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

I solved a shift assignment problem for a large manufacturing plant recently. First we tried generating purely random schedules and returning any one which passed the is_schedule_valid test - the fallback algorithm. This was, of course, slow and indeterminate.

Next we tried genetic algorithms (as you suggested), but couldn't find a good fitness function that closed on any viable solution (because the smallest change can make the entire schedule RIGHT or WRONG - no points for almost).

Finally we chose the following method (which worked great!):

1. Randomize the input set (i.e. jobs, shift, staff, etc.).
2. Create a valid tuple and add it to your tentative schedule.
3. If not valid tuple can be created, rollback (and increment) the last tuple added.
4. Pass the partial schedule to a function that tests could_schedule_be_valid, that is, could this schedule be valid if the remaining tuples were filled in a possible way
5. If !could_schedule_be_valid, simply rollback (and increment) the tuple added in (2).
6. If schedule_is_complete, return schedule
7. Goto (2)

You incrementally build a partial shift this way. The benefit is that some tests for valid schedule can easily be done in Step 2 (pre-tests), and others must remain in Step 5 (post-tests).

Good luck. We wasted days trying the first two algorithms, but got the recommended algorithm generating valid schedules instantly in under 5 hours of development.

Also, we supported pre-fixing and post-fixing of assignments that the algorithm would respect. You simply don't randomize those slots in Step 1. You'll find that the solutions doesn't have to be anywhere near optimal. Our solution is O(N*M) at a minimum but executes in PHP(!) in less than half a second for an entire manufacturing plant. The beauty is in ruling out bad schedules quickly using a good could_schedule_be_valid test.

The people that are used to doing it manually don't care if it takes an hour - they just know they don't have to do it manually any more.