The Doctor Rostering Problem - Asser Fahrenholz

Chapter 4. Solving the DRP 18
4.3.1 A construction heuristic
The initial solution is the basis for optimisation and as such, is an important part of any
heuristic modelled to solve this problem. One goal of a construction heuristic is often
to be fast as to allow time to be focused on other parts of the process. In the context of
this DRP, several construction heuristics can be identified:
Zero solution is a straightforward and easy solution to construct and consists of noth-
ing but an empty schedule. This is a very fast (O(1)) solution to generate but is
infeasible (over all shifts) due to constraint H4 on page 10.
Random solution consists of randomly assigning doctors to shifts that are unassigned,
until all shifts are assigned a doctor. This can be done by assigning each shift a
random doctor, or, for each doctor, assigning that doctor to approximately n
m
random shifts. The random solution does not guarantee feasibility and is worse,
in running time (O(n)), than the zero solution.
Greedy solution is based on the concept of choosing what looks best, given a candi-
date set and a selection function, here and now. That is, it bases its choice upon
knowledge of the present and past shifts, but not the future ones as they have not
yet been assigned a doctor. It makes no reconsideration of past choices, contrary
to e.g. dynamic programming algorithms, that bases decisions on all previous de-
cisions and as such, may reconsider the past. Several notions of the candidate set
are used in the literature, but in the context of this project, I define the Local
Candidate List as a list unique to each shift consisting of all doctors, ordered by
their heuristic value when assigning them to the given shift. The greedy algorithm
picks the best doctor from the candidate list and assigns it to the shift at hand.
The basic version of the greedy is deterministic, i.e. given the same input, greedy
always returns the same output. In an adaptive greedy algorithm (Resende and
Ribeiro [20]), the doctor is randomly chosen from the local candidate list. To rule
out the possibility of choosing the worst doctor for the shift, I introduce the Re-
stricted Candidate List as the n best, measured by either a heuristic value or by a
percentage, elements in the candidate list. Figure 4.2 on the next page illustrates
various kinds of RCL parameters for a minimisation problem. Another option for
the RCL list, is to define it as a list of ordered pairs, consisting of all unassigned
shifts coupled with the doctor that has the highest heuristic value when assigned to
the specific shift. This option was discarded due to the time required to construct
the list being O(n · m) and the fact that the list would have to be reconstructed
for each shift. The greedy solution does not guarantee feasible solutions, though
the odds has improved vastly, from that of the random solution.