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Shift scheduling: Does it have to be np hard?

mankowitz asked
Last Modified: 2008-04-24
What is a good way to schedule shifts for various workers? For example, suppose I have 5 workers and 60 consecutive shifts to fill (each is a 12 hour shift in a 30 day month). I would like to have several constraints, such as certain workers will want certain days off. A person can not work two adjacent shifts (24 hours in a row). A person should not work more than 5 days in a row.

Now, one way to do this is compute all the possibilities for the 60 shifts and rank the schedules by goodness of fit. The only problem is that I would have to generate 5^60 schedules (=8.67361738 × 10^41) in order to make sure I've checked everything. Even if it took only 1ms to check each scheduke, the age of the universe is nothing compared to how long this will take. Is there any way to shorten this?
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There are many techniques, domain pruning, heuristics and so on to solve NP-hard problems, its all part of Constraint Logic Programming (CLP). If you don't want to program everything from scratch, you can use some CLP system (like ECLiPSe: http://eclipse.crosscoreop.com/index.html).

There you usually define your problem as set of variables (shifts in your case), their domains (workers) and constraints that must be met (consecutive shifts must not be done by the same worker, Joe doesn't work on Sundays, etc.).

Then you press the button and let the magic happen :-). Of course the success depends on size of the problem (it is still NP-hard) and suggesting good heuristics to the system also helps. On the above mentioned page are also examples, maybe JobShop (http://eclipse.crosscoreop.com/examples/jobshop.html) fits your problem.

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