Hi julio and Edson.

I don’t understand why are you assuming that both models are the same. As Edson pointed, the first model is a MILP formulation, on the other hand, the second problem has a constraint with bilinear expresion, therefore is a MINLP formulation. As you can guess, if the constraints are different the feasible region changes from one model to another, therefore both models are not the same and it’s totally expectable different solutions, even if the cost function is common for both models.

Best Regards!!!

2011/8/2 Edson Valle

Julio

I think you don’t need to care about it, since you can solve both small problems within precision, it the problems get large, then, you must care about it.

If you are interested, in the second one you are adding a non-linear factor when you multiply a binary by a continuous variable, doesn’t seem good since they are already related by the inequalities, I would avoid the second case. The difference in the solution you commented before come from the fact that the models are different (as explained before and pointed by Daniel) and it’s a solver issue, not GAMS. Depending on the solver your’re using, even the same constraints, but in different order can lead to solutions with minor differences (I had this experience with Ipopt solver). I hope I could make this points clear

regards

Edson

2011/8/2 Julio LÃ³pez

Hi Daniel, excuse me, not explain the problem.

The problem consist in determine the costs of installing of the recourses qc and qr.

Some colleagues say that the second form would be better results with the first, and that the models are the same. They argue, qc, wc and qr, wr are associated, therefore the best way to write the model in GAMS is like the second

I would like to know their opinions and arguments about.

The question is, which is the the correct form of write the model in gams.

1.- min f = [CFC*wc + CVC*qc] + [CFR*wr + CVR*qr]

s:a

Pg -ps - Pd - Pk = 0

Qk - qg - Qd - qc + qr = 0

-50 <= ps <= 100

-100 <= qg <= 100

0 <= qc <= 100*wc*

0 <= qr <= 100wr

wc, wr ={0,1}

2.- min f = [CFC*wc + CVC*qc] + [CFR*wr + CVR*qr]

s:a

Pg -ps - Pd - Pk = 0

Qk - qg - Qd - qc*wc + qr*wr = 0

-50 <= ps <= 100

-100 <= qg <= 100

0 <= qc <= 100*wc*

0 <= qr <= 100wr

wc, wr ={0,1}

CFC, CVC. CFR, CVR, Pg, Pd, Pk, Qk, Qd are know constant values

ps, pg, qc, qr, are continue variables

wc, wr are binary variables

Solver COPNOPT

Tanks

## Julio

\

Edson Valle

edsoncv@gmail.com

Daniel AndrÃ©s Navia LÃ³pez

Ingeniero Civil QuÃmico

Mg.Sc.Ciencias de la IngenierÃa, MenciÃ³n IngenierÃa QuÃmica

MÃ¡ster en InvestigaciÃ³n en IngenierÃa de Procesos y Sistemas

626752875

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