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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 1 Chapter 15. Simulation

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 2 Outline Simulation Process Monte Carlo Simulation Method – –Process – –Empirical Distribution – –Theoretical Distribution – –Random Number Look Up Performance Measures and Managerial Decisions

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 3 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.

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 4 Why Simulate? To enhance decision making by capturing a situation that is too complicated to model mathematically (e.g., queuing problems) It is simple to use and understand Wide range of applications and situations in which it is useful Software is available that makes simulation easier and faster

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 5 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.

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 6 Simulation Basics We need an instrument to randomly simulate this situation. Let’s call this the “simulator”. Imagine a simple “simulator” with two outcomes.

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 7 So how can it help us? Waiting Line Service System Customers arrivals Let’s look at a health care example. How can we simulate the patient arrivals and service system response?

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 8... 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 this simulator...

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 9 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

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 10 Calculation of Performance Statistics ArrivalsQueue (Waiting Line)ServiceExit ???? Waiting Line Service System Customers arrivals

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 11 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

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 12 Number of Arrivals Average number waiting Avg. time in Queue Service Utilization Avg. Service Time Avg. Time in System Performance Measures

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 13 But what if we have multiple arrival patterns? Can we use a dice or any other shaped object that could provide random arrival and service times? We could use Monte Carlo Simulation and a Random Number Table! Can we use a dice or any other shaped object that could provide random arrival and service times? We could use Monte Carlo Simulation and a Random Number Table!

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 14 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

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 15 Step 1: Selection of an appropriate probability distribution Step 2: Determining the correspondence between distribution and random numbers Step 3: Obtaining (generating) random numbers and run simulation Step 4: Summarizing the results and drawing conclusions MONTE CARLO METHOD

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 16 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 100 observations, the following frequencies, shown in table below, were obtained for arrivals in a busy public health clinic. Empirical Distribution

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 17

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 18 The second popular method for constructing arrivals is to use known theoretical statistical distributions that would describe patient arrival patterns. From queuing theory, we learned that Poisson distribution characterizes such arrival patterns. However, in order to use theoretical distributions, one must have an idea about the distributional properties for the Poisson distribution, namely its mean. In the absence of such information, the expected mean of the Poisson distribution can also 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 Theoretical Distribution λ = (0*.18)+(1*.40)+(2*.15)+(3*.13)+(4*.09)+(5*.05) = 1.7

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 19 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

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 20

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 21 Finding Random Numbers Numbers must be both uniformly distributed and must not follow any pattern Always avoid starting at the same spot on a random number table Numbers must be both uniformly distributed and must not follow any pattern Always avoid starting at the same spot on a random number table 2419 4572

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 22 Figure 15.1 Random Numbers* * Random numbers are generated using Excel

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 23

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 24

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 25 Using information from Tables 15.7 and 15.8, we can delineate the performance measures for this simulation experiment as: 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 minutes, calculated by dividing 20 hours by the number of patients: 20 ÷ 16 = 1.25. Performance Measures

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 26 Figure 15.2 Excel-Based Simulated Arrivals

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 27 Figure 15.3 Excel Program for Simulated Arrivals

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 28 r 1 < r t r 1 >= r t r 2 < r t r 2 >= r t Marketing and referral systems to increase business volume Appointment Scheduling Increase Capacity Busy time during regular hours r 1 = --------------------------------- Total busy time, including during over time Total regular hours open r 2 = ------------------------------------------ r t = Target utilization rate (e.g., 90%) Figure 15.4 Performance-Measure-Based Managerial Decision Making Status Quo

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 29 Advantages of Simulation Used for problems difficult to solve mathematically Can experiment with system behavior without experimenting with the actual system Compresses time Valuable tool for training decision makers Used for problems difficult to solve mathematically Can experiment with system behavior without experimenting with the actual system Compresses time Valuable tool for training decision makers

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 30 Limitations Does not produce an optimum Can require considerable effort to develop a suitable model Monte Carlo is only applicable when situational elements can be described by random variables Does not produce an optimum Can require considerable effort to develop a suitable model Monte Carlo is only applicable when situational elements can be described by random variables

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Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 31 The End

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