simulation in healthcare ozcan: chapter 15 ise 491 fall 2009 dr. burtner
DESCRIPTION
When Optimization is not an Option... Chapter 15: Quantitative Methods in Health Care ManagementISE 491 Fall 2009 Dr. Burtner 3 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.TRANSCRIPT
Simulation in Healthcare
Ozcan: Chapter 15
ISE 491 Fall 2009Dr. Burtner
Outline
Simulation Process Monte Carlo Simulation Method
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 2
When Optimization is not an Option. . .
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 3
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.
Why Use Simulation?
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 4
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
Simulation Process
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 5
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 6
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.
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 7
. . . 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.
Let’s use a coin toss. . .
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 8
Table 15.1 Simple Simulation Experiment for Public Clinic
Time Coin tossfor arrival
Arrivingpatient
Queue Coin tossfor service
Physician Departingpatient
1) 8:00 - 8:59 H #1 H #1 -
2) 9:00 - 9:59 H #2 #2 T #1 #1
3)10:00 -10:59 H #3 #3 T #2 #2
4)11:00 -11:59 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 9
Table 15.2 Summary Statistics for Public Clinic Experiment
Patient Queuewait time
Servicetime
Total timein 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 10
Number of Arrivals
Average number waiting
Avg. time in Queue
Service Utilization
Avg. Service Time
Avg. Time in System
Performance Measures
MONTE CARLO METHOD
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 11
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 12
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
Steps in the Monte Carlo Method
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 13
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.
Using an Empirical Distribution 1
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 14
Table 15.4 Probability Distribution for Patient Arrivals
Number of arrivals
Frequency
Probability
Cumulative probability
Corresponding 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
Using an Empirical Distribution 2
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 15
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
Using a Theoretical Distribution 1
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 16
Table 15.5 Cumulative Poisson Probabilities for λ=1.7
Arrivalsx
Cumulativeprobability
Correspondingrandom 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
Using a Theoretical Distribution 2
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 17
Table 15.6 Cumulative Poisson Probabilities for
Arrivals: λ=1.7 Patients arrived
Cumulative probability
Corresponding random numbers
0 .183 1-183 1 .493 184-493 2 .757 494-757 3 .907 758-907
4 & more 1.000 908 to 000
Service: μ =2.0 Patients served
Cumulative probability
Corresponding random numbers
0 .135 1 to135 1 .406 136 to 406 2 .677 407 to 677 3 .857 678 to 857
4& more 1.000 858 to 000
Using a Theoretical Distribution 3Using a Theoretical Distribution 3
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 18
Table 15.7 Monte Carlo Simulation Experiment for Public Health Clinic
Time
Random numbers
& (arrivals)
Arriving patients
Queue
Random numbers &
(service)
Physician
Departing Patients
1) 8:00 - 8:59 616 (2) #1,#2 - 764 (2) #1,#2 #1,#2 2) 9:00 - 9:59 862 (3) #3,#4,#5 #4,#5 180 (1) #3 #3 3)10:00 -10:59 56 (0) - - 903 (4+) #4,#5 #4,#5 4)11:00 -11:59 583 (2) #6,#7 - 780 (3) #6,#7 #6,#7 5)12:00 -12:59 908 (4) #8,#9,#10,#11 #9,#10,#11 164 (1) #8 #8 6) 1:00 - 1:59 848 (3) #12,#13,#14 #11,#12,#13,#14 546 (2) #9,#10 #9,#10 7) 2:00 - 2:59 38 (0) - #12,#13,#14 351 (1) #11 #11 8) 3:00 - 3:59 536 (2) #15,#16 900 (4+) #12,#13,#14,#15,#16 #12,#13,#14,#15,#16
Using a Theoretical Distribution 4
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 19
Table 15.8 Summary Statistics for Public Clinic Monte Carlo Simulation Experiment
Patient
Queue wait time
Service time
Total time in system
#1 0 0.5 0.5 #2 0 0.5 0.5 #3 0 1.0 1.0 #4 1 0.5 1.5 #5 1 0.5 1.5 #6 0 0.5 0.5 #7 0 0.5 0.5 #8 0 1.0 1.0 #9 1 0.5 1.5
#10 1 0.5 1.5 #11 2 1.0 3 #12 2 0.2 2.2 #13 2 0.2 2.2 #14 2 0.2 2.2 #15 0 0.2 0.2 #16 0 0.2 0.2
Total 12 8 20
Using a Theoretical Distribution 5
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 20
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.
Performance Measures from Tables 15.7 and 15.8
Advantages and Limitations of Simulation
Advantages Used for problems difficult to
solve mathematically Can experiment with system
behavior without experimenting with the actual system
Chapter 15: Quantitative Methods in Health Care Management ISE 491 Fall 2009 Dr. Burtner 21
Limitations Does not produce
an optimum Can require
considerable effort to develop a suitable model