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MSCI 223 coursework 2019




Morecaster General Hospital has a busy Accident and Emergency (A&E) department (note: in some countries this is just called the Emergency Department). At the moment its performance is not considered satisfactory as patients often have to wait a long time in A&E. The schedule for the number of staff currently varies from day to day based on a variety of factors such as staff availability, holidays etc. The hospital is planning to recruit some extra staff but it does not know how many staff it needs.


The hospital would like to know how many staff it should have at different times of the day to achieve a good performance.


A&E department


The hospital have provided you with the following information about how the A&E department currently works:


Two categories of patient arrive at A&E: urgent and non-urgent. Patients receive various treatments and assessments in A&E and then leave. Leaving A&E is called “discharge”. The patient may leave A&E to various destinations – for example, they may go home, to another care provider (such as a care home), or to a ward in the hospital.


Patients arrive at random at the A&E department. The total number of patients arriving have been counted in three time intervals over several weeks. The average numbers for the time intervals are as follows:


Time interval



Midnight – 8 a.m.



8 a.m. – 4 p.m.



4 p.m. – midnight




For example, this means that on average 48 non-urgent patients and 1 urgent patient arrive between midnight and 8 a.m.


The urgent patients have serious injuries and usually arrive by ambulance. When they arrive they receive urgent care (such as resuscitation). This must happen immediately once they arrive. If necessary, doctors doing other tasks will stop what they are doing to provide the urgent care. The hospital only has facilities for providing urgent care to three patients simultaneously. If there are three patients receiving urgent care treatment and another urgent case occurs then the patient will be sent to a different hospital. The data for urgent care times has a mean of 60 minutes and a standard deviation of 20 minutes. A lognormal distribution is thought to be realistic for this data.


If a doctor stops doing a task to provide urgent care then that task may be complete by any doctor - i.e., another doctor can complete the original task.


After receiving urgent care, 60% of urgent patients leave the A&E department and are discharged (they usually go to a ward in the hospital). 40% of urgent patients receive further treatment in A&E. This treatment does not need to happen immediately but it does have priority over non-urgent patients. After the treatment these patients are then discharged (again usually to a hospital ward). Urgent patients receive at most one treatment activity in A&E. The data for these treatment times has a mean of 30 minutes and a standard deviation of 15 minutes. A lognormal distribution is also thought to be realistic for this data.


Non-urgent patients have a variety of conditions or injuries and are dealt with by a “triage” process. First the patients see the reception staff (1 person) and are registered (their name and personal details are recorded). The only information available for the time taken for this activity is estimates that the minimum is 1.5 minutes, the mode is 2.5 minutes, and the maximum is 5 minutes.


They then see a triage nurse who makes a preliminary assessment of the patient. The only information available for the time taken for this activity is estimates that the minimum is 3 minutes, the mode is 5 minutes, and the maximum is 10 minutes.


After seeing the triage nurse some patients are discharged. If they are not discharged the patient next sees a doctor for a more detailed assessment. After seeing the doctor some patients have to get specific treatment from a doctor in A&E (such as a medical procedure or a scan). The sequence of activities is that patients always alternately see the doctor and get treatment. Patients receive a maximum of two treatments and three doctor assessments in A&E. They may be discharged after any of these activities. The percentages are as follows:



% to next process

% discharged




1st doctor assessment



1st treatment



2nd doctor assessment



2nd treatment



3rd doctor assessment




The times for the doctor assessments are believed to follow a lognormal distribution. The times for the 1st assessment have mean of 15 minutes and a standard deviation of 4 minutes. The times for the 2nd assessment have a mean of 12 minutes and a standard deviation of 6 minutes. The times for the 3rd assessment also have a mean of 12 minutes and a standard deviation of 6 minutes.


The times for the treatments have not been analysed. However, a spreadsheet containing a sample of 100 treatment times is provided on Moodle with this document. It is believed that there is no difference in the distribution of times for 1st and 2nd treatments.


Staff work shifts of: midnight – 8 a.m., 8 a.m. – 4 p.m., 4 p.m. – midnight. The hospital can schedule any number of nurses and doctors to each shift. A nurse costs 0.6 of the cost of a doctor. The standard pay rate applies to the shift of 8 a.m. – 4 p.m. Doctors and nurses working on the shift from midnight – 8 a.m. receive extra pay and cost an additional 30%, those working on the shift from 4 p.m. – midnight cost an additional 20%.


The triage assessments are done by nurses. The doctor assessments and the treatments for urgent and non-urgent patients are all provided by doctors. Although there are different types and levels of doctor, at this stage the hospital would just like to know the total number of doctors required (i.e., assume that the doctors can carry out any assessments and treatments). Also assume that each assessment and treatment is provided by one doctor (i.e., doctors work alone).


The availability of space and facilities mean that there are maximum numbers for each process that can simultaneously take place at any one time. The maximum number of triage assessments is 5, the maximum number of doctor assessments is 6, the maximum number of non-urgent treatments is 6, the maximum number of urgent care is 3, the maximum number of urgent treatments is 3.


Patients wait between processes in the waiting area. There is plenty of space in this area.


The current government performance target is that 95% of patients should be discharged from A&E within 4 hours of arriving at A&E. The hospital aims to meet this target. It is possible in the future that 90% might be considered acceptable and the hospital would like to know what difference it would make if they use this target instead. The hospital would like to minimise staff costs whilst providing a good service. They are also interested in any other useful measures of performance although they are not sure what these might be.


Your task


The hospital know that you have expertise in simulation modelling and they would like you to build a simulation model of the A&E department and to use the model to provide advice on how they should run the department. Your report should include specific recommendations on what the hospital should do.


No other information is available at the moment and so you will need to base your analysis on the above description of the system. State any assumptions that you make about the system. You should build your own simulation model starting with the blank Witness Startup model.


The hospital may be able to obtain more information and data that could be used for further work on the model over the summer, although they are not sure what would be useful. Please include in your report an explanation of what further data would be helpful and how you would use it. The hospital are also interested in knowing about any limitations of the model and your analysis.


Simulation software


You must use the Witness simulation software for your model.




Each group is required to submit the following two items through Moodle. Only one person in the group needs to submit the files (do not submit the files several times under the different people in the group).


     A written group report as a Microsoft Word document describing the project. The maximum length of the report (excluding appendices) is 5000 words. You can assume that the reader of the report is familiar with simulation. Hence, you do not need to explain general simulation concepts or simulation terminology. You need to explain clearly how your model works and what you did for each of the simulation tasks. Credit can only be given based on what you put in the report and so allow enough time for writing the report. Some analysis can be included in an appendix but do not include many pages of model code or statistical output in the appendices without any explanation in the report.


     A Witness simulation model file containing a working version of your model.




Tuesday 7th May 2019, 5 p.m.


This is the submission deadline and any submission after this deadline is subject to standard departmental penalties, unless you have been given an extension for exceptional reasons. The extension must be granted by me before the deadline.