MIE 360: Systems Modelling and Simulation (Fall 2023):
Project Assignment
• Due by Wednesday December 6th.
• Your submission must include a report in PDF format and a Simio (SPFX) file. The
report (including figures and tables) must not be longer than 12 pages but can include
an appendix with no page limit.
• You must use the attached template (either in Word or Latex) for the project report.
• The project may be done in groups of 2-3 students. All team members need to sign and
submit the attribution table (see last page of the template).
• Include at the top of your report the names and student numbers of all team members.
• You may use R / Excel / Python for the input modelling part of the project.
• If you submit the complete Simio file for your model by November 29th, your group will
receive a 5% bonus on the final project mark. You may revise the Simio file for the final
submission.
1 Background
Long waiting times for access to care is a major area of concern for many Canadian hospi-
tals. In this project, you will use simulation to study the performance of various operational
strategies aimed at reducing waiting times at a large Canadian hospital.
The hospital operates a busy Emergency Department (ED) and has a large inpatient
department. A large proportion of the patients visiting the ED are admitted into the inpatient
wards of the hospital, which will be the primary focus of this project. During the admission
process, if there are no available beds in the hospital for a patient, he/she will have to wait
in the ED until a bed becomes available. Currently, the hospital is experiencing long waiting
times (referred to as boarding times). It could take many hours until a bed becomes available.
This not only affects the health outcome of the patients, it also increases the duration of their
stay in he hospital which further contributes to the congestion at the hospital.
2 Description of the Operations and Data
Requests for inpatient beds from the ED arrive randomly in time (see Section 3 for details and
data). Before being admitted to the inpatient department, patients are classified into 9 medical
specialties based on the diagnosis performed in the ED: Surgery, Cardiology, Orthopedic,
Oncology, General Medicine, Neurology, Renal Disease, Respiratory, and Gastroenterology-
Endocrine. The proportion of patients belonging to each of the 9 medical specialties is provided
in Table 1.
Table 1: Patient distribution based on medical diagnosis.
Category
Surg Card Gen Med Ortho Gastro-Endo Onco Neuro Renal Respi
Proportion 22% 18% 16% 14% 8% 7% 6% 5% 4%
The inpatient department consists of 12 wards each having a fixed number of beds and
suited for treating specific patient specialties. Eligibility of the ward for each specialty and
the bed capacities are provided in Table 2. If a patient qualifies for multiple wards, they are
assigned to the one with the greatest number of free beds. If the number of free beds is equal,
they are admitted to the ward with the shortest queue. If queues are equal, one of the eligible
wards are chosen at random with equal probability.
After a patient is assigned to a ward, if there is available capacity in that ward, the patient
is immediately boarded and the treatment starts. Otherwise they wait in the ED until a bed
becomes available in the particular ward they are assigned to. Once a patient is admitted,
his/her Length of Stay (amount of time they spend in the hospital and occupy a bed) depends
on how long the treatment takes as well as some other operational factors. The treatment
time (time of admission until treatment is completed) is subject to uncertainty; see Section 3
for details.
When the treatment of a patient is completed, he/she remains in the bed until a physi-
cian approves the discharge. The approval process takes 30 minutes (with little variability),
however, physicians only approve discharges during a certain period of time during the day.
Currently, discharge approvals are made from 3PM to 5PM and by 5 physicians separately for
each ward. If a discharge approval process is in progress at 5PM, the physician will complete
the process.
Upon approving a patient’s discharge, the patient leaves the bed but before the bed can
be assigned to the next patient, it needs to be cleaned. The cleaning process takes a variable
amount of time depending on the type of cleaning required. Time-stamps are not collected
for cleaning times but based on expert opinion we can assume a Triangular(30,45,60) provides
2
Table 2: Eligibility of the wards for treating patients of different specialty groups and the bed
capacities.
Ward ID Specialities # of Beds
1 Gen Med 58
2 Neuro 14
3 Renal 27
4 Neuro 6
5 Gastro-Endo 26
6 Surg 34
7 Card 24
8 Ortho 70
9 Onco 35
10 Respi 14
11 Surg, Card 24
12 Surg, Card 24
a reasonable distribution for the cleaning times (in minutes). There are enough cleaners
available almost all the time, so you can assume there is ample cleaner capacity available.
3 Deliverables
3.1 Input Modelling
• Bed request count data from the ED is provided in ArrivalData.xlsx for different hours
of the day and over 100 days. Use this data to estimate an appropriate model of bed
request arrivals.
• Treatment times for the patients from each medical specialty follow a different distribu-
tion. The treatment time data collected for Card, Renal, Respi, Ortho and Gastro-Endo
specialties are provided in TreatmentTimes.csv. Use the data to fit appropriate distri-
butions for treatment times. For the remaining specialties, the decision support group
at the hospital has already provided you with the distributions which you can find in
Table 3 and use in your model. The unit of time is days.
Remark: When entering distribution parameters in Simio, make sure they are consistent
with the parameter specification required by the software. For example, for the Exponential
distribution Simio asks for the mean value (and not the rate). Also, for the Log-normal
distribution, you are expected to provide mean and standard deviation of the underlying Normal
3
Table 3: Treatment time distributions (in days) for patients of different medical specialty
groups.
Service Times
Specialty Distribution Parameters
Surg Exponential λ = 0.4237
Gen Med Lognormal µ = 0.921, σ = 0.949
Onco Gamma shape = 0.612, scale = 9.689
Neuro Lognormal µ = 0.53, σ = 1.133
distribution. For the Gamma distribution, Simio requires you to define the distribution with
either (shape, scale) or (shape, rate) depending on where you are defining the distribution.
3.2 Base Model
Develop a simulation model of the operations of the inpatient wards as described above in
Simio.
• Provide a clear description of the logic of the model, specifically how you have modeled
(1) the limited availability of physicians for completing the discharge process, and (2)
the post-treatment cleaning process before the bed can become available for the next
patient.
• Use the model to provide an estimate (including a 95% confidence interval) of the fol-
lowing performance measures of the system. Present the results in a table. Provide a
clear explanation of the design of experiments (how you select the warm up and number
of replications) to obtain the estimates in your report.
– Long-run average waiting times and queue lengths for each of the 12 inpatient
wards.
– Long-run average bed utilization for each ward.
– Long-run average waiting time of patients whose bed request arrives between 9AM-
12PM. Report the total wait as well as separately for each specialty group.
– Long-run fraction of Oncology patients whose waiting time exceeds 5 hours.
4
3.3 Scenario Analysis
3.3.1 Scenario Comparison: Comparing Two Alternatives
• The hospital management is considering allowing Oncology patients to be routed to
Ward 8 (in addition toWard 9) following the same rule as described on Page 2 for patients
qualifying for multiple wards. Because Ward 8 is specialized for treating Orthopedic
patients, it is expected that Oncology patients treated in this ward will experience a 5%
increase in their treatment time. Use your model to estimate the impact of the suggested
change on the performance of the system and with respect to the relevant performance
measured estimated above. Would you recommend this change?
3.3.2 Reducing the Waiting Times: Comparing Multiple Alternatives
• Currently, physicians are available to approve discharges between 3PM to 5PM. The
hospital would like to keep the length of the discharge approval period equal to 2 hours,
but is open to changing the time period as long as the same time period is used for all
wards. Use your model to find the optimal discharge approval period that minimizes the
total long-run average waiting time of patients for inpatient beds. Explain and justify
the method used for comparing multiple scenarios in your report.
4 Suggested Timeline
Milestone Completion Date Related topics
Read this document and
plan group meetings and activities
November 3 –
Complete input modelling November 17
Input Modelling and Estimation,
Modelling Arrival Processes
Complete base model November 27
Labs 1-3
Output analysis
Complete scenario analysis
and finalize report
December 6
Labs 4-5
Comparing alternative systems
Simulation optimization