Hi All,
I am fairly new to glpk and linear programming. I am working on a
scheduling problem, and have been facing some problems in the
specification of one of its constraints.
The variables in my problem are binary, encoding the schedule for a
given series of jobs. In my problem I have a total of *n* time slots
that can be used to schedule certain jobs: If I was considering a total
of three jobs I would have three sets of variables - xA, xB and xC, all
of dimension *n* -, and for a given index *i* (1 <= i <= n) if xA[i] = 1
then job A would be scheduled for time slot *i*.
My problem is related to the fact that, while some jobs only require one
time slot to complete; others may require multiple, consecutive time
slots. Imagine that a given job - job B, for example - requires 2 time
slots. I know that xB must only take the value "1" in 2 consecutive time
slots, taking the value "0" in the remaining (n-2) slots. But how can I
write this as a problem constraint?
I have tried to make use of the *exists* keyword but as far as I can
understand I cannot use it in constraints in linear problems... An
obvious constraint that comes to mind is to make the sum of xB for all
*i *be equal to 2 (sum{i in 1..n} xB[i] = 2), but this only restricts
the total number of assigned slots and does not make them consecutive.
Any suggestions/comments are very welcome.
Best regards,
Joaquim
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