Which algorithm for assigning shifts (discrete optimization problem)

Question

I\'m developing an application that optimally assigns shifts to nurses in a hospital. I believe this is a linear programming problem with discrete variables, and therefore p

Answer 1

Metaheuristics did very well at the International Nurse Rostering Competition 2010.

For an implementation, see this video with a continuous nurse rostering (java).

Answer 2

One thing you can do is to try to look for symmetries in the problem. E.g. can you treat all nurses as equivalent for the purposes of the problem? If so, then you only need to consider nurses in some arbitrary order -- you can avoid considering solutions such that any nurse i is scheduled before any nurse j where i > j. (You did say that individual nurses have preferred shift times, which contradicts this example, although perhaps that's a less important goal?)

Answer 3

This is a difficult problem to solve well. There has been many academic papers on this subject particularly in the Operations Research field - see for example nurse rostering papers 2007-2008 or just google "nurse rostering operations research". The complexity also depends on aspects such as: how many days to solve; what type of "requests" can the nurse's make; is the roster "cyclic"; is it a long term plan or does it need to handle short term rostering "repair" such as sickness and swaps etc etc.

The algorithm you describe is a heuristic approach. You may find you can tweak it to work well for one particular instance of the problem but as soon as "something" is changed it may not work so well (e.g. local optima, poor convergence).

However, such an approach may be adequate depending your particular business needs - e.g. how important is it to get the optimal solution, is the problem outline you describe expected to stay the same, what is the potential savings (money and resources), how important is the nurse's perception of the quality of their rosters, what is the budget for this work etc.