I have an integer programming model for Parallel Machine Scheduling. The parallel machine scheduling problem have $i$ jobs, $j$ process and $k$ number of machines. Each processes has to be done in given sequential. I got this model from an article and wrote it in GAMS. But in the result, the all values for $y(i,j,i',j',k)$ were equal to $0$. I think, it is because there is no constraint for the value $y$. But I don't know how to do it? Is there anyone that has knowledge about scheduling and its model? Please help!
The article is here and the model is at the page 2 and 3. No need to rewrite here.Please see:
At first sight the mathematical model looks fine. The $Y$s are used to express that two jobs cannot overlap (i.e. either earlier or later). If you know a solution, it is often a good idea to plug that into the model and see what happens. In GAMS you can fix variables by
x.fx(i,j) = p(i,j);where $p$ holds the solution values. If you don't know a solution, construct a minimal data set (e.g. 2 jobs, 1 machine) and plug in the solutions you found by hand.