Finally, I found the answer to the problem. In general, both [1] and [2] are necessary to ensure the correct modelling of [Rel 1]. Nevertheless, the fact is that in my problem, the cases that all follow the form of [Rel 1] are not independent. So, by forcing both [1] and [2] to only one of them ensures that both [1] and [2] are set to all cases, even if [2] is not set explicitly. In other words, the fact of dependency of the cases in my model, allows to set only the [1], while [2] implicitly holds, provided that both [1] and [2] are set to only one of the total cases. Hope that the information on this topic will be helpful to some one and I ma sorry if I waste your time.
2016-02-22 1:44 GMT+02:00 ΤΑΣΣΟΠΟΥΛΟΣ ΙΩΑΝΝΗΣ <[email protected]>: > Good evening to everyone. > I am facing a rather peculiar situation which is as follows: > I have a MIP problem with several constraints (about five). All of them > have the same type (with different parameters, though). > The form of these constraints is: > Let U denotes some integer variables (indices not included for simplicity > reasons), where > - Lower <= U <= Upper (where -Lower and Upper depend on the variable > U) > Let D be a binary variable. > I mast model the following: > > D = 1 if U > 0 (i.e. 1 <= U <=Upper) and D = 0 otherwise (i.e. -Lower <= U > <= 0). [Rel 1] > > I have tested the following model: > > [1] U <= Upper*D > [2] U + Lower >= (Lower + 1)*D > > As it is easily verified these two constraints ensure the relation [Rel 1]. > Now, I noticed that if I exclude the second form of constraints ([2]) > from my model at all, an error occurs . To be more exact, D takes wrong > value, when -Lower <= U <= 0. > At the other hand, if I include both [1] and [2], the solution is correct > but the execution time is too much while the value of objective function is > high. (but correct). > To make things even more complex, I noticed that when I exclude again the > form [2] from all my constraints, but I keep it in only one of them, the > model works perfectly. The execution is done fast and the objective value > is almost optimal. > Now the question is: in order to model a condition like [Rel 1] are both > [1] and [2] constraints necessary or [1] should be enough? > Thanks in advance for spending your time on my issue and for any answer. > > > > _______________________________________________ > Help-glpk mailing list > [email protected] > https://lists.gnu.org/mailman/listinfo/help-glpk > > -- Ioannis X. Tassopoulos
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