1. Construct a queueing model that replicates a week of collecting and processing DNA samples. a. First develop a flow diagram of how the process works, from the reporting of a crime, to the eventual match/no match on the DNA database. b. Identify any conditional aspects of the process, for example if there are any stages of the process where resources only become available once the previous sample has been processed. c. Second, write out the relevant equations associated with each step of the process, and construct a formula for the overall time in system. d. Use relevant notation and write out equations using Equation Editor in Word. e. Note – the rule of thumb is that any reader can pick up your report and replicate your results by following the methods. 2. Use mean values of each parameter to construct an “average” solution. a. Unit of interest – a DNA sample collected by a CSI. That is, each sample must be modelled individually. b. Assume both CSI and forensics lab operations work 24/7. c. Model precisely ONE WEEK of sampling – any samples that are have not been completely processed by one week are not included in your analysis. d. The unit of time to use in the model is minutes. e. There is one Rapid DNA sequencer, which is only run once all eight spaces in the cartridge are filled with samples. f. You MUST use Excel to model the process. g. You MUST create, develop and save all your work in one file saved on your OneDrive account. There are no exceptions to this. See Saving and Sharing instructions on pages 10-12. 3. Results to find from your “average” model solution: a. To the nearest ten, how many samples will be processed by the end of the seven days? How many of those samples will result in a DNA match? b. What is the mean time to process a sample? c. What percentage of samples meet the police force’s ambition to process samples in less than one day? d. Is there any stage of the process that looks under-resourced? Why? Construct a queueing model that replicates a week of collecting and processing DNA samples. a. First develop a flow diagram of how the process works, from the reporting of a crime, to the eventual match/no match on the DNA database. b. Identify any conditional aspects of the process, for example if there are any stages of the process where resources only become available once the previous sample has been processed. c. Second, write out the relevant equations associated with each step of the process, and construct a formula for the overall time in system. d. Use relevant notation and write out equations using Equation Editor in Word. e. Note – the rule of thumb is that any reader can pick up your report and replicate your results by following the methods. 2. Use mean values of each parameter to construct an “average” solution. a. Unit of interest – a DNA sample collected by a CSI. That is, each sample must be modelled individually. b. Assume both CSI and forensics lab operations work 24/7. c. Model precisely ONE WEEK of sampling – any samples that are have not been completely processed by one week are not included in your analysis. d. The unit of time to use in the model is minutes. e. There is one Rapid DNA sequencer, which is only run once all eight spaces in the cartridge are filled with samples. f. You MUST use Excel to model the process. g. You MUST create, develop and save all your work in one file saved on your OneDrive account. There are no exceptions to this. See Saving and Sharing instructions on pages 10-12. 3. Results to find from your “average” model solution: a. To the nearest ten, how many samples will be processed by the end of the seven days? How many of those samples will result in a DNA match? b. What is the mean time to process a sample? c. What percentage of samples meet the police force’s ambition to process samples in less than one day? d. Is there any stage of the process that looks under-resourced? Why? 7 4. Construct a simulation model using the information provided to you above, and your average model as the starting point. a. Unit of interest – a DNA sample collected by a CSI. That is, each sample must be modelled individually. b. Each iteration of the simulation is one week of processing samples. c. Use the same assumptions as for the Task 2 model. d. You MUST use @RISK. Do NOT save raw simulation data in the file. e. You must save all your work in one file saved on your OneDrive account. There are no exceptions to this. See Saving and Sharing instructions on pages 10-12. f. You will need to determine the appropriate probability distribution for each input. g. Run the model for 10,000 iterations. h. Set the random number seed to the customer id. 4. Results to find for the simulation model: a. Present all time units in minutes. b. Summarise* the distribution for the mean time a sample waits in the queue for the: CSI to arrive; for sample preparation; for DNA sequencing; and finally for validation. c. Comment on any observations/insights from the queueing time distributions you have plotted and summarised in Task 4a. d. Summarise* the distribution for the mean number of samples processed, and the mean number of samples matched to the DNA database, in one week. e. Plot and summarise the distribution for the mean time to process a sample. f. Plot and summarise the distribution for the percentage of samples that are processed in under 24 hours (each iteration being one week of sampling). g. How confident are we that at least half of all samples in one week will be processed in 24 hours or less? h. Conduct an appropriate Sensitivity Analysis that shows the main influence on the time it takes a sample to be processed. i. Conduct any other relevant, ad-hoc analyses that you think will yield useful insights to help reduce the time to process samples further. 5. What-if Scenario modelling a. Taking your further analyses from Tasks 4f and 4g as the basis for improving the model, construct 2-3 plausible scenarios that will improve the confidence that at least half of all samples from one week are processed in 24 hours or less. b. Modify at least two stages of the model (these must be reasonably unique – do not copy scenarios from others). c. Rerun simulation model with the same random number seed and compare results to that produced in Task 4. d. By plotting and comparing relevant probability distributions, explain how your modified scenario has reduced the time taken to process samples, and how it has impacted the likelihood of processing samples in under one day. 6. Insights and recommendations a. In your report, provide a short summary of your insights and recommendations for how to improve the Rapid DNA process that was trialled over the past few months. *Appropriate metrics to summarise a distribution are either mean(5th percentile;95th percentile) or median(5th percentile;95th percentile), depending on the skewness of the distribution.