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I get the point is to show a problem solving technique, but I'm either missing something, or they are missing a constraint.

In several solutions, a nurse works shift 2 one day, then shift 0 the next. In fact, Nurse 3 keeps getting stuck with the back to back shifts.

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Are you referring to the first model? Only 5/5184 solutions are displayed. There's no objective function and the branching is probably defaulting to a simple systematic search with min domain, min value heuristic. If these are the first 5 solutions in the search tree, it's not surprising that nurse 3 keeps getting stuck with back to back shifts (does not work day 3)

They listed the constraint of no back-back shifts in the text but didn't implement it as a constraint.

By back to back, do you mean nurse 3 works shift 2 day 1 and shift 0 day 2? Or that nurse 3 always works two days in a row in the listed solutions?

The example doesn't mention back to back shifts, only that a nurse can at most work one shift a day which in turn implies the constraint that no nurse can work shifts back to back (in the same day).

One could easily add the constraint that a nurse scheduled on shift 2 cannot work shift 0 the next day.

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