1 / 31

Chapter 15. Simulation

Chapter 15. Simulation. Outline. Simulation Process Monte Carlo Simulation Method Process Empirical Distribution Theoretical Distribution Random Number Look Up Performance Measures and Managerial Decisions. When Optimization is not an option. SIMULATE!.

nomlanga-fitzgerald
Download Presentation

Chapter 15. Simulation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 15. Simulation 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 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 ifapproach. 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 Yasar A. Ozcan

  5. Simulation Process • Define the problem and objectives • 2. Develop the simulation model • 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 • Repeat steps 4 and 5 until you are satisfied with the • results. 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. Yasar A. Ozcan

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

  8. Let’s use this simulator. . . • . . . 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. Yasar A. Ozcan

  9. Table 15.1 Simple Simulation Experiment for Public Clinic Yasar A. Ozcan

  10. System Customers Waiting Line Service arrivals Calculation of Performance Statistics Arrivals Queue (Waiting Line) Service Exit ? ? ? ? Yasar A. Ozcan

  11. Table 15.2 Summary Statistics for Public Clinic Experiment Yasar A. Ozcan

  12. Performance Measures • Number of Arrivals • Average number waiting • Avg. time in Queue • Service Utilization • Avg. Service Time • Avg. Time in System 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! 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 Yasar A. Ozcan

  15. MONTE CARLO METHOD 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 Yasar A. Ozcan

  16. Empirical Distribution 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. Yasar A. Ozcan

  17. Yasar A. Ozcan

  18. Theoretical Distribution 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 λ = (0*.18)+(1*.40)+(2*.15)+(3*.13)+(4*.09)+(5*.05) = 1.7 Yasar A. Ozcan

  19. Table 15.5 Cumulative Poisson Probabilities for λ=1.7 Yasar A. Ozcan

  20. 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 2419 Yasar A. Ozcan 4572

  22. Figure 15.1 Random Numbers* * Random numbers are generated using Excel Yasar A. Ozcan

  23. Yasar A. Ozcan

  24. Yasar A. Ozcan

  25. Performance Measures • 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. Yasar A. Ozcan

  26. Figure 15.2 Excel-Based Simulated Arrivals Yasar A. Ozcan

  27. Figure 15.3 Excel Program for Simulated Arrivals Yasar A. Ozcan

  28. Figure 15.4 Performance-Measure-Based Managerial Decision Making r1 < rt r1 >= rt Marketing and referral systems to increase business volume r2 < rt Status Quo Appointment Scheduling Increase Capacity r2 >= rt Busy time during regular hours r1 = --------------------------------- Total regular hours open Total busy time, including during over time r2 = ------------------------------------------ Total regular hours open rt = Target utilization rate (e.g., 90%) 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 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 Yasar A. Ozcan

  31. The End Yasar A. Ozcan

More Related