1. Chapter 10. Simulation An Integrated Approach to Improving Quality and Efficiency Daniel B. McLaughlin Julie M. Hays Healthcare Operations Management

2. Copyright 2008 Health Administration Press. All rights reserved. 10-2 Chapter 10. Simulation Uses of Simulation Simulation Process Monte Carlo Simulation Queueing (Waiting Line) Theory Discrete Event Simulation (DES) Advanced DES

3. Copyright 2008 Health Administration Press. All rights reserved. 10-3 Simulation Process of modeling reality to gain a better understanding of the phenomena or system being studied Simulation versus the “real world” -More cost effective -Less dangerous environment -Faster -More practical Does not require mathematical models or computers

4. Copyright 2008 Health Administration Press. All rights reserved. 10-4 Types of Simulation Performance Proof Discovery Entertainment Training Education Prediction

5. Copyright 2008 Health Administration Press. All rights reserved. 10-5 Simulation Process Model development -Define the problem or question -Develop the conceptual model -Collect data -Build computer model Model validation Simulate and analyze output

6. Copyright 2008 Health Administration Press. All rights reserved. 10-6 Simulation Process Model Development Problem/ question definition Develop conceptual model Collect data Build computer model Model Validation Quantitative comparison Expert opinion Simulation and Analyses DOE Replication Data collection, storage, and organization Analysis

7. Copyright 2008 Health Administration Press. All rights reserved. 10-7 Monte Carlo Simulation Model the output of a system by using input variables that could not be known exactly Random variables (those that are uncertain and have a range of possible values) characterized by a probability distribution Solution is a distribution of possible outcomes that can be characterized statistically

8. Copyright 2008 Health Administration Press. All rights reserved. 10-8 Simple Monte Carlo Example Distribution of Charges

9. Copyright 2008 Health Administration Press. All rights reserved. 10-9 Simple Monte Carlo Example Fifty percent of the clinic’s patients do not pay for their services, and it is equally likely that they will pay or not pay. The payment per patient is modeled by: Probability of payment × Charges/patient = Payment/patient A deterministic solution to this problem would be: 0.5 × $70/patient = $35 per patient

10. Copyright 2008 Health Administration Press. All rights reserved. 10-10 Simple Monte Carlo Example Payment Distribution

11. Copyright 2008 Health Administration Press. All rights reserved. 10-11 Simple Monte Carlo Example The Flaw of Averages On average each patient pays $35. However: -Fifty percent of the patients pay nothing. -A small percentage pay as much as $120. -No individual patient pays $35. Monte Carlo simulation can reveal hidden information and a clearer understanding of the risks and rewards of a situation or decision.

12. Copyright 2008 Health Administration Press. All rights reserved. 10-12 VVH Monte Carlo Example CAP Payment Distribution Created with BestFit  4.5, a software product of Palisade Corp., Ithaca, NY; www.palisade.com

13. Copyright 2008 Health Administration Press. All rights reserved. 10-13 VVH Monte Carlo Example Input Distributions Probability Distribution of Cost of Reaching a Score Greater Than 0.90 $10,000$30,000$50,000 Cost of Reaching a Score Greater Than 0.90 P(X) Probability Distribution of Quality Scores 0 0.02 0.04 0.06 0.60.70.80.9 Quality Score P(X)

14. Copyright 2008 Health Administration Press. All rights reserved. 10-14 VVH Monte Carlo Example Deterministic Analysis Profit= Revenue – Cost Revenue= (Rev/mon × 12 mon/yr) × Quality bonus or penalty = ($250,000/mon × 12 mon/yr) × 0.01 = $30,000/yr Cost = $30,000/yr Profit= $30,000/yr – $30,000/yr = $0

15. Copyright 2008 Health Administration Press. All rights reserved. 10-15 VVH Monte Carlo Example CAP Pay-for-Performance Simulation Trials Created with @Risk 4.5, a software product of Palisade Corp., Ithaca, NY; www.palisade.com

16. Copyright 2008 Health Administration Press. All rights reserved. 10-16 VVH Monte Carlo Example Simulated Distribution of Profits Created with @Risk 4.5, a software product of Palisade Corp., Ithaca, NY; www.palisade.com

17. Copyright 2008 Health Administration Press. All rights reserved. 10-17 VVH Monte Carlo Example Tornado Graph Created with @Risk 4.5, a software product of Palisade Corp., Ithaca, NY; www.palisade.com

18. Copyright 2008 Health Administration Press. All rights reserved. 10-18 Simple Queueing System Customer population—finite or infinite Arrival process—often Poisson with mean arrival rate Queue discipline—first come, first served (FCFS) is one example Service process—often exponential with mean service rate  Arrival Customer Population Input Source Buffer or Queue Server(s) Exit

19. Copyright 2008 Health Administration Press. All rights reserved. 10-19 Queueing Notation A/B/c/D/E -A = Inter-arrival time distribution -B = Service time distribution -c = Number of servers -D = Maximum queue size -E = Size of input population M/M/1 queueing system -Poisson arrival distribution -Exponential service time distribution -Single server -Infinite possible queue length -Infinite input population -Only one queue

20. Copyright 2008 Health Administration Press. All rights reserved. 10-20 Queueing Solutions M/M/1, <  Capacity utilization = Percentage of time the server is busy Average total number of customers in the system = = Arrival rate × time in the system

21. Copyright 2008 Health Administration Press. All rights reserved. 10-21 Queueing Solutions M/M/1, <  Average waiting time in the queue Average time in the system = Average waiting time in the queue + Average service time = Average length of the queue (or average number in the queue)

22. Copyright 2008 Health Administration Press. All rights reserved. 10-22 VVH M/M/1 Queue Example Goal: Only one patient waiting in line for the MRI Data: -Mean service rate (  ) is four patients/hour and is exponentially distributed -Arrivals follow a Poisson distribution and the mean arrival rate is three patients/hour ( )

23. Copyright 2008 Health Administration Press. All rights reserved. 10-23 VVH M/M/1 Queue Example If one customer arrives every 20 minutes and it takes 15 minutes to perform the MRI, the MRI will be busy 75 percent of the time. Capacity utilization of MRI = Percentage of time MRI is busy

24. Copyright 2008 Health Administration Press. All rights reserved. 10-24 VVH M/M/1 Queue Example Average time waiting in line Average time in the system Average total number of patients in the system or = Arrival rate × Time in the system = 3 patients/hour × 1 hour = 3 patients

25. Copyright 2008 Health Administration Press. All rights reserved. 10-25 VVH M/M/1 Queue Example Average number of patients waiting in line = VVH needs to decrease the utilization,  = / , of the MRI process VVH can -Increase the service rate (  ) -Decrease the arrival rate ( ) -Do a combination of both

26. Copyright 2008 Health Administration Press. All rights reserved. 10-26 Discrete Event Simulation (DES) Basic Simulation Model Entities are the objects that flow through the system. Queues hold the entities while they are waiting for service. Resources or servers are people, equipment, or space for which entities compete.

27. Copyright 2008 Health Administration Press. All rights reserved. 10-27 Discrete Event Simulation (DES) Simulation Model Logic States are variables that describe the system at a point in time. Events are variables that change the state of the system. The simulation jumps through time from event to event, and data are collected on the state of the system.

28. Copyright 2008 Health Administration Press. All rights reserved. 10-28 DES Random Data 123456789 0.170.370.360.590.140.170.240.060.35 0.170.540.901.491.631.802.042.102.45 0.210.560.020.370.340.111.020.010.20 Entity Number Expon (0.33) Expon (0.25) Service Time Inter-arrival Time Time of Arrival0.00

29. Copyright 2008 Health Administration Press. All rights reserved. 10-29 DES Simulation Event List

30. Copyright 2008 Health Administration Press. All rights reserved. 10-30 DES Simulation Event List

31. Copyright 2008 Health Administration Press. All rights reserved. 10-31 DES Arena  Screenshot Arena® screen shots reprinted with permission from Rockwell Automation.

32. Copyright 2008 Health Administration Press. All rights reserved. 10-32 DES—Arena  Output Arrival rate = 3 patients/hour; Service rate = 4 patients/hour; 200 hours Arena® screen shots reprinted with permission from Rockwell Automation.

33. Copyright 2008 Health Administration Press. All rights reserved. 10-33 DES—Arena  Output Arrival rate = 3 patients/hour; Service rate = 4 patients/hour; 200 hours Arena® screen shots reprinted with permission from Rockwell Automation.

34. Copyright 2008 Health Administration Press. All rights reserved. 10-34 DES—Arena  Output Arrival rate = 3 patients/hour; Service rate = 4 patients/hour; 10 hours Arena® screen shots reprinted with permission from Rockwell Automation.

35. Copyright 2008 Health Administration Press. All rights reserved. 10-35 DES—Arena  Output Arrival rate = 3 patients/hour; Service rate = 4 patients/hour; 10 hours Arena® screen shots reprinted with permission from Rockwell Automation.

36. Copyright 2008 Health Administration Press. All rights reserved. 10-36 VVH Simulation Current situation—on average, 1.5 patients in queue Goal—1.0 patients in queue Solution—decrease arrival rate or increase the service rate Simulation results: -Decrease arrival rate to 2.7 -Increase service rate to 4.4 Actual improvement: -Service rate of 4.2 patients/hour -Need arrival rate of 2.8 patients/hour

37. Copyright 2008 Health Administration Press. All rights reserved. 10-37 DES—Arena  Output Arrival rate = 2.8 patients/hour; Service rate = 4.2 patients/hour; 10 hours Arena® screen shots reprinted with permission from Rockwell Automation.

38. Copyright 2008 Health Administration Press. All rights reserved. 10-38 DES—Arena  Output Arrival rate = 2.8 patients/hour; Service rate = 4.2 patients/hour; 10 hours Arena® screen shots reprinted with permission from Rockwell Automation.

39. Copyright 2008 Health Administration Press. All rights reserved. 10-39 Simulation Simulation is a powerful tool for modeling processes and systems to evaluate choices and opportunities. Simulation can be used in conjunction with other initiatives such as Lean and Six Sigma to enable continuous improvement of systems and processes.