Re: LP problem

Sabrina_25 wrote:

> / Hello,
> / I have a LP-Problem, which I want to solve with CPLEX or similar
> / software. My problem is: How do I solve a complex LP-problem like
> / the one described below with CPLEX or similar?
> / The LP comes from a paper, where the author solved this problem with CPLEX.
>
> /
> /                  m   k
> /    w[j][N](x) = sum(sum(r[i][j](tl)*x[i]))
> /                 i=1 l=1
> /  LP-Problem:
> /                   K
> /      max         sum( p[j]*w[j][N](x) )
> /  u,x e X,y,z     j=1
> /
> /         L                                 N   K
> /s.t.    sum(Chi[i]*(y[i] + 1/((1-a[i])*N)*sum(sum(p[j]*z[i][j][k]))))<= gamma,
> /        i=1                               k=1 j=1
> /
> /        z[i][j][k] >= u[j][k] - y[i],
> /        u[j][k] >= u[j][k-1] - r[j][k](x),
> /        u[j][k] >= 0, u[j][0] = 0, z[i][j][k] >= 0,
> /        i = 1..L, j = 1..K, k = 1..N,
> /
> / where u[j][k], y[i] and z[i][j][k] are auxiliary variables.
> / x=(x1,x2,x3,...,xm).
>
> / The difficult thing for me are the multiple sums in s.t.
> / Thanks for any suggestions!
> / Sabrina

As you discovered, you got to get the problem into a form that
CPLEX can understand. One widely used format that CPLEX
(and pretty much every other serious LP solver) accepts is the
MPS format. Perhaps the authors of the paper have an MPS
version of their problem that they can send you. Can't hurt to
try to contact them by email.

Or you could instantiate the problem yourself. You will
obviously need data, including specific values for L,K,N,m.
Often those would not be part of the published paper, so you
have to contact the authors again (or make up your own data).

And likely the problem will be quite large, so you will want to
use an algebraic modelling language to help you. If your
problem is not too large (no more than 300 constraints and
300 variables, including any auxiliary variables you might need)
you can use the student version of AMPL (www.ampl.com)
for this purpose.

HTH