
From:  Joaquim Leitão 
Subject:  [Helpglpk] Help solving a scheduling optimisation problem 
Date:  Thu, 12 Jul 2018 22:34:04 +0100 
Useragent:  Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Thunderbird/52.8.0 
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 (n2) 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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