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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.

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    This is some kind of optimization problem, yet you do not specify how to compare two distributions.2012-11-06
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    @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 ?2012-11-06
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    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?2012-11-06
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    Each distribution will be given a priority. The distribution with highest priority gets most of the weighting.2012-11-06
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    No-no-no, suppose two hypothetical situations: in one you've given $a_1$ to the first guy, $a_2$ to the second guy etc., in the other you've given $b_1$ to the first guy, $b_2$ to the second guy etc. How do you determine which allocation/split/solution/how-do-you-call-it is better than the other?2012-11-06
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    @AlexeiAverchenko I honestly have no idea. If I limit the distributions to one ( as in give the guys a_1,a_2 etc ...) I wouldn't need to worry about b .. yeah ? no ? seriously don't know2012-11-06
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    I'm trying to get you to completely state your problem. Sorry, but math doesn't make up your mind for you. If you want to find the best way to allocate resources, you first have to define in what sense is one way better than another.2012-11-06
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    @AlexeiAverchenko sorry that im complicating this for you .. Basically I have a battery that stores energy (0 = depleted and 100 = full ) ... I want to split it to various components .. for now lets say a Light, a heater and an oven. I want the heater to have maximum priority so that it will always get max power even when the battery starts depleting...Such that the heater will provide maximum temperature satisfaction while the light and oven energy supply is reduced (due to lower priority). Does this make more sense ?2012-11-06

2 Answers 2

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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.

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    Im interested in the simple weighting you mentioned ... Can you please elaborate on that ?2012-11-06
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    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 it2012-11-06
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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.