The Doctor Rostering Problem - Asser Fahrenholz

Chapter 5. Optimal solution 32
The GAMS report, included in appendix B.2, reports that the objective function value
Z(S) = 2 and that the solution is optimal.
Both the greedy algorithm and GRASP are tested with and without the partial enumer-
ation described in section 4.4.2, and RCL equal to 1 (only the best element), 50 (list size
is cut in half) and 100 (list size is unchanged). Three tests are done and the results are
shown in figure 5.1 on the following page, where Z(S) and V (S) indicate the objective
function value and the number of hard constraints that are violated, respectively.
The results indicate that the enumeration makes a difference and that the solutions found
are near-optimal, when using the enumeration. Specifically we can see that the greedy
construction (with enumeration and RCL = 1 finds optimal solution, figure 5.1(a) on
the next page) are superior to grasp (both with and without enumeration, for RCL = 1).
This indicates that the construction heuristic is the dominant factor of performance for
GRASP. Further investigation of this is found in chapter 7. Over all instances and RCL-
parameters, GRASP (w. enumeration) is superior, as it, at worst, finds solution with
V (S) = 1 (see figure 5.1(a) on the following page).
The assigning of a day results in near-optimal to optimal objective function values. As
such, it is a valuable observation that, for this test-instance, further enumeration, such
as assigning a whole week of shifts at the same time, is not needed. In this conclusion,
I recognise the importance of testing GAMS with other instances of the problem. It is
unfortunate that there was not time to do so.
The best greedy solution and the best GRASP solution respectively, can be seen in
appendix B.3 together with the solution found by GAMS. There are, as suspected,
similarities amongst the solutions. This indicates that the solution space is locked to a
certain degree.