The simulation model is developed with the purpose of evaluating and comparing the policies produced with the MDP model. The simulation model is able to represent the NGS system, with more detail than the MDP model can. For example, samples can arrive one by one instead of in batches. Different performance measures for the policies are evaluated, to compare the MDP models with the simplified policies.Section 7.3.1describes the parameter settings for the simulation runs.Section 7.3.2gives the results of the simulation runs and the comparison between the policies.
7.3.1
Parameter selection
As described inChapter 6, the input parameters for the simulation model consist of the arrival distribu- tion for single DNA samples and the policy for processing the samples. The runtime of the simulation can also be seen as an input parameter.
The arrival distribution is taken fromTable 2.2. The simulation is run for a lot of different policies, which are the results from the MDP model ofSection 7.2. In addition to the policies obtained from the MDP, several simplified policies are simulated.
The running time of the simulation is set on 100 years. The sample generator of the simulation gen- erates samples according to the same random number stream every simulation. It is run for a long timespan to eliminate the effect of the starting value of the random number stream.
7.3.2
Results
The results of one simulation run consist of two documents with data. One document contains all information regarding single samples: the arrival date and the processing start and end time. This information is used to calculate the sojourn time and access time per sample and the means of these performance measures. The other document contains all information about the system: how many samples are put in a process per day and the queue size per day. With this information, the mean queue size is calculated, as well as the number of times a process is started and the percentage of started processes over all possible process starts. Several policies turn out to have the exact same simulation results. Duplicates are recorded inTable 7.7and ignored for the remainder of the research.
Table 7.7: Simulation duplicates Policy Simulation duplicates
8100 8101 4100 4102 0100 0101 8102 4103 0103 0120 8120 4120 2120 0130 8121 8122 0123 0133 8130 8131 8132 6132 6121 0121 0122 6130 2132 6131 2122 0132
The different policies are compared by five performance measures: the mean sojourn time of the sam- ples in days, the maximum sojourn time of the samples in days, the percentage of samples that has a sojourn time bigger than 12 days, the mean queue size and the percentage of started processes over the course of the simulation. The comparison is displayed inTable 7.8. The policies are grouped by similarity. First, a simplified policy is described, followed by the policies resulting from the MDP, that can be reduced to the simplified policy. For example, policy 8121 ofTable 7.5can be simplified the policy 16 16 0. Some policies have two simplified policies that seem a logical reduction. Then the policies will appear twice in the comparison table.
Table 7.8: Comparison of the simulation results Policy Mean s.t Max. s.t. Percentage
with s.t>12 Mean queue
Percentage of starts
All All All 9.845 19 5.63 6.548 61.14
All All 16 9.872 19 5.45 6.569 61.21 8100 9.866 19 5.46 6.567 61.03 All All 0 9.882 19 5.41 6.472 61.08 8102 9.883 19 5.41 6.475 61.10 All 0 0 10.500 19 15.45 9.804 47.32 16 All 16 10.364 20 16.16 8.204 44.98 6121 10.351 21 15.79 8.123 45.31 16 All 0 10.368 20 16.14 8.213 45.03 8122 10.359 21 30.66 8.151 45.32 2122 10.766 21 15.78 9.782 41.91 0132 10.351 21 15.79 8.123 45.31 16 16 16 10.509 22 18.00 9.341 38.05 8120 10.420 21 17.07 9.030 39.30 8130 10.906 23 31.27 11.015 34.45 6130 10.872 23 31.22 10.811 35.20 16 16 0 10.709 20 19.59 9.952 37.61 8131 10.913 23 31.06 11.028 34.38 8132 11.255 23 36.06 12.175 32.84 6131 10.881 23 31.03 10.846 35.13 8121 10.442 21 17.31 9.110 39.14 16 0 0 11.246 22 30.80 12.667 34.33 24 All 0 11.338 22 33.04 11.564 37.57 2122 10.766 21 30.66 9.782 41.91 24 16 16 11.505 23 35.38 12.798 32.07 8130 10.906 23 31.27 11.015 34.45 6130 10.872 23 31.22 10.811 35.20 24 16 0 11.568 23 36.57 12.923 31.84 8131 10.913 23 31.06 11.028 34.38 8132 11.255 23 36.06 12.175 32.84 6131 10.881 23 31.03 10.846 35.13 24 0 0 12.456 26 54.51 17.552 27.64 Page 35
The performance measures represent two different objectives. On the one hand is the throughput time of samples, represented by the mean sojourn time, the maximum sojourn time and the mean queue size. On the other hand is the costs of processing, represented by the percentage of starts.
A surprising result can be seen in the comparison of policy All All 0 and policy 8102. The simpli- fied policy performs just as good or better than policy 8102 on all performance measures. The other comparisons are more straightforward. The simplified policy performs better cost wise and worse con- sidering throughput time, or vice versa.
From the values of the maximum sojourn time can be concluded that every policy is usable in the diag- nostics laboratory. All the samples are finished well before their deadline of 42 days. It can also be seen that none of the policies can guarantee rush samples to meet their 14 day deadline. The performance that states the percentage of samples with a sojourn time of more than 12 days is used to evaluate this fact further. If the rush samples are done processing later than 12 days after their arrival, there is not enough time to interpret and write a report about the results. The best policy for including rush samples would be policy All All 0; the amount of samples that will be late is 5.41%.
The cost for processing are the highest for policy All All 16 and the lowest for policy 24 0 0, based on the percentage of starts. The policy 24 0 0 would be a good policy to consider if rush samples will not be incorporated into the NGS processes, since costs are low and the samples still easily meet their due date.
Chapter 8
Conclusion and recommendations
The goal of this research is to improve the scheduling tactics of the NGS processes in the diagnostics laboratory of the UMCG. Currently, a static schedule is used, where three processes can be executed in two weeks. Based on the amount of samples waiting to be processed, the technicians decide whether or not to start a process according to the schedule. There is no further aid for making the decision to start a process. This research aims to improve the scheduling tactics, by providing guidelines for when to start a certain process.
An attempt is made to solve the scheduling problem with the use of a Markov Decision Process model. Several simplifications are necessary to make the MDP model work. These simplifications include the use of a schedule and the arrivals of samples in batches. A Mixed Integer Linear Program is developed to produce the schedule, according to which the MDP operates. The MDP model produces processing policies for the NGS processes, according to the schedule. The MDP model can only evaluate batched arrivals, due to necessary simplifications. Therefore, a simulation model is developed to investigate the behaviour of the policies for single sample arrivals.
On the basis of the results, obtained inChapter 7, several conclusions can be drawn. Guided by the research questions ofSection 1.2,Section 8.1states the conclusions. The conclusions will be discussed inSection 8.2. Based on the conclusions and discussion, several recommendations are given to the diagnostics laboratory of the UMCG. These recommendations are discussed inSection 8.3.
8.1
Conclusions
The conclusions will be discussed by means of the research questions. First, the research question is repeated, than an answer to the question will be given.
1. What is the current situation of the NGS processes, the organizational characteristics and the throughput time of samples, at the diagnostics laboratory of the UCMG?
The diagnostics laboratory of the UMCG is currently using a static schedule to plan the NGS processes. The schedule is two weeks long and contains three processes. The technicians decide which processes to start, based on the size of the queue. Organisational characteristics of the NGS processes are described inChapter 2. An analysis of the current sojourn times, access times, queue sizes or number of starting processes has not been performed. Because the system with the static schedule has just been introduced, there is not enough data available for a reliable analysis. Historical data from before the introduction of the static schedule does not seem useful, since the situations are barely comparable. 2. What is the optimal way to organise the NGS processes, when minimizing the throughput time of
the samples?
If the diagnostics laboratory only wants to minimize the throughput time of the samples, they should use the simplified policy All All 0. This policy has the lowest sojourn times of all the evaluated policies.
3. What is the optimal way to organise the NGS processes, when mainly considering the costs of processing and the occupation of the resources?
If the diagnostics department mainly wants to minimize the costs, they should use the simplified policy 24 0 0. This policy has the least amount of processes starting, minimizing the processing costs.
4. Is it possible to incorporate the testing of Rush samples into the NGS processes?
Rush samples cannot be guaranteed to meet their deadline, using the scheduling tactics developed in this research. Since all the evaluated policies have a maximum sojourn time of at least 19 days, it can not be guaranteed that the rush samples have a test result before their due date.
However, it is possible to incorporate the rush samples. When policy All All 0 is used, only about 5.5% of the rush samples will be to late. Rush samples with an extended due date of 21 or 28 days will be guaranteed to be on time.
Having answered all the subquestions of this research, it is time to review the main research ques- tion:
What is the optimal way to organize the NGS processes, weighing the throughput time of DNA samples and the costs for the laboratory, using the current available resources?
As can be concluded from the answers on the subquestions, the optimal way to organise the NGS processes depends on the chosen performance criterion. If the laboratory wishes to incorporate rush samples in the NGS processes, it is best to use the policy All All 0. This policy does not guarantee that all rush samples will manage to have a result before their due date, but it is the policy where the most rush samples will. If the laboratory decides not to incorporate the rush samples into the NGS processes, they can focus more on minimizing the costs. Then, the policy 24 0 0 would be a good fit. This policy still has a result for every sample well before their due date, but also starts significantly less processes, minimizing the processing costs.