Hi!

I’m trying to model the lifetime of a technology i to calculate optimal year a of investment.

for this I have two binary variables

GAMMA(a,i) - takes the value (1) if technology exists and (0) otherwise

PHI(a,i) - takes the value (1) if i has been bought in year a and (0) otherwise.

My problem collides between the following two equations:

- after i has been bought in year a, it has to exist in year a+1:

GAMMA(a,comp_max)-GAMMA(a-1,comp_max) =g= 0;

- technology i has a limitted lifetime

sum(a,(GAMMA(a,comp_max))) =e= lifetime(comp_max) ;

The problem relies in the fact that when eq. 2) is fulfilled, eq 1) is violated:

There are other equations that relate GAMMA and PHI, but I believe the main problem relies in the two eqs. listes above.

I would be extremely thankful for any suggestion!