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Shift scheduling/rostering is obviously very widely researched, with tons of papers around it. I found the review papers by Van den Bergh et al. [1] and Ernst et al. [2], but am looking for something that actually shows the various types of math models that have been used for this with the relevant extensions.

Could you please point me to the relevant books/book chapters/papers for this? Thanks!

[1] Van den Berg, J.; Beliën, J.; De Bruecker, P.; Demeulemeester, E.; De Boeckab, L. Personnel scheduling: A literature review. EJOR.

[2] Ernst, A. T.; Jiang, H.; Krishnamoorthy, M.; Sier, D. Staff scheduling and rostering: A review of applications, methods and models. EJOR.

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    $\begingroup$ If this is for research, I guess you could start with the latest formulations such as those proposed in Romer, 2021 and Lai et al, 2020 which outperform the previous formulations. $\endgroup$
    – rasul
    Sep 9, 2021 at 11:32

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For what it's worth, we've been gathering a bunch of Design Patterns in chapter 20 of OptaPlanner's User Guide. Here are some of the drawings:

enter image description here enter image description here

There's also a video that explains this deeper.

Besides these modeling basics, there are orthogonal features to consider (document in other places in the user guide):

  • Pinning: allow the user to lock in a shift assignment to an employee, before solving (so the solver has to work around it)
  • Continuous planning: every week publish the schedule 3 weeks in advance, don't paint yourself in a corner, ...
  • Non-disruptive replanning: making changes on a published schedule
  • Publishing, fairness constraints, rotation schedules, ...

A drawing of Continuous Planning with Rotation:

enter image description here

And there's a video to explain these advanced topics too.

These patterns are illustrated in 2 implementations:

that have been the basis for production deployments across the globe.

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  • $\begingroup$ Thanks Geoffrey, this looks very interesting. However, I was more looking for the mathematical formulation underlying the rostering. Do you have any material for that? $\endgroup$
    – Richard
    Sep 9, 2021 at 9:40
  • $\begingroup$ For fair distribution of shifts across employees, here's my blog post discussing different mathematical formula on quantifying the penalty. $\endgroup$
    – Geoffrey De Smet
    Sep 9, 2021 at 10:09
  • $\begingroup$ Beyond that, we don't accept constraints as mathematical equations, but as OO/FP code, so others - using more traditional solvers - will be able to help for you better with that. $\endgroup$
    – Geoffrey De Smet
    Sep 9, 2021 at 10:13

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