Proportional Distribution I have a problem regarding supply distribution. 
I distribute widgets on a monthly basis; I have many customers and each of them request a different quantity each month. My monthly supply is limited and I cannot fill every order. How do I distribute fairly, across the board? There must be some sort proportional way to do it. 
Let me know if I need to provide additional information.
Thanks
 A: The answer to your question depends on how you define "fairly". I think you are right that in each particular month you give each customer the same fraction of his or her order: (your monthly supply)/(total ordered that month). 
You may have to decide what to do with fractions of widgets. If that matters a lot it might be difficult - it's like the problem of apportioning representatives in a parliament in proportion to votes or populations.
If you want to do something better for customers who were shortchanged in previous months the problem is much harder, because it's harder to say what "fair" means.
A: I assume if every customers receive the same proportion due their request, then the distribution is fair. Let $M$ the number of available widgets. And $n_i$ is the number of request of widgets of custumer $i$. You have $c$ customers. Them total request  is $R=\sum_{i=1}^c n_i$. 
Therefore you should distribute $\frac{n_i}{R}\cdot M$ widgets to customer $i$. The precondition is that $M$ is divisible by $R$. Otherwise the fractions have to be rounded. In this case the costumers don´t get their exact (fair) proportions.
