sci.op-research

Hi

I have written a GAMS code for solving an MIP. I have been using CPLEX
to solve it. The code works for small-size problems (n=7). But as the
number of binary variables increases (e.g. for n=15, 225 binary
variables) running the code takes a long time to solve it. I have
brought my code in the following. The model is a scheduling problem
with considering release time and idle insert.

1- Can somebody help me with a suggestion for solving this problem.
2- Lagrangian Relaxation would be useful for it.
3- Does CPLEX provide an implementation of the Langrangian Relaxation
or ...
4- Are there any C/C++ implementation of these techniques that I can
plug in to my existing C++ code.

Thanks
Mehdi Mahnam

Jobs i,j=1,2,...,n
Binary variable x(i,j) means job i precedes job j
Positive variables Emax, Tmax, s(i)
M= large number like 9999
Parameters
p(i) processing time of job i
r(i) release time of job i
d(i) due date of job i

objective.. Z=e=Emax+Tmax;
S1(i).. s(i)=g=r(i);
S2(i,j)$(ord(i)<>ord(j)).. s(j)=g=(s(i)+p(i)-(M*(1-x(i,j))));
L1(i).. x(i,i)=e=0;
L2(i,j)$(ord(i)<>ord(j)).. x(i,j)+x(j,i)=e=1;
Earliness(i).. Emax=g=d(i)-s(i)-p(i);
Tardiness(i).. Tmax=g=s(i)+p(i)-d(i);