The Doctor Rostering Problem - Asser Fahrenholz

Chapter 4. Solving the DRP 19
(a) RCL: 50% elements
(rounded
down)
(b) RCL: 5 elements
(c) RCL: Value
below 5.0
Figure 4.2: Various types of RCL parameters
(d) RCL: Value
below 60 % of the
worst
The various construction heuristics all bring advantages and disadvantages. These are
outlined in table 4.1.
Feasible Construction Evaluation
Zero solution No O(1) O(1)
Random solution Perhaps O(n) O(n)
Greedy solution Perhaps O(n · m) O(n)
Table 4.1: The initial solutions
Out of the described heuristics, the adaptive greedy algorithm is chosen as the con-
struction heuristic of this project, along with the RCL parameter type shown in figure
4.2(a). This type of RCL parameter ensures that a certain degree of randomisation can
be achieved, contrary to the RCL parameter shown in figure 4.2(b), where an absolute
size is chosen (this can not ensure a certain degree of randomisation when the size of
the RCL varies).
The adaptive greedy algorithm is outlined in algorithm 4.1.
Algorithm 4.1 Adaptive greedy - require: RCL parameter p, schedule S
for all Unassigned Shift in S do
RCList = {}
for all Doctors do
RCList ← RCList ∪ V alueOf(Doctor, Shift)
end for
Sort(RCList)
Restrict RCList according to p
Pick a doctor randomly from RCList and assign it to Shift
end for