1. Simulation in Healthcare Ozcan: Chapter 15 ISE 491 Fall 2009 Dr. Burtner

2. 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 ManagementISE 491 Fall 2009 Dr. Burtner 2

3. 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.

4. Why Use Simulation? Chapter 15: Quantitative Methods in Health Care ManagementISE 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

5. Simulation Process Chapter 15: Quantitative Methods in Health Care ManagementISE 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.

6. Chapter 15: Quantitative Methods in Health Care ManagementISE 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.

7. Chapter 15: Quantitative Methods in Health Care ManagementISE 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...

8. Chapter 15: Quantitative Methods in Health Care ManagementISE 491 Fall 2009 Dr. Burtner 8 Table 15.1 Simple Simulation Experiment for Public Clinic TimeCoin toss for arrival Arriving patient QueueCoin toss for service PhysicianDeparting patient 1) 8:00 - 8:59H#1H - 2) 9:00 - 9:59H#2 T#1 3)10:00 -10:59H#3 T#2 4)11:00 -11:59T---#3 5)12:00 -12:59H#4H - 6) 1:00 - 1:59H#5 H#4 7) 2:00 - 2:59T---#5- 8) 3:00 - 3:59H#6 T#5

9. Chapter 15: Quantitative Methods in Health Care ManagementISE 491 Fall 2009 Dr. Burtner 9 Table 15.2 Summary Statistics for Public Clinic Experiment PatientQueue wait time Service time Total time in system #1022 #2112 #3112 #4022 #5123 #6112 Total4913

10. Chapter 15: Quantitative Methods in Health Care ManagementISE 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

11. 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 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 ManagementISE 491 Fall 2009 Dr. Burtner 11

12. Chapter 15: Quantitative Methods in Health Care ManagementISE 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

13. Chapter 15: Quantitative Methods in Health Care ManagementISE 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

14. Chapter 15: Quantitative Methods in Health Care ManagementISE 491 Fall 2009 Dr. Burtner 14 Using an Empirical Distribution 2

15. Chapter 15: Quantitative Methods in Health Care ManagementISE 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

16. Chapter 15: Quantitative Methods in Health Care ManagementISE 491 Fall 2009 Dr. Burtner 16 Table 15.5 Cumulative Poisson Probabilities for λ=1.7 Arrivals x Cumulative probability Corresponding random numbers 0.1831 to183 1.493184 to 493 2.757494 to 757 3.907758 to 907 4.970908 to 970 5 & more1.00970 to 000 Using a Theoretical Distribution 2

17. Chapter 15: Quantitative Methods in Health Care ManagementISE 491 Fall 2009 Dr. Burtner 17 Using a Theoretical Distribution 3

18. Chapter 15: Quantitative Methods in Health Care ManagementISE 491 Fall 2009 Dr. Burtner 18 Using a Theoretical Distribution 4

19. Chapter 15: Quantitative Methods in Health Care ManagementISE 491 Fall 2009 Dr. Burtner 19 Using a Theoretical Distribution 5

20. Chapter 15: Quantitative Methods in Health Care ManagementISE 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

21. Advantages and Limitations of Simulation Advantages Used for problems difficult to solve mathematically Can experiment with system behavior without experimenting with the actual system 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 ManagementISE 491 Fall 2009 Dr. Burtner 21 Limitations Does not produce an optimum Can require considerable effort to develop a suitable model Limitations Does not produce an optimum Can require considerable effort to develop a suitable model