The Doctor Rostering Problem - Asser Fahrenholz
The Doctor Rostering Problem - Asser Fahrenholz
The Doctor Rostering Problem - Asser Fahrenholz
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Chapter 3. <strong>The</strong> model and design 11<br />
⎧<br />
⎪⎨ 1 if rule o is violated on<br />
yiko =<br />
⎪⎩<br />
0<br />
day i for doctor k<br />
otherwise<br />
⎧<br />
⎪⎨ 1 if rule 3 is violated on day i<br />
yijk3 =<br />
⎪⎩<br />
0<br />
shift j for doctor k<br />
otherwise<br />
⎧<br />
⎪⎨ 1 if the LHS of rule o is zero,<br />
tiko =<br />
⎪⎩<br />
0<br />
allows yiko to remain zero too<br />
otherwise<br />
⎧<br />
⎪⎨ 1 if the LHS of rule 3 is zero,<br />
tijk3 =<br />
⎪⎩<br />
0<br />
allows yijk3 to remain zero too<br />
otherwise<br />
<strong>The</strong> y-variables are used as counting variables, indicating how many violations of a soft<br />
constraint the doctor has. <strong>The</strong> t-variables are used for the specific case of the left hand<br />
side of the equation is zero. This variable, and the fact that we are dealing with a<br />
minimisation problem, allows the y-variable to remain zero.<br />
<strong>The</strong> following are the soft constraints that apply when constructing a model for the<br />
DRP:<br />
B0 No doctor should have both the Monday noon shift and the following Friday afternoon<br />
shift in the same week:<br />
min δB0<br />
<br />
i<br />
yik0<br />
<br />
∀ k<br />
st. xi2k + x (i+4)3k = 1 + yik0 − tik0<br />
∀ k, i ∈ M<br />
(B0)<br />
B1 No doctor should have both the Friday afternoon shift and the following Monday<br />
noon shift:<br />
min δB1<br />
<br />
i<br />
yik1<br />
<br />
∀ k<br />
st. xi3k + x (i+3)2k = 1 + yik1 − tik1<br />
∀ k, i ∈ F ∧ i < n − 3<br />
(B1)