Intro DES-Capacity

Introduction into Discrete Event
Simulation Methodology (DES):
The Use of DES for Capacity Analysis
and Planning
Alexander Kolker
Data Scientist

2
OUTLINE
• Examples:
•Capacity of hospital surgical services
•Smoothing elective scheduled surgeries
•The concept of simulation and its use in healthcare services
with random patient volumes and random service time
•Demonstrating manually a simple discrete event simulation
model: step-by-step
•Reviewing components of simulation modeling
•Demonstrating simulation models for capacity analysis and
planning in healthcare settings with variable patient volumes
Alexander Kolker. All rights reserved

Alexander Kolker. All rights reserved 3
SIMULATE!
• In general, simulation is a process of studying a complex
system using its mathematical representation (a model), e.g.
• Flight simulator-the aircraft response to the cockpit input
controls
• Nuclear plant operators simulators-reactor output response to the
various operator inputs
• Surgical and physiology procedures simulators on mannequins
•Simulation is a methodology of choice for situations that are
too complex, or dangerous, or not suitable for performing
actual multiple physical manipulations
•Our focus here is simulation of healthcare business
operations

Some Typical Business Healthcare Questions to get
Answered:
• How many nurses are needed in an inpatient unit in
order to provide required patient coverage?
• Is another CT scanner needed to radiology service
in order to reduce wait time?
• How many beds are needed to staff at different
times of the day or days of the week?
• What additional resources (nurses, beds, etc.), if
any, are needed to decrease the rate of ‘left without
being seen’ in the ED?

(cont.)
• How many phlebotomists are needed to guarantee
acceptable waiting times for blood draw?
• How many beds or staff should be budgeted for?
and so on…..
• Key Point:
There is no way to answer any of the above (or
similar) business questions without analytic
quantitative analysis based on simulation
modeling.
Everything else would be just guessing.

Basic types of business simulation:
• System Dynamics (SD)- operates mostly with macro-level
patient volumes and flows, and large-scale patient categories.
Most appropriate for analyzing the large-scale nationwide
healthcare systems, and the implications of the different
policies implementation.
• Discrete Event Simulation (DES)- operates mostly with
individual patients and their attributes.
Most appropriate for analyzing business operations of separate
hospitals and clinics.
• Agent-Based Simulation (ABS)- operates mostly with the
actions and interactions of autonomous entities. Includes emerging
rules of behavior that did not exist in the original model design.
Most appropriate for analyzing an effect of emerging individual
behavior on the system response as a whole.

(cont.)
• All three methodologies can be merged if it is
warranted by the problem to be solved
• However, the most powerful and versatile
simulation methodology used for Healthcare
business analytics is Discrete Event Simulation

Discrete Event Simulation (DES) Methodology.
What is it, and how does a simple DES model work?
•A discrete event simulation (DES) model of a
system/process is a computer model that mimics the
dynamic behavior of the system/process as it evolves
over time in order to quantitatively analyze its
performance, i.e. getting system output as response
on the various multiple random inputs.

(cont.)
•DES models track patients (documents, work-pieces)
moving through the distinct steps of the system
(called events) at distinct (discrete) points of time
•Therefore, it is called Discrete Events
•The detailed track is recorded for all processing times
and waiting times. Then the system’s output statistics
is gathered for the various inputs values.

•The validated and verified model is then
used to study response of the
system/process to input variables in order to
identify the ways for its improvement
(scenarios) based on some improvement
criteria

11
So, how can it help us?
Waiting Line Service
System
Customers
arrivals
Let’s look at an example.
How can we simulate the random patient arrivals
and service system response, e.g. wait time and
queue size?
arrivals Queue (Waiting Line) Service Exit

Inter-arrival time,
min
Service time,
min
2.6 1.4
2.2 8.8
1.4 9.1
2.4 1.8
Suppose that we measured the actual time
between patient arrivals and the service time

Let’s start at the time, t=0, with no patients in the system.
We will be tracking any change (event) that happened in the system.
A summary of what is happening in the system looks like this:
Event
#
Time Event that happened in the system
1 2.6 1-st customer arrives. Service starts that should end at
time = 4 (2.6+1.4)
2 4 Service ends. Server waits for patient.
3 4.8
(2.6+2.2)
2-nd patient arrives. Service starts that should end at time
= 13.6 (4.8+8.8). Server idles 0.8 minutes.
4 6.2
(4.8+1.4)
3-rd patient arrives. Joins the queue waiting for service.
5 8.6
(6.2+2.4)
4-th patient arrives. Joins the queue waiting for service.
6 13.6 2-nd patient’s (from event 3) service ends. 3-rd patient
at the head of the queue (1-st in, 1-st out) starts service
that should end at time 22.7 (13.6+9.1).
7 22.7 4-th patient starts service…and so on.

• These simple but tedious logical and numerical event-
tracking operations (algorithm) are suitable, of course,
only for a computer operations
• However, they illustrate the basic principles of a typical
discrete event simulation model, in which discrete events
(changes) in the system are tracked when they occur over
the time
In this particular example, we were tracking events at discrete
points in time t=2.6, 4.0, 4.8, 6.2, 8.6, 13.6, 22.7 min
What is next?....

• Once the simulation is completed for any length of
time, the system’s output statistics is calculated,
such as:
• the average patient and server waiting time
• the number of patients in the queue
• the confidence intervals
• any other custom process statistics/ information

In this example, only 2 patients out of 4 waited in
the queue.
Patient 3 waited 13.6-6.2=7.4 min and patient 4
waited 22.7-8.6=14.1 min, so the simple average
waiting time for all four patients is
(0+0+7.4+14.1)/4=5.4 min.
Notice, however, that the first two patients did not
wait at all while patient 4 waited 2.6 times longer
than the average.

Similarly, the average number of waiting patients (the
average queue size) is 0.5 (2 waiting patients out of 4).
Key Points:
•DES models are capable of tracking thousands of
individual entities arriving randomly or in a complex
pattern
• Each entity has its own unique attributes, enabling
one to simulate the most complex systems with
interacting events and component interdependencies.

Typical DES applications include:
•staff and production scheduling
•capacity planning
•cycle time and cost reduction
•throughput capability
• resources and activities utilization
•bottleneck finding and analysis
• DES is the most powerful tool to perform quantitative ‘what-
if’ analysis and play different scenarios of the process
behavior as its parameters change with time
• This simulation capability allows one to make experiments
on the computer, and to test different options before going to
the hospital floor for actual implementation.

The basic elements (building blocks) of a simulation model:
•Flow chart of the process, i.e. a diagram that depicts logical
flow of a process from its inception to its completion
•Entities, i.e. items to be processed, e.g. patients, documents,
customers, etc.
•Activities, i.e. tasks performed on entities, e.g. medical
procedures, exams, customer check-in, etc
•Resources, i.e. agents used to perform activities and move
entities, e.g. service personnel, equipment, nurses, physicians
•Entity routings that define directions and logical conditions
flow for entities

Typical information (data) usually required to populate the
model includes:
• Arrival pattern and quantities, e.g. periodic,
random, scheduled, daily pattern, etc.
• The time that the entities spend in the activities, i.e.
service time.
This is usually not a fixed time but a statistical distribution.
• Capacity of each activity, i.e. the max number of entities
that can be processed concurrently in the activity
•The maximum size of input and output queues for the
activities
•Resource assignments: their quantity and scheduled shifts

Example 1: Process Simulation Methodology to Plan for the Facility
Renovation of the Surgical Suite at the Children’s Hospital of
Wisconsin (CHW)

Step 1: Problem Description:
• Children’s Hospital of Wisconsin believes that it has maximized the
capacity of its current operating rooms and special procedure rooms.
• Surgical services are spread in the facility requiring a majority of
patients to arrive to one floor for preoperative preparation and then
transport to another floor for their surgical procedure.
• As a result, the CHW is in the planning stages for a major facility
renovation of its surgical suite to increase capacity, patient, physician
and staff satisfaction, and efficiency of surgical services.
• The expansion will also allow for the streamlining of patient flow
both in preoperative services and within the operating room areas.

Step 2. Questions to be answered using simulation (DES)
• Is the designed number of general and specialized operating
rooms and prep/post operative beds adequate to meet the
projected patient flow and volume increases through 2013?
• If the design does not meet the need, how many operating
rooms and/or prep/post operative beds would be needed?
• Ensure that the renovation cost is under control and
maintain a high level of quality and satisfaction standards

Step 3. System performance criteria
• Patient delay to be admitted to a pre-operative surgical bed should
not exceed 15 minutes.
• Delay to enter operating room from a pre-operative surgical bed
should not exceed the following:
 General OR – 2 hours
 Urgent OR – 3 hours
 Cardiovascular OR – 5 hours
 Neurosurgery OR – 3 hours
 Orthopedic OR – 2 hours
 Cardiac Cath Lab – 2 hours
• Percent of patients waiting longer than the acceptable delay to enter
operating room from a pre-operative surgical bed should not exceed
5%.
• Delay to enter post anesthesia care beds (PACU) from an operating
room should not exceed 5 minutes.

Step 4. Model design: simulation scenarios to be analyzed.
• Scenario 1: Baseline operations - all surgical services function as
currently specified between two floors, but move 2 general operating
rooms onto 4-th floor to serve otolaryngology (OTO),
gastroenterology (GI), and pulmonary (PUL) patients volumes from
the 3-rd floor.
• Scenario 2: Move GI, OTO and PUL patient volume from the 4-th floor
to a separate service area into the outside Surgical Service Center.
• Scenario 3: Move GI and PUL patient volume into the separate
service area. OTO moved to 4-th floor.
Total annual patient volume included in the simulation models is in
the range from 15,000 to 18,500 for the annual projected patient
volume increase from 2009 to 2013.

Decision variables are:
•The number of pre-operative beds and PACU (Post-
Anesthesia Care Unit) beds
• The number of general and specialized Operating
Rooms, as well as special procedure rooms (SPR)
and
• Their allocation for surgical services.

3-rd floor 4-th floor
Layout of the simulation model-flow map

Example of Input Data File (total 18,520 records)
Action Logic
W
eek
W
eekday
Time
Quantity
Service =GEN Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 8:34 AM 1
Service =GEN Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 10:07 AM 1
Service =NEURO Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 10:30 AM 1
Service =GEN Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 12:50 PM 1
Service =ORTHO Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 1:28 PM 1
Service =ORTHO Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 3:12 PM 1
Service =OTO Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 3:12 PM 1
Service =ORTHO Status=OP Surgery=not_done PICU=No Surg_Type=Elec 1 Tue 7:30 AM 1
Service =OTO Status=OP Surgery=not_done PICU=No Surg_Type=Elec 1 Tue 7:31 AM 1
Service =CV_Surg Status=InP Surgery=not_done PICU=No Surg_Type=Elec 1 Tue 7:50 AM 1
Service =CATH Status=SS Surgery=not_done PICU=No Surg_Type=Elec 1 Tue 7:52 AM 1
Service =GEN Status=OP Surgery=not_done PICU=Y Surg_Type=Other 1 Tue 8:02 AM 1
Service =GEN Status=IA Surgery=not_done PICU=No Surg_Type=Elec 1 Tue 8:05 AM 1
Service =ORTHO Status=InP Surgery=not_done PICU=Y Surg_Type=Trauma 1 Tue 8:06 AM 1
Service =ORTHO Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Tue 8:13 AM 1
Service =UROL Status=OP Surgery=not_done PICU=No Surg_Type=Elec 1 Tue 8:55 AM 1
Service =HEMA Status=OP Surgery=not_done PICU=Y Surg_Type=Other 1 Tue 9:05 AM 1
Patient attributes
Arrival pattern

SIMULATION OUTPUT
• Based on simulation of these scenarios, it is recommended:
• use scenario 3 as the most feasible to meet
performance criteria
• re-allocate the number of beds:
-make 10 Prep beds on the 3-rd floor (instead of 8)
and
-25 prep/post beds on the 4-th floor (instead of 31)
The number of OR:
3-rd floor:
-12 ORs (5 general, 2 CV, 1 Neuro, 2 Ortho, 2 Urgent) and 1 Cath Lab
4-th floor:
- 2 procedure ORs (SPR) and 2 general ORs (total 4 interchangeable OR)

A Big Picture: Interdependency of Hospital Departments and Hospital-
Wide Patient Flows (Kolker, A., Chapter 2, Patient Flow, 2-nd Ed, Springer, 2013)
Emergency
random
Scheduled-smoothed

Example 2: Smoothing of Scheduled Elective
Procedures
Step 1: Problem Description
• In most hospitals, random (emergency) surgeries compete for
the same operating rooms (OR) resources with scheduled
(elective) surgeries.
• While the variable number of daily emergency surgeries is
beyond hospital control (natural random variability), there
is a significant variation in the number of daily scheduled
elective surgical cases (artificial non-random variability)

• A daily load leveling of elective cases would reduce the
chances of excessive peak demand for the system’s capacity
(operating rooms and ICU) and, consequently, would reduce
patient waiting time.
• In 2011 The Leapfrog Group Hospital Survey included in the
new section Patient Experience of Care the use of smoothing
elective patient scheduling.
The Leapfrog Bibliography: Smoothing Patient Scheduling

Step 2: Question to be answered using
simulation modeling (DES)
What is a quantitative effect of the daily
load leveling (smoothing) of elective
surgeries on wait for surgical and post-
surgical procedures in the presence of the
competing demand for OR resources from
random emergency surgeries?

Step 3. Model design.
It is required to develop two simulation models:
(i) baseline model that uses current elective and emergency
admission schedules (mixed patient arrival pattern) to
calculate the delay for emergency and scheduled patients;
(ii) model with load-leveled (smoothed) elective schedule and
the same emergency admissions to calculate the delay for
emergency and scheduled patients.
A comparison of the difference in the delay helps to make a
conclusion.

It was assumed that 3 interchangeable operating
rooms (OR) are available in this case.
The emergency surgery duration is in the range
from
1.5 to 2.5 hours, with this most likely time of 2.1
hours.
Elective surgeries duration is in the range from
1.5 to 3 hours, with the most likely time of 2.4
hours.

36
Elective, emergency and daily load leveled admissions for the 4-week period
Week Day of week Number of
elective
admissions
Number of
emergency
admissions
Number of daily-
leveled (smoothed)
elective admissions
1 Monday 9 16 6
1 Tuesday 11 14 7
1 Wednesday 8 14 7
1 Thursday 5 20 7
1 Friday 5 15 7
2 Monday 10 18 7
2 Tuesday 13 20 7
2 Wednesday 11 9 7
2 Thursday 8 11 7
2 Friday 3 20 7
3 Monday 5 17 7
3 Tuesday 9 11 7
3 Wednesday 8 15 7
3 Thursday 6 15 7
3 Friday 6 20 7
4 Monday 7 15 7
4 Tuesday 4 13 7
4 Wednesday 3 12 7
4 Thursday 4 11 7
4 Friday 3 20 6
Total 138 306 138
Input Data.
CHW, June,
2009

Wk #
Wk #
Ideal Smoothed elective
schedule

Simulation Output:
• The original un-smoothed elective schedule along with
competing emergency cases resulted in the average patient
waiting time:
0.74 hours for emergency cases (99% CI is 0.73 – 0.76 hours) and
1.2 hours for elective cases (99% CI is 1.19 - 1.24 hours).
• The smoothed (load-leveled) elective schedule along with the
same competing emergency cases resulted in the average
patient waiting time
0.58 hours for emergency (99% CI is 0.57 – 0.6 hours) and
0.82 hours for elective cases (99% CI is 0.8 – 0.84 hours).
• Thus, in this example, elective daily smoothing results in about
21% reduction in waiting time for emergency surgeries and
about 32% reduction in waiting time for elective cases.

Take-away:
Elective schedule smoothing (daily load-
leveling) is indeed a very powerful approach of
reducing patient waiting time and improving
efficiency.

• A simple simulation model also allows testing an effect of
the different smoothing schemes.
• For example, if nearly the same daily number of elective
cases is not possible due to some practical limitations, it is
possible to test another less perfect smoothing scheme to
make sure that the end result is still worth the effort of its
implementation (or maybe not) .
• No traditional management methods are capable of
providing such insights for decision-making.

41
The Power of Simulation Modeling
• Used for studying behavior of the complex
systems/processes with random components
• Provides a framework for experimenting with
system behavior without experimenting with the
actual system
• Compresses time for new improved system design
• Valuable tool for training decision-makers

Intro DES-Capacity

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