The Doctor Rostering Problem - Asser Fahrenholz

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Chapter 7. Tests, results and discussion 45 Imported shifts From table 7.3 on the previous page, we can see that test instance 5 with Cons = 18 has an average metaheuristic output of (251,20), which then decreases, over the results of e.g. test instance 2 with (164,12), to test instance 9 with (4,2). It clearly does make the problem harder when we add night shifts, evening shifts and wishes. It would have been interesting to investigate what amount of these shifts, for each doctor, that is needed, before feasibility cannot be guaranteed. Unfortunately, there was not time to do so. Amount of doctors When comparing test 0 (196,14), 2 (164,12), 3 (258,18) and 6 (109,6), we see the same results as we did for the effect of varying amounts of imported shifts. There is then the problematic result of test 7, which actually comes out with the highest average V(S) out of the four (246,22). This could be due to the instance containing some periods of time that are over constrained, such that no amount of optimisation could solve that period to feasibility. It is peculiar that test 2 and 6 produces the results that they do considering that the cons of test 6 is higher than that of test 2. I propose that the length of the schedule is also a factor in how hard the problem is to solve. Schedule length When the length of the schedule varies, we see an immediate effect on the numbers in table 7.3 on the preceding page. Test 4 (349,32) , 6 (109,6) and 7 (246,22) varies the most in length and also varies greatly in average values. With test instance 4 being the longest, the test also produces the worst results, contrary to test 6 that actually has a higher Cons but produces far better results. I conclude that the length of the schedule has great effect on the average results of tests. This is actually not unexpected, as the implementation of the neighborhoods is such, that the transformation is done on a random set of shifts. When the length of the schedule increases, the ”length” between the shifts that are invalidating constraints also increase. Had there been implemented a form of guiding mechanism for the neighborhood transformation, targeting the transformations at shifts that are invalidating one or more constraints, I suspect the results would have been different from what we see here.
Chapter 7. Tests, results and discussion 46 7.2.2 Metaheuristic parameter effects In this section I will discuss the effects of changing the metaheuristic parameters. In the tables presented in this section, the average results of SA is the results of giving SA the output from GRASP. As such, there are a much higher number of SA runs than there is GRASP. The RCL parameter The RCL parameter is fundamental to GRASP and allows the metaheuristic to ran- domise the construction of the initial solution in each iteration. Imps Z(S) V(S) GRASP 1 17,1875 3,5625 25,9375 GRASP 100 14,625 392,75 19,3125 GRASP 50 13,5 5,625 21,125 Table 7.4: RCL effect: Test 0 Imps Z(S) V(S) GRASP 1 19,625 5 32 GRASP 100 15,3125 363,6875 27,875 GRASP 50 13,625 6,125 27,5 Table 7.5: RCL effect: Test 1 Table 7.4 shows how, against suspecion, a more random RCL parameter, GRASP 100 (393,19) actually results in a lower V(S). It does come with a cost, namely the high Z(S). In this case, I suspect that a more balanced result, such as for the GRASP 50 (6,21), would be more preferable to the medical practice. The same goes for test 1, where GRASP 100 (364,28) produces a lower V(S) than GRASP 1 (5,32). This is, also described earlier, a key observation, which is not that far from what Resende and Feo [19] says. A fully greedy RCL may produce good mean values, but when we increase the randomisation, we may produce better results. The conclusion that a fully greedy RCL parameter is not optimal is supported by test 8 and 9, shown in table 7.7 and 7.6 respectively. In these tables we see an obvious reduction in V(S) when going from fully greedy to fully random RCL parameter, even on test 9 where there are no night shifts, evening shifts or wishes. Imps Z(S) V(S) GRASP 1 7,6875 3,375 8,125 GRASP 100 8,75 7,5 1 GRASP 50 6,0625 2,875 3,375 Table 7.6: RCL effect: Test 9 Imps Z(S) V(S) GRASP 1 15,5 4,9375 19 GRASP 100 11,0625 185,0625 9,625 GRASP 50 14,625 4,625 14,9375 Table 7.7: RCL effect: Test 8 Over all tests, the average values of the solutions grouped by RCL parameters are shown in table 7.8 on the following page. In this table we can see that the average value of Z(S) increases significantly when the metaheuristic manage to decrease V(S).
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TECHNICAL UNIVERSITY OF DENMARK The
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TECHNICAL UNIVERSITY OF DENMARK Abs
Page 5 and 6: Acknowledgements Foremost, I would
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Appendix C. Tests 96 JST PZH HP SDA
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Appendix C. Tests 98 C.1.8 Instance
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Appendix C. Tests 100 Cons 12 Imps
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Appendix C. Tests 102 Test 3 RCL 1
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Appendix C. Tests 116 160 140 120 1
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Bibliography 118 [10] Michael R. Ga
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