[Help-glpk] Question about modeling in MathProg

[aly]

Hi All,

I have 3 modeling questions about MathProg (GLPK). They might be simple, but I 
just wanna make sure. I'd appreciate any help:


1. Suppose we have a set of periods T. Also, there are two variables, x_t and 
y_t. Now, there is a constraint that is "x_(t-1) - x_t = y_t \for all t=2,..,T."

I'm thinking of defining it as:

"s.t. balance{t in 2..T}: x[t-1]-x[t]==y[t];", after defining the set T in the 
beginning by "set T;"; and the variables x_t and y_t by "var x{t in T}>=0;" and 
"var y{t in T}>=0;" respectively.


Is that right?


2. Continuing on the previous question, suppose another constraint for t=1 is 
"initial-x_t=y_t \for t=1.", where initial is a parameter.

Is it defined by "s.t. balance1: initial -x[1] == y[1];" after defining the 
parameter initial by "param initial;" ?



3. Suppose there are a variable z_tu, where the 2 indices t and u are defined 
on the set T, a parameter d_t, and a constraint "\sum_{u>t} z_{ut} = \sum_{u<t} 
z_{tu} + d_t \for all t \in T".

After defining the set T, variable z_tu and parameter d_t by "set T;", "var z{t 
in T, u in T}>=0;" and "param d{t in T};" respectively, I think of defining the 
constraint by "s.t. delivery{t in T} sum{u in T} z[u,t]==sum{u in 
T}z[t,u]+d[t];", but that might not be right!

Could you verify it for me, please?



Thanks a lot,

Aly




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