The Doctor Rostering Problem - Asser Fahrenholz

Chapter 8. Future considerations 54
Combined, these three elements relate two sets of shifts to each other through a
comparator. The end user specifies the end point through r1 and r2, that are the
offset of days and the offset of shifts. I.e. equation H0 would be modelled by the
comparator = and the offset 0 and 1 respectively. As we move on to implement
other rules, a more specific representation of the subset i and j is needed. Several
subset could be premade and ready for the end user to choose from, e.g. holidays,
weekdays, Mondays, . . . Fridays, and likewise for the shifts.
Type 2 describes demands on certain shifts. A default demand could be specified by
the user, such that only shifts that deferred from this default demand would need
to be specified. These would consist of the following elements:
1. the point p(i, j) on which to specify the demand
2. the demand of doctors
Type 3 is for dividing the assignments of shifts equally. This would simply be hard-
coded and be available for the user to enable or disable.
For all types, the user should be able to specify whether the rule is a hard or soft
constraint.
8.2 Neighborhood delta function and feasibility
The most time consuming task of the heuristics is the calculation of a new objective func-
tion value when exploring a given neighborhood (and feasibility of said neighborhood).
To reduce the time spent on finding the new objective function value, a delta function
can be implemented, allowing the calculation of only the changes a neighborhood brings,
as opposed to the total objective function value.
We note again, that selection of the shifts for a new neighbor is, as described in section
4.3.2, random. Random selection of shifts to rotate or invert also means infeasible
solutions explored in the Local Search. As mentioned earlier, due to how constrained the
problem is, we allow infeasibility. Hence, the heuristics not only seek global optimum of
solution value, but also minimisation of the number of violated shifts. This means, that
it is not enough to check the objective function value when exploring a neighborhood,
but also check the hard constraints (for feasibility).
A delta function is generally a function calculating the value of a change. This means
that we need the value of the old (shift,doctor)-assignments (of the shifts that are affected
by the neighborhood). To do this, it is required, that for each (shift,doctor)-assignment