The Doctor Rostering Problem - Asser Fahrenholz

Chapter 3. The model and design 9
⎧
1 if on day i, doctor k has a shift
⎪⎨
j outside the house. It follows that
bijk =
the doctor is not available for the surrounding shifts
⎪⎩ 0 otherwise
⎧
⎪⎨
sij =
⎪⎩
⎧
1 if on day i, doctor k has
⎪⎨
requested shift j off. The doctor is then
cijk =
available for the surrounding shifts
⎪⎩ 0 otherwise
l if on day i, shift j must be assigned 1+l
doctors. This happens on noonshifts following weekends and
holidays, and afternoonshifts preceding holidays
0 otherwise
The index j defines: 1: Night shift, 2: Noon shift, 3: Afternoon shift, 4: Evening shift.
Furthermore, shift j is said to be an assignment shift (as) if it doesn’t lie on a holiday,
nor a weekend and is not a night- nor evening shift.
Let n be the number of days in the problem, and m be the number of doctors:
i ={1, 2 . . . n}
k ={1, 2 . . . m}
In the following, I assume the schedule starts on a Monday, that the index of this day
is 1 and that the schedule ends on a Sunday and the index of this day is n.
I also define the sets of days:
3.2 Hard constraints
M : i%7 = 1 ∀i
F : i%7 = 5 ∀i
This section describes the constraints that must be satisfied for the solution to be feasible: