The Doctor Rostering Problem - Asser Fahrenholz

Chapter 9
Conclusion
This master thesis presents the reader with a solution to a real world doctor rostering
problem, covering the scheduling of a number of doctors over a period of time with
respect to a range of criteria that ensures satisfied work members.
The problem, set down by a roster planning doctor, has been compared to that of
standard nurse scheduling problems and has been found too small, due to problem size,
shift types, and a range of very peculiar constraints, for the solution to be of any real
value in NSP research beyond that of entry level planning. The research presented in this
thesis may be of more value in the area of the Gotlieb class-teacher problem research.
A mathematical model of the hard and soft constraints is described and an objective
function describing the value of solutions is presented along with an estimation on the
size of the problem.
The problem is proven to be NP-complete and on this basis, solving the problem with
heuristics are chosen over exact methods, which would require exponential time to finish.
For these heuristics, various initial solutions are discussed and a greedy approach is se-
lected. Once a solution generation has been established, two simple neighborhoods, the
rotation and inversion, of the solutions and exploration of these through local search is
described. GRASP, a metaheuristic framework is then discussed along with possible ex-
tensions and the Simulated Annealing algorithm used for optimising already constructed
solutions is presented. After the methods for solving the problem has been described,
the steps taken to implement these methods has been described.
The solutions found by the heuristics are then compared to a solution found by an
optimal solver (GAMS). Due to problem size and complexity, only a subproblem of a
given dataset is tested. It is found that GAMS is able to solve the problem to optimality
as is the heuristics.
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