Originally posted by: nr-mz

Hello everybody

I would like to write you to draw your attention on an issue i am dealing with. Any helping idea is appreciated.

Actually I am using cplex 12.6.1 for solving a model in Resource Constrained Project Scheduling Problems. The binary decision variables of the model is defined as following:

Zit =1 if activity i starts at time period t, 0 otherwise.

For setting a time window in start of the activities, as it is also dealt with in the other seminal works in literature,I have defined the earilest and latest start date for activities. The relevant constraint in OR model is:

For all i belong to activities,     Sigme (over t , t from earliest start(i) to latest start(i)): Zit =1;

Obviously, the total number of binary variables of the model would be: sigma (over i): latest start(i)- earliest start(i). 

In order to reduce the solution time of the model, an idea could be to reduce the total number of binary decision variables. For that purpose, I am using an algorithm that can sucessfully tighten the interval (ealiest star(i), latest start(i)). But after resolving the model with new tighten intervals ( that is to say with less binary variables) the solution time of the model increases significantly !!!

In deed, I am wondering what could be the reason of this issue.

Could anybody, please, give me helping ideas..

Best regards

Originally posted by: UserCplex

My thought are that when you did not tighten the interval, CPLEX presolve itself figures this out and ends up reducing the problem size dramatically.

When you did tighten the interval, CPLEX is not able to reduce the problem further and ends up solving a harder problem?

Also, the branching sequence in both cases could be different in that in the former, tight bounds are established pretty early while in the latter case, bounds are weaker. Look at the number of branch and bound nodes explored and this may give some ideas.

These are all obviously guesses. Good luck with your problem.

Originally posted by: nr-mz

Thank you so much for your answer. Yeah I totaly agree with you.. But another strange point is that every time I run the model, I get different solution times. Once it takes 60 seconds once thirty seconds and ect. Is it so normal to have different solution time in every different run, for the same model with the same data?

Thank you so much

I take it this is the same question as here?

Originally posted by: nr-mz

Yeah that was it. But actually, my problem in this post is that when I reduce the number of binary variables, the soloution time increases !! Actully I wonder how this problem occures..

I thnak you so much for your attention...

Best regards,

The increase in solution time is not unexpected. Model size or number of (binary) variables is not a reliable indicator for how difficult a model is.