simulation in healthcare ozcan: chapter 15 ise 491 fall 2009 dr. burtner

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. . .


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?


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


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.


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.


. . . 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. . .


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


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


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



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


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


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


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


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



Table 15.6 Cumulative Poisson Probabilities for

Arrivals: λ=1.7 Patients arrived



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



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


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



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



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


Limitations Does not produce

an optimum Can require

considerable effort to develop a suitable model

simulation in healthcare ozcan: chapter 15 ise 491 fall 2009 dr. burtner

Documents