Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

For the following scenario :

$E=100$ (energy available = $100$%)

Components = $N$ (can be $1,2,3,\dots,\infty$)

Now I want to split $E=100$ for each component, however, components are prioritised :

Example, component $1$ has first priority, component $2$ has second highest priority, and the rest have low priorities.

Application : If $E=100$

  • $C_1=1$ (component $1$ has priority 1 )
  • $C_2=2$
  • $C_3=3,C_4=3,C_5=3$

Then $C_1$ must get the maximum value of $E$, while $C_2$ gets the second highest value ... $C_{345}$ must get the same equal lowest value of $E$

What mathematical model achieves this ?

Splitting $100/5$ will only give me equal values for all components, but im not sure how to achieve this with priorities.

share|improve this question
3  
Intriguing selection of tags. –  joriki Nov 6 '12 at 15:19
1  
@joriki thank you –  NLed Nov 6 '12 at 16:01
    
This is some kind of optimization problem, yet you do not specify how to compare two distributions. –  Alexei Averchenko Nov 6 '12 at 16:17
    
@AlexeiAverchenko to be honest, I have no idea what to call this .. I am not familiar with the mathematical terms or titles. I just thought they have something to do with models and division ... Can you elaborate what you mean by specifying how to compare two distributions ? -- Also, did you mark my question down ? –  NLed Nov 6 '12 at 16:19
    
Suppose you have two distributions $(a_1, a_2, \ldots, a_n)$ and $(b_1, b_2, \ldots, b_n)$. How do you determine which one is better for you purposes? –  Alexei Averchenko Nov 6 '12 at 16:21

2 Answers 2

up vote 3 down vote accepted

Unless you have a model of how benefit changes with money spent, the solution will simply always be 100/0/0/0/0 split, since you are maximising the highest priority.

If you had a utility function specifying that say, Roads were top priority up to 5%, then lowest priority afterwards then you would get a 95/5/0/0/0 split etc.

If you just want a simple weighting, then just add up the weights , eg 5+2+1+1+1=10 then assign 100/10*weight percentage points to each category.

share|improve this answer
    
Im interested in the simple weighting you mentioned ... Can you please elaborate on that ? –  NLed Nov 6 '12 at 15:53
    
can someone please explain what @Nick mentioned as 'If you just want a simple weighting, then just add up the weights , eg 5+2+1+1+1=10 then assign 100/10*weight percentage points to each category.' ?? Can you please explain this and use another example, I dont get it –  NLed Nov 6 '12 at 23:13

C1 gets 90, C2 gets 7, C3-C5 get 1. For a mathematically unique answer you need to define priorities more completely. There is an infinite collection of solutions to your example as stated.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.