Models for Global Constraint Applications - Cork Constraint ...

constraint [33] and a pattern constraint [39] are used instead of the among and
sequence constraints of CHIP. They both have somewhat different expressive
power and use, but can express typical rules occurring in rostering.
4.2.4 Objective
There is no clearly defined objective that should be optimised in rostering problems.
In most cases, users look for feasible solutions, or even infeasible solutions
which minimise constraint violations. There are two balancing rules which may
play the role of objectives: one is to balance any excess capacity in an even
way over time and between shifts, the other is to treat people evenly, so that
all persons obtain the same workload, expressed in shift (types) to be worked,
weekend assignment, or assignments over public holidays.
4.3 Additional Constraints
So far we have described the core constraints encountered in the nurse rostering
problem, but there are many more constraints that can be added.
4.3.1 Preferences
The rostering system produces a plan for a period of four weeks into the future
and in principle may assign any nurse to any of the shifts in that planning
horizon. Often, persons have strong preferences for working particular shifts
or for not working at certain times. It is trivial to take a small number of
preferences into account by forcing an assignment or removing values from the
domain of a variable. The problem is that taking all preferences together will
nearly always lead to an infeasible problem.
One approach to solve this issue is to use hierarchical constraint programming
as presented in [34], where the solver tries to minimise the number of
constraint violations.
A disadvantage of this approach is that the global constraints have to be
extended to handle constraint violations. In a limited way this has been attempted
in the sequence constraint of CHIP, with additional indicator variables
to indicate where violations occur. These variables can then be used in new
constraints for example to balance the violations evenly through the schedule.
Another approach is to treat preferences as heuristic choices which are tried
in the search process. This is very easy to program, but it is quite difficult to
balance preference treatment for all nurses in the roster.
A third approach is an interactive constraint solving process, where a user
enters choices via a user interface and sees what effect this choice has. This
was proposed in [74], but relies on very strong constraint propagation to be
workable. As soon as an infeasible constraint is added, this must be detected,
giving the user the choice how to restore a feasible constraint set.
4.3.2 Qualifications
A rather common extension is to consider different qualifications of nurses and
demands on each type of qualification for each shift. If the qualifications partition
the set of nurses, then the problem can be trivially decomposed and each
subproblem solved independently. If qualifications overlap, then the model may
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