The Doctor Rostering Problem - Asser Fahrenholz

Chapter 5
Optimal solution
This chapter provides a comparison of solutions to the DRP provided by GAMS, the
adaptive greedy algorithm and the GRASP metaheuristic described in section 4.3 re-
spectively. Testing of SA has been left to chapter 7. Only a subproblem comparison is
done due to the complexity of the problem and therein the explosion in time required
by GAMS to reach a solution.
The model implemented in GAMS is the mathematical model described in chapter 3. In
this model, a binary variable for every day, shift and doctor exists. It could potentially
be done with positive variables equal to the id of the doctor assigned to each shift, but
then the problem of assigning two doctors to a shift arises.
5.1 Comparison
To properly measure how good the solutions found through the heuristics described in
chapter 4 are, we need to compare them to some solution, whose bounds we can prove.
That is, find an optimal solution and measure the heuristic value of that particular
solution to the heuristic value of schedules found through the heuristics. This will give
an indication of how far from optimum the heuristics are.
Due to the explosion of time when increasing the problem, the length of the schedule
given to GAMS has been reduced to 4 weeks. The GAMS-model included in the GAMS-
report in appendix B.2 includes the night shifts, evening shifts and wishes in appendix
B.1. The subproblem modelled in GAMS is relaxed due to the fact that the RDO
constraint is not included for these four weeks. Should time have allowed, GAMS testing
of several datasets including more and less constrained problems would have been of
higher priority.
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