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# Simulation

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### Simulation

1. 1. Simulation Modeling Prepared by Lee Revere and John LargeTo accompany Quantitative Analysis 15-1 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
2. 2. IntroductionSimulation is one of the most widelyused quantitative analysis tools. It isused to: imitate a real-world situation mathematically. study its properties and operating characteristics. draw conclusions and make action decisions.To accompany Quantitative Analysis 15-2 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
3. 3. Introduction: Seven Steps of Simulation Define a Problem Introduce Important Variables Construct Simulation Model Specify Values to be Variables Conduct the Simulation Examine the Results Select Best Course of ActionTo accompany Quantitative Analysis 15-3 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
4. 4. Advantages of Simulation Straightforward and flexible Computer software make simulation models easy to develop Enables analysis of large, complex, real-world situations Allows “what-if?” questions Does not interfere with real-world system Enables study of interactions Enables time compression Enables the inclusion of real-world complicationsTo accompany Quantitative Analysis 15-4 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
5. 5. Disadvantages of Simulation Often requires long, expensive development process. Does not generate optimal solutions; it is a trial-and-error approach. Requires managers to generate all conditions and constraints of real- world problem. Each model is unique and not typically transferable to other problems.To accompany Quantitative Analysis 15-5 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
6. 6. Simulation Models Categories Monte Carlo consumer demand inventory analysis queuing problems maintenance policy Operational Gaming Systems SimulationTo accompany Quantitative Analysis 15-6 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
7. 7. Monte Carlo SimulationThe Monte Carlo simulation isapplicable to business problemsthat exhibit chance, or uncertainty.For example: 1. Inventory demand 2. Lead time for inventory 3. Times between machine breakdowns 4. Times between arrivals 5. Service times 6. Times to complete project activities 7. Number of employees absentTo accompany Quantitative Analysis 15-7 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
8. 8. Monte Carlo Simulation (continued)The basis of the Monte Carlo simulationis experimentation on the probabilisticelements through random sampling. It isused with probabilistic variables. Five steps: 1. Set up probability distributions 2. Build cumulative probability distributions 3. Establish interval of random numbers for each variable 4. Generate random numbers 5. Simulate trialsTo accompany Quantitative Analysis 15-8 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
9. 9. Harry’s Auto Tires: Monte Carlo ExampleA popular radial tire accounts for a largeportion of the sales at Harry’s Auto Tire.Harry wishes to determine a policy formanaging his inventory of radial tires. Demand Frequency Probability for Tires 0 10 0.05 = 10/200 1 20 0.10 2 40 0.20 3 60 0.30 4 40 0.2 5 30 0 0.15 200 1.00Let’s use Monte Carlo simulation toanalyze Harry’s inventory…To accompany Quantitative Analysis 15-9 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
10. 10. Harry’s Auto Tires: Monte Carlo Example (continued)Step 1: Set up the probability distributionfor radial tire. Demand Probability 1 0.9 Using historical data, Harry determined 0.8 that 5% of the time 0 tires were demanded, 0.7 10% of the time 1 tire was demand, etc… 0.6 p(X) 0.5 0.4 0.3 0.2 P(1) = 10% 0.1 0 0 1 2 3 4 5 XTo accompany Quantitative Analysis 15-10 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
11. 11. Harry’s Auto Tires: Monte Carlo Example (continued)Step 2: Build a cumulative probabilitydistribution. Demand Cumulative Probability 1 15% of the time the demand was 0 0.9 or 1 tire: P(0) = 5% + P(1) = 10% 0.8 0.7 0.6 P(X) 0.5 0.4 0.3 0.2 0.1 0 0 1 2 3 4 5 XTo accompany Quantitative Analysis 15-11 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
12. 12. Harry’s Auto Tires: Monte Carlo Example (continued) Step 3: Establish an interval of random numbers. Probability Random Demand Number Interval Must be in correct proportion 0 10 0.05 0.05 01 - 05 1 20 0.10 0.15 06 - 15 2 40 0.20 0.35 16 - 35 3 60 0.30 0.65 36 - 65 4 40 0.20 0.85 66 - 85 5 30 0.15 1.00 86 - 00Note: 5% of the time 0 tires are demanded, so the randomnumber interval contains 5% of the numbers between 1 and 100 To accompany Quantitative Analysis 15-12 © 2006 by Prentice Hall, Inc. for Management, 9e Upper Saddle River, NJ 07458 by Render/Stair/Hanna
13. 13. Harry’s Auto Tires: Monte Carlo Example (continued) Step 4: Generate random numbers. 52 06 50 88 53 30 10 47 99 37 66 91 35 32 00 84 57 07 37 63 28 02 74 35 24 03 29 60 74 85 90 73 59 55 17 60 82 57 68 28 05 94 03 11 27 79 90 87 92 41 09 25 36 77 69 02 36 49 71 99 32 10 75 21 95 90 94 38 97 71 72 49 98 94 90 36 06 78 23 67 89 85 29 21 25 73 69 34 85 76 96 52 62 87 49 56 59 23 78 71 72 90 57 01 98 57 31 95 33 69 27 21 11 60 95 89 68 48 17 89 34 09 93 50 44 51 50 33 50 95 13 44 34 62 64 39 55 29 30 64 49 44 30 16 88 32 18 50 62 57 34 56 62 31 15 40 90 34 51 95 26 14 90 30 36 24 69 82 51 74 30 35 36 85 01 55 92 64 09 85 50 48 61 18 85 23 08 54 17 12 80 69 24 84 92 16 49 59 27 88 21 62 69 64 48 31 12 73 02 68 00 16 16 46 13 85 45 14 46 32 13 49 66 62 74 41 86 98 92 98 84 54 33 40 81 02 01 78 82 74 97 37 45 31 94 99 42 49 27 64 89 42 66 83 14 74 27 76 03 33 11 97 59 81 72 00 64 61 13 52 74 05 82 82 93 09 96 33 52 78 13 06 28 30 94 23 37 39 30 34 87 01 74 11 46 82 59 94 25 34 32 23 17 01 58 73 To accompany Quantitative Analysis 15-13 © 2006 by Prentice Hall, Inc. for Management, 9e Upper Saddle River, NJ 07458 by Render/Stair/Hanna
14. 14. Harry’s Auto Tires: Monte Carlo Example (continued) Step 5: Simulate a series of trials. Using random number table on previous slide, simulated demand for 10 days is: Tires Interval of Demanded Random Numbers 0 01 - 05 1 06 - 15 2 16 - 35 3 2 36 - 65 4 66 - 85 5 3 1 86 - 100Random number: 52 06 50 88 53 30 10 47 99 37Simulated demand: 3 1 3 5 3 2 1 3 5 3 To accompany Quantitative Analysis 15-14 © 2006 by Prentice Hall, Inc. for Management, 9e Upper Saddle River, NJ 07458 by Render/Stair/Hanna
15. 15. Three Hills Power Company: Monte Carlo ExampleThree Hills provides power to a largecity. The company is concerned aboutgenerator failures because a breakdowncosts about \$75 per hour versus a \$30per hour salary for repairpersons whowork 24 hours a day, seven days a week.Management wants to evaluate theservice maintenance cost, simulatedbreakdown cost, and total cost.Let’s use Monte Carlo simulation toanalyze Three Hills system costs.To accompany Quantitative Analysis 15-15 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
16. 16. Three Hills PowerGenerator Breakdown Times: Monte Carlo (continued) Steps 1-3: Determine probability, cumulative probability, and random number interval - BREAKDOWNS. Random Number Times Observed Number of Interval Cumulative Probability ½ 5 0.05 0.05 01 - 05 1 6 0.06 0.11 06 - 11 1½ 16 0.16 0.27 12 - 27 2 33 0.33 0.60 28 - 60 2½ 21 0.21 0.81 81 - 81 3 19 0.19 1.00 82 - 00 Total 100 1.00 To accompany Quantitative Analysis 15-16 © 2006 by Prentice Hall, Inc. for Management, 9e Upper Saddle River, NJ 07458 by Render/Stair/Hanna
17. 17. Three Hills Power Generator Repair TimesSteps 1-3: Determine probability,cumulative probability, and randomnumber interval - REPAIRS.Repair Time Cumulative Required Probability (Hours) 1 28 0.28 0.28 01 - 28 2 52 0.52 0.80 29 - 80 3 20 0.20 1.00 81 - 00To accompany Quantitative Analysis 15-17 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
18. 18. Three Hills PowerGenerator Breakdown Times: Monte Carlo (continued)Steps 4 & 5: Generate random numbers and simulate. Machine is down Time Repair Time Repair Repair Time Breakdowns Breakdown Simulation Can Begin No. of hrs. Random Random Time b/t Number Number Time of Ends Trial 1 57 2 2:00 2:00 7 1 3:00 1 2 17 1.5 3:30 3:30 60 2 5:30 2 3 36 2 5:30 5:30 77 2 7:30 2 4 72 2.5 8:00 8:00 49 2 10:00 2 5 85 3 11:00 11:00 76 2 13:00 2 : : : : : : : : : 14 89 3 4:00 6:00 42 2 8:00 4 15 13 1.5 5:30 8:00 52 2 10:00 4.5 To accompany Quantitative Analysis 15-18 © 2006 by Prentice Hall, Inc. for Management, 9e Upper Saddle River, NJ 07458 by Render/Stair/Hanna
19. 19. Three Hills PowerGenerator Breakdown Times: Monte Carlo (continued) Cost Analysis: Service maintenance: = 34 hrs of worker service X \$30 per hr = \$1,020Simulate machine breakdown costs: = 44 total hrs of breakdown X \$75 lost per hr of downtime = \$3,300Total simulated maintenance cost of thecurrent system: = service cost + breakdown costs = \$1,020 + \$3,300 = \$4,320 To accompany Quantitative Analysis 15-19 © 2006 by Prentice Hall, Inc. for Management, 9e Upper Saddle River, NJ 07458 by Render/Stair/Hanna
20. 20. Operational Gaming Simulation ModelOperational gaming refers tosimulation involving competingplayers.Examples: Military games Business gamesTo accompany Quantitative Analysis 15-20 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
21. 21. Systems Simulation ModelSystems simulation is similar tobusiness gaming because it allowsusers to test various managerialpolicies and decision. It models thedynamics of large systems.Examples: Corporate operating system Urban government Economic systemsTo accompany Quantitative Analysis 15-21 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna
22. 22. Verification and ValidationVerification of simulation modelsinvolves determining that thecomputer model is internallyconsistent and follows the logic ofthe conceptual model.Validation is the process ofcomparing a simulation modelto a real system to assureaccuracy.To accompany Quantitative Analysis 15-22 © 2006 by Prentice Hall, Inc.for Management, 9e Upper Saddle River, NJ 07458by Render/Stair/Hanna