Project2Fall2023New
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441
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Date
Dec 6, 2023
Type
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3
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ISE441 Fall, 2023
Project 2: FirstTreatment, Inc. Staffing
Deliverable 1 (Approximation) Due: Tuesday, Nov. 21st, 2023
Deliverable 2 (Model) Due: Tuesday, Nov. 28th, 2023
Deliverable 3 (Report) Due:
Friday
, Dec. 8th, 2023
FirstTreatment, Inc. plans to open for-profit healthcare clinics throughout the United States Your job is to
help FirstTreatment estimate the costs to operate such facilities for different patient loads, which will be
part of their business plan. The primary continuing cost for a health care clinic is staffing, which will be
the focus of your analysis. There are requirements for providing timely treatment, but having more staff
and equipment than needed makes a facility expensive to operate.
The CEO wants “
optimal staffing
.”
FirstTreatment's facility design consists of five stations: (i) Sign-In/Triage station; (ii) Registration;
(iii) Examination; (iv) Trauma; and (v) Treatment. Each of these are staffed separately.
All patients enter at Sign-in/Triage, where a staff member quickly assesses their condition. Patients with
severe injuries or illness are sent directly to Trauma; once their condition is stabilized they move to
Treatment; then they are discharged or transported to a hospital.
Patients with less severe problems proceed from Sign-In/Triage to Registration, and then to Examination
for evaluation. After the evaluation, roughly 40% are immediately discharged; the others go to Treatment
before they are discharged.
The following distributions to represent patient contact time have been estimated by a different team:
•
Sign-in/Triage: Exponential with mean 3 minutes
•
Registration: Rayleigh with mean 5 minutes
•
Examination: Normal with mean 16 minutes and variance 3 minutes
2
•
Trauma: Exponential with mean 90 minutes
•
Treatment:
o
For trauma patients, Rayleigh with mean 30 minutes
o
For non-trauma patients, Rayleigh with mean 13.3 minutes
Patient arrivals will be modeled as a Poisson arrival process, and the movement of patients between
stations is so brief that it can be treated as a constant 1 minute (even though there is some variability).
Staffing levels at each station will clearly depend on patient load, percentage of trauma patients, and the
patient service-level requirements. FirstTreatment has asked you to look at a range of options for trauma
load (these are distinct scenarios, not random quantities). The percentage of trauma patients depends
very much on where the healthcare facility is located; it could be as low as 8% or has high as 12% of all
patients. Patient load obviously varies by city, but for this project we will look at a medium-sized city
where they expect 450 patients per day, on average. FirstTreatment clinics will be open 24 hours per day,
and for the purpose of planning FirstTreatment is willing to consider long-run average performance with
a constant patient load of 450/24-hour day.
FirstTreatment
’s
standards for the waiting time at each station are the following:
Station
Sign-In
Registration
Examination
Trauma
Treatment
Ave Wait (min)
6
10
15
2
15
FirstTreatment wants you to deliver the optimal staff level for two scenarios: 8% trauma patients and 12%
trauma patients. By “optimal” they mean
the minimum staffing needed to hit these targets as closely as
possible. It has been suggested that this could be achieved by minimizing the deviations from each target.
One way to do this is to minimize the
absolute value of the deviation from the target
for each station.
instance, for the Examination station this statistic is
|AveWait@Exam − 15|
There is a similar term for each station, and the overall objective function is to minimize the long-run
average of the sum of these deviations.
Once the optimal staffing level is determined for each scenario (8% and 12%), FirstTreatment would like
to know what the actual average waiting time at trauma and treatment will be, and which service
distributions
are the most “critical.”
Deliverable 1
: Develop a queueing model of FirstTreatment at the 12% trauma patient level. Approximate
the
minimum number of staff needed at each station just to keep up
. These will be the lower bounds for
your decision variables in the optimization.
Deliverable 2:
Build your Simio model at the minimum staffing level for the 12% trauma scenario.
Implement the absolute difference performance measure. Make effective use of common random
numbers. Run 25 replications of 72 hours each.
Note that the Rayleigh distribution is not built into Simio so you will have to implement it. The Rayleigh
distribution has cumulative distribution function
𝐹(𝑥) = 1 − 𝑒
−𝑥
2
/(2𝜎
2
)
, 𝑥 > 0
with a single parameter
𝜎
2
that you need to fit. It will help you to know that the
mean
of the Rayleigh
distribution is
√𝜋𝜎
2
/2
.
For input modeling, you need to find the value of
𝜎
2
for each station using the
information you have about the mean value.
The Wikipedia page for the Rayleigh distribution is quite good
if you need more help. Include in Deliverable 2 a write-up that explains how you got your Rayleigh
parameters, and how you implemented the distribution in Simio.
Deliverable 3:
We will treat this as a steady-state simulation. Determine a warm-up period at the 12%
trauma patients and minimum staff level using
total time in the system for patients
as your response.
Include the mean plot in your results section, along with a brief explanation of how you determined the
warm-up period in your experiment design section.
Change the Simio icons into something more intuitive (and appropriate) for the situation. There will be a
prize for the best animation.
Optimize staff at both the 8% and 12% trauma levels using sound optimization methods, and document
how you did it. Answer all questions raised by FirstTreatment in your report. Your audience is the analytics
group, which is very technical but does not know much about simulation. They would also like your
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