Help solving a scheduling optimisation problem

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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