I am currently working on a scheduling system which schedules individuals based on timeslots that have the following attributes: (1) Day of Week (2) Month (3) Session(AM/PM).

The individuals currently indicate their preference for whether they prefer the AM/PM session for each day of the week in each month eg. (Monday|Jan|AM), this would mean that the person would prefer to do AM session for Mondays of January. Furthermore they are allowed to indicate that they do not want to be scheduled for certain months of the year, eg. he's able to choose that he does not want to do February time slots and thus my system is required to schedule him accordingly. [Complexity]

As such I currently am required to schedule this large set of data (individuals - 30 people / timeslots - 202). [Large Set]

I have been referred to by some advisors to look into Integer linear programming / linear programming in order to help me schedule these individuals optimally, thus I am currently looking into libraries such as Gurobi to help optimise the solution of this issue. I hope to be enlightened about the following question:

Would solution optimisers such as Gurobi be implementable in my scenario?

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    $\begingroup$ If you have an LP problem, then yes, Gurobi is a solver for LP problems. Are you asking about modeling your problem, or are you asking what Gurobi is capable of? $\endgroup$ – Juho Jan 28 '15 at 17:18
  • $\begingroup$ Thanks for replying me! Im currently trying to model the problem too at the same time but i wanted to ask if it's even implementable to solve the problem before i model it. $\endgroup$ – SEET WEI ZHONG BRANDON SEET Jan 28 '15 at 17:51
  • $\begingroup$ Now that i know it's implementable im actually struggling with modelling the problem into the objective function and its constraints $\endgroup$ – SEET WEI ZHONG BRANDON SEET Jan 28 '15 at 17:51

Yes, your program can be modelled as an integer linear programming (ILP) instance, and yes, Gurobi is an ILP solver and can be used to solve your problem once you express it as ILP. I suggest you spend some quality time with a textbook that describes linear programming and integer linear programming.

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