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## Homework Statement

I've tried hours and hours to model this problem but i didn't succeed. Can you help me ?

*We want to realize n projects in the next T years. For each project, a*

profitability index pi is known, which expresses the expected final

gain (in Euro) and a cost profile ai = (ai1, ai2, ..., aiT) for each

year of the period considered. Moreover, in each year j of the period

a budget of bj € is available. Which projects should be selected to

maximize the expected profit while respecting budget constraints?

profitability index pi is known, which expresses the expected final

gain (in Euro) and a cost profile ai = (ai1, ai2, ..., aiT) for each

year of the period considered. Moreover, in each year j of the period

a budget of bj € is available. Which projects should be selected to

maximize the expected profit while respecting budget constraints?

*Assume that the projects have a duration of T '< T years. For each*

selected project, we also want to identify the start year.

selected project, we also want to identify the start year.

*note: take care that if i start a project at year 2 , all the [itex]a_{i}[/itex] are shifted by 2 from the initial year ( that is 1))*

## Homework Equations

## The Attempt at a Solution

[/B]

Sometime ago i succeeded in modeling the non-bold part of the problem, however if i try to add also the last requirement i don't understand what to change of my original formulation, that is :

[tex]max \sum_{i=1}^{n} p_{i}x_{i}[/tex]

[tex] \sum_{i=1}^{n} a_{ij}x_{i}=b_{j} , j=1..T[/tex]

[tex]x_{i}\in \left \{ 0,1 \right \} , i=1..n[/tex]