Originally posted by: SystemAdmin

Hi everyone,

I am currently trying to model a large power system investment problem. In my current model, I defined binary decision variables which represent the investment amount for each time step which allows investment, and the accumulated investment which represent the total amount of investment since step 0. For example, we have a 10 year investment problem, on year 1,5 invetsments are allowed, so, I write:

x1=S1
x1=S2
x1=S3
x1=S4
x1+x5=S5
x1+x5=S6
x1+x5=S7
x1+x5=S8
x1+x5=S9
x1+x5=S10

x represent the investment on year 5 or 10, and S is the accumulated investment ("up-to-date"). However, I am not sure if this approach is efficient or not. I am thinking maybe the below one will be easier for cplex to solve:

x1=S1
S1=S2
S1=S3
S1=S4
x1+x5=S5
S5=S6
...

Of course, I guess simply eliminate S2,S3,S4 by replacing them by S1 will be simpler, but this will bring extra difficulties in modeling and analyzing, so I will consider it only when it has been proved to be much better than the current modeling method.

So, does anybody knows if this really matters or not? Will it make some differece in computational time when we define a new variable which could be replaced using an existing one in our model? Thank you so much for reading this... Any suggestions is greatly appreciated:)
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Originally posted by: SystemAdmin

I think the answer to your question is that the presolver will take care of any algebraic reductions it deems helpful. The second approach is slightly sparser than the first one (which is good), but I think I would not worry about it unless solution time became excessive ... and even then, I might rely on the "judgment" of the presolver.

Paul

Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. (Goethe)
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