1. QMF Simulation

2. Outline What is Simulation What is Simulation Advantages and Disadvantages of Simulation Advantages and Disadvantages of Simulation Monte Carlo Simulation Monte Carlo Simulation Simkin drills Simkin drills Simulate by hand Simulate by hand Simulate by Excel Simulate by Excel

3. What is simulation?

4. Numerical technique of experimentation Numerical technique of experimentation Attempts to duplicate a system Attempts to duplicate a system Features Features Behavior Behavior Requires description of system Requires description of system Many application areas Many application areas Operations management Operations management Finance & economics Finance & economics Ecosystems Ecosystems Simulation

5. Simulation The idea behind simulation is to: Imitate a real-world situation mathematically Imitate a real-world situation mathematically Study its properties and operating characteristics Study its properties and operating characteristics Draw conclusions and make action recommendations based on the results of the simulation study Draw conclusions and make action recommendations based on the results of the simulation study

6. Advantages of Simulation is very flexible, relatively straightforward is very flexible, relatively straightforward can be used to analyze large and complex real-world problems for which closed-form analytical solutions are not possible can be used to analyze large and complex real-world problems for which closed-form analytical solutions are not possible allows for the inclusion of real-world complications which most other techniques do not permit allows for the inclusion of real-world complications which most other techniques do not permit makes possible “time compression” makes possible “time compression” allows one to ask “what if” type questions allows one to ask “what if” type questions does not interfere with the real-world system does not interfere with the real-world system allows us to study the interactive effect of individual components or variables allows us to study the interactive effect of individual components or variables

7. Can be expensive and time consuming Can be expensive and time consuming Does not yield optimal solution Does not yield optimal solution Requires good managerial input Requires good managerial input Results not generalizable to other situations Results not generalizable to other situations © 1984-1994 T/Maker Co. Disadvantages of Simulation

8. Monte Carlo Simulation Technique Step A: Setup for Monte Carlo Simulation Step B: Generate values for random variables Step C: Perform calculations

9. EZ Mart – Simulate demand Weekly demand at a local E-Z Mart convenience store for 1-gallon jugs of low-fat milk for the last 50 weeks has varied between 60 and 65 jugs, as shown in the following table. Demand in excess of stock cannot be backordered. Demand (gallons) Number of weeks 605 617 6217 6311 646 654 Total50

10. Setup for the Monte Carlo Simulation Technique Step 1: Setup probability distribution for important variables Step 2: Build cumulative distribution for each variable Step 3: Establish interval of random numbers for each variable

11. EZ-Mart Simulate demand for 10 weeks

12. Step 1: Setup probability distribution for important variables

13. P(demand is 60) = 5/50 = 0.10 Step 1: Setup probability distribution for important variables

14. P(demand is 61) = 7/50 = 0.14 Step 1: Setup probability distribution for important variables

16. Step 2: Build Cumulative Probability Distribution for Demand P(demand <= 61) = 0.10 + 0.14 = 0.24

17. Step 2: Build Cumulative Probability Distribution for Demand P(demand <= 62) = 0.20 + 0.34 = 0.58

18. Step 2: Build Cumulative Probability Distribution for Demand

19. Step 3: Assign random number intervals for demand

22. EZ Mart Cumulative Distribution & Random Number Assignment

23. EZ Mart Simulate Demand WeekR.N.Demand152 237 382 469 598 696 733 850 988 1090

24. WeekR.N.Demand152 237 382 469 598 696 733 850 988 1090 R.N. – Random number From Table F.4 p. 854 1 st column

25. EZ Mart Simulate Demand WeekR.N.Demand152 237 382 469 598 696 733 850 988 1090

26. WeekR.N.Demand15262 237 382 469 598 696 733 850 988 1090

27. WeekR.N.Demand15262 23762 382 469 598 696 733 850 988 1090

28. WeekR.N.Demand15262 23762 38264 469 598 696 733 850 988 1090

29. WeekR.N.Demand15262 23762 38264 46963 59865 69665 73362 85062 98864 109064

30. EZ Mart Simulate using Excel =rand() is an Excel function that generate a random number between 0 and 1.0 =rand() is an Excel function that generate a random number between 0 and 1.0 =Vlookup() is an Excel function that looks up a value in a table =Vlookup() is an Excel function that looks up a value in a table Three parameters for vlookup Three parameters for vlookup Cell with the value that is to be looked up Cell with the value that is to be looked up Range of the table with the leftmost column having the values that are looked up Range of the table with the leftmost column having the values that are looked up Column number in the table with the values that are to be returned Column number in the table with the values that are to be returned Go to Excel

31. Vlookup function If you are given a spreadsheet and the Excel function: If you are given a spreadsheet and the Excel function: =Vlookup(b15, c5:e18,3) You should be able to determine the value that excel will place in the cell with the vlookup function. You should be able to determine the value that excel will place in the cell with the vlookup function.