## lifetime of technology

Problems with modeling
gnab2006
User
Posts: 1
Joined: 2 years ago

### lifetime of technology

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:

1) 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;

2) 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!

Renger
Posts: 550
Joined: 3 years ago

### Re: lifetime of technology

Hi

I haven't tested this, but perhaps these remarks help to solve the issue:
• Equation 2 means that there will be no investment in a technology the number of maximum lifetime years before the end of the considered time horizon. I would, therefore, change the =E= in =L=.
• The equation 2 sums over all years, but it might be better to check for the years up to the year a of the actual gammas. (although this change might not be necessary).
All in all, this would change the second equation in:

Code: Select all

``````alias(a, aa);
sum(aa\$(ord(aa) LT ord(a)), (GAMMA(aa,comp_max))) =L= lifetime(comp_max) ;
``````
Cheers

Renger
____________________________________
Enjoy modeling even more: Read my blog on modeling at The lazy economist