the total amount owed, determining the shortfall by subtracting the pooled funds, and then evenly distributing this shortfall among all debtors. Each debtor receives their owed amount minus a uniform deduction, ensuring that losses are equitably shared. This approach is efficient and can be executed manually or with the aid of spreadsheet software like Excel.

PREREQUISITES
  • Basic understanding of financial mathematics
  • Familiarity with Excel for data visualization
  • Knowledge of equitable distribution principles
  • Ability to perform arithmetic operations involving totals and averages
NEXT STEPS
  • Research mathematical optimization techniques for equitable fund distribution
  • Learn advanced Excel functions for financial modeling
  • Explore algorithms for solving allocation problems in finance
  • Investigate case studies on pooled fund distribution in debt management
USEFUL FOR

Financial analysts, debt managers, and anyone involved in equitable fund distribution among multiple parties will benefit from this discussion.

mrcleanhands
Firstly, I'm not even sure how to frame this mathematically, but I'd be curious to know what kind of problem it is and what kind of subjects within maths it requires to be able to solve it.

Here's my problem--
I've set it up in excel to help you visualise it.
sss.png

There is a different amount of money owed to different people (Amounts Owed). There is a fund which'll be used to pay out those people (Pooled funds). The pooled funds do not equal the total amount owed. If I divide the amount of pooled funds by 4 and hand it out to each person evenly, the dollar loss amounts will be uneven (since each person is owed a different amount). What I'm trying to do is solve for values highlighted green (how much money is given to each person) such that the total dollar losses for each person will equal (that red column).

Is there some way to do this on paper very efficiently, or is it only a problem for the computer?
 

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1) Calculate the total owed.
2) Subtract the total pooled funds from that.
3) Divide the result by the number of people and label it $x. (That tells you how much short the pooled funds are per person.)
4) Give each person the amount owed minus $x.

Then each person will get what he is owed minus the same amount, $x.
 
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Just divide the total amount that you're short by 4, and subtract that from the amount owned for every person.
 

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