Transcript ISE491F09 Ozcan Chapter_15 Part 1 JMB Publish

Simulation in Healthcare
Ozcan: Chapter 15
ISE 491 Fall 2009
Dr. Burtner
Outline


Simulation Process
Monte Carlo Simulation Method




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Process
Empirical Distribution
Theoretical Distribution
Random Number Look Up
Performance Measures and Managerial
Decisions
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
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When Optimization is not an Option. . . SIMULATE
Simulation can be applied to a wide
range of problems in healthcare
management and operations.
In its simplest form, healthcare
managers can use simulation to
explore solutions with a model that
duplicates a real process, using a
what if approach.
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
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Why Use Simulation?
It enhances decision making by capturing a
situation that is too complicated to model
mathematically (e.g., queuing problems)
It can be simple to use and understand
It has a wide range of applications and situations
Simulation software such as ARENA can be used
to model relatively complex processes and
facilitate multiple what-if analyses
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
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Simulation Process
1. Define the problem and objectives
2. Develop the simulation model
3. Test the model to be sure it reflects the situation
being modeled
4. Develop one or more experiments
5. Run the simulation and evaluate the results
6. Repeat steps 4 and 5 until you are satisfied with the
results.
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
5
Simulation: Basic Demonstrations
The Ozcan text provides
simulation demonstrations
using a simple simulators
such as coin tosses and
random number generators.
Imagine a simple “simulator”
with two outcomes.
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ISE 491 Fall 2009
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Let’s use a coin toss. . .
. . . to simulate patients arrivals in public
health clinic.
If the coin is heads, we will assume that
one patient arrived in a determined time
period (assume 1 hour). If tails, assume no
arrivals.
We must also simulate service patterns.
Assume heads is two hours of service and
tails is 1 hour of service.
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
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Table 15.1 Simple Simulation Experiment for Public Clinic
Time
Coin toss
for arrival
Arriving
patient
1) 8:00 - 8:59
H
#1
2) 9:00 - 9:59
H
#2
3)10:00 -10:59
H
4)11:00 -11:59
Queue
Coin toss
for service
Physician
Departing
patient
H
#1
-
#2
T
#1
#1
#3
#3
T
#2
#2
T
-
-
-
#3
#3
5)12:00 -12:59
H
#4
H
#4
-
6) 1:00 - 1:59
H
#5
#5
H
#4
#4
7) 2:00 - 2:59
T
-
-
-
#5
-
8) 3:00 - 3:59
H
#6
#6
T
#5
#5
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
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Table 15.2 Summary Statistics for Public Clinic Experiment
Patient
Queue
wait time
Service
time
Total time
in system
#1
0
2
2
#2
1
1
2
#3
1
1
2
#4
0
2
2
#5
1
2
3
#6
1
1
2
Total
4
9
13
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
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Performance Measures
Number of Arrivals
Average number waiting
Avg. time in Queue
Service Utilization
Avg. Service Time
Avg. Time in System
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
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MONTE CARLO METHOD
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A probabilistic simulation
technique
Used only when a
process has a random
component
Must develop a
probability distribution
that reflects the random
component of the system
being studied
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
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Steps in the Monte Carlo Method
Step 1: Select an appropriate probability distribution
Step 2: Determine the correspondence between
distribution and random numbers
Step 3: Generate random numbers and run simulation
Step 4: Summarize the results and draw conclusions
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
12
Using an Empirical Distribution 1
If managers have no clue pointing to the type of probability
distribution to use, they may use an empirical distribution,
which can be built using the arrivals log at the clinic.
For example, out of 1000 observations, the following
frequencies, shown in table below, were obtained for arrivals
in a busy public health clinic.
Table 15.3 Patient Arrival Frequencies
Number
of arrivals Frequency
0
180
1
400
2
150
3
130
4
90
5 & more
50
Sum
1000
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
13
Using an Empirical Distribution 2
Table 15.4 Probability Distribution for Patient Arrivals
Number
Cumulative Corresponding
of arrivals Frequency Probability probability random numbers
0
180
.180
.180
1 to 180
1
400
.400
.580
181 to 580
2
150
.150
.730
581 to 730
3
130
.130
.860
731 to 860
4
90
.090
.950
861 to 950
5 & more
50
.050
1.00
951 to 000
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
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Using a Theoretical Distribution 1
In order to use theoretical distributions such as tge
Poisson, one must have an idea about the distributional
properties (the mean).
The expected mean of the Poisson distribution can be
estimated from the empirical distribution by summing the
products of each number of arrivals times its
corresponding probability (multiplication of number of
arrivals by probabilities).
In the public health clinic example, we get
λ = (0*.18)+(1*.40)+(2*.15)+(3*.13)+(4*.09)+(5*.05) = 1.7
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
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Using a Theoretical Distribution 2
Table 15.5 Cumulative Poisson Probabilities for λ=1.7
Arrivals
x
Cumulative
probability
Corresponding
random numbers
0
.183
1 to183
1
.493
184 to 493
2
.757
494 to 757
3
.907
758 to 907
4
.970
908 to 970
5 & more
1.00
970 to 000
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
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Using a Theoretical Distribution 3
Table 15.6 Cumulative Poisson Probabilities for
Patients
arrived
0
1
2
3
4 & more
Patients
served
0
1
2
3
4& more
Arrivals: λ=1.7
Cumulative
Corresponding
probability
random numbers
.183
1-183
.493
184-493
.757
494-757
.907
758-907
1.000
908 to 000
Service: μ =2.0
Cumulative
Corresponding
probability random numbers
.135
1 to135
.406
136 to 406
.677
407 to 677
.857
678 to 857
1.000
858 to 000
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
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Using a Theoretical Distribution 4
Table 15.7 Monte Carlo Simulation Experiment for Public Health Clinic
Time
1) 8:00 - 8:59
2) 9:00 - 9:59
3)10:00 -10:59
4)11:00 -11:59
5)12:00 -12:59
6) 1:00 - 1:59
7) 2:00 - 2:59
8) 3:00 - 3:59
Random
numbers
&
(arrivals)
616 (2)
862 (3)
56 (0)
583 (2)
908 (4)
848 (3)
38 (0)
536 (2)
Arriving
patients
#1,#2
#3,#4,#5
#6,#7
#8,#9,#10,#11
#12,#13,#14
#15,#16
Queue
Random numbers
&
(service)
Physician
Departing
Patients
764 (2)
180 (1)
903 (4+)
780 (3)
164 (1)
546 (2)
351 (1)
900 (4+)
#1,#2
#3
#4,#5
#6,#7
#8
#9,#10
#11
#12,#13,#14,#15,#16
#1,#2
#3
#4,#5
#6,#7
#8
#9,#10
#11
#12,#13,#14,#15,#16
#4,#5
#9,#10,#11
#11,#12,#13,#14
#12,#13,#14
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
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Using a Theoretical Distribution 5
Table 15.8 Summary Statistics for Public Clinic Monte Carlo Simulation Experiment
Patient
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
#11
#12
#13
#14
#15
#16
Total
Queue
wait time
0
0
0
1
1
0
0
0
1
1
2
2
2
2
0
0
12
Service
time
0.5
0.5
1.0
0.5
0.5
0.5
0.5
1.0
0.5
0.5
1.0
0.2
0.2
0.2
0.2
0.2
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Chapter 15: Quantitative Methods in Health Care Management
Total time
in system
0.5
0.5
1.0
1.5
1.5
0.5
0.5
1.0
1.5
1.5
3
2.2
2.2
2.2
0.2
0.2
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Dr. Burtner
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Performance Measures from Tables 15.7 and 15.8
Number of arrivals: There are total of 16 arrivals.
Average number waiting: Of those 16 arriving patients; in 12 instances
patients were counted as waiting during the 8 periods, so the average number
waiting is 12/16=.75 patients.
Average time in queue: The average wait time for all patients is the total
open hours, 12 hours ÷ 16 patients = .75 hours or 45 minutes.
Service utilization: For, in this case, utilization of physician services, the
physician was busy for all 8 periods, so the service utilization is 100%, 8 hours
out of the available 8: 8 ÷ 8 = 100%.
Average service time: The average service time is 30 minutes, calculated by
dividing the total service time into number of patients: 8 ÷ 16 =0.5 hours or 30
minutes.
Average time in system: From Table 15.8, the total time for all patients in the
system is 20 hours. The average time in the system is 1.25 hours or 1 hour 15
min., calculated by dividing 20 hours by the number of patients: 20÷16 = 1.25.
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
20
Advantages and Limitations of Simulation
Advantages
Limitations
 Used for problems difficult to  Does not produce
solve mathematically
an optimum
 Can experiment with system  Can require
behavior without
considerable effort
experimenting with the
to develop a
actual system
suitable model
Chapter 15: Quantitative Methods in Health Care Management
ISE 491 Fall 2009
Dr. Burtner
21