1. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-1 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Prepared by Lee Revere and John Large Chapter 15 Simulation Modeling

2. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-2 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Learning Objectives Students will be able to: 1.Tackle a wide variety of problems by simulation. 2.Understand the seven steps of conducting a simulation. 3.Explain the advantages and disadvantages of simulation. 4.Develop random number intervals and use them to generate outcomes. 5.Understand the alternative simulation packages available commercially.

3. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-3 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter Outline 15.1 Introduction 15.2 Advantages and Disadvantages of Simulation 15.3 Monte Carlo Simulation 15.4 Simulation and Inventory Analysis 15.5 Simulation of a Queuing Problem 15.6 Fixed Time Increment and Next Event Increment Simulation Models

4. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-4 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter Outline 15.7 Simulation Model for Maintenance Policy 15.8 Two Other Types of Simulation 15.9 Verification and Validation 15.9 Role of Computers in Simulation

5. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-5 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Introduction  imitate a real-world situation mathematically.  study its properties and operating characteristics.  draw conclusions and make action decisions. Simulation is one of the most widely used quantitative analysis tools. It is used to:

6. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-6 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Introduction: Seven Steps of Simulation Define a Problem Conduct the Simulation Introduce Important Variables Construct Simulation Model Specify Values to be Variables Examine the Results Select Best Course of Action

7. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-7 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 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 complications

8. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-8 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 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.

9. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-9 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Simulation Models Categories  Monte Carlo  consumer demand  inventory analysis  queuing problems  maintenance policy  Operational Gaming  Systems Simulation

10. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-10 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Monte Carlo Simulation The Monte Carlo simulation is applicable to business problems that 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 absent

11. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-11 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Monte Carlo Simulation (continued) 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 trials The basis of the Monte Carlo simulation is experimentation on the probabilistic elements through random sampling. It is used with probabilistic variables.

12. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-12 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Harry’s Auto Tires: Monte Carlo Example A popular radial tire accounts for a large portion of the sales at Harry’s Auto Tire. Harry wishes to determine a policy for managing his inventory of radial tires. Let’s use Monte Carlo simulation to analyze Harry’s inventory… 0 100.05 1200.10 2400.20 3600.30 4400.2 0 5300.15 Demand Frequency Probability for Tires 200 1.00 = 10/200

13. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-13 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Harry’s Auto Tires: Monte Carlo Example (continued) Step 1: Set up the probability distribution for radial tire. Using historical data, Harry determined that 5% of the time 0 tires were demanded, 10% of the time 1 tire was demand, etc… P(1) = 10%

14. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-14 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Harry’s Auto Tires: Monte Carlo Example (continued) Step 2: Build a cumulative probability distribution. 15% of the time the demand was 0 or 1 tire: P(0) = 5% + P(1) = 10%

15. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-15 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Harry’s Auto Tires: Monte Carlo Example ( continued) Demand Frequency Probability Cumulative Probability Random Number Interval 0100.05 01 - 05 1200.100.1506 - 15 2400.200.3516 - 35 3600.300.6536 - 65 4400.200.8566 - 85 5300.151.0086 - 00 Step 3: Establish an interval of random numbers. Must be in correct proportion Note: 5% of the time 0 tires are demanded, so the random number interval contains 5% of the numbers between 1 and 100

16. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-16 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 52 37 82 69 98 96 33 50 88 90 50 27 45 81 66 74 30 06 63 57 02 94 52 69 33 32 30 48 88 14 02 83 05 34 50 28 68 36 90 62 27 50 18 36 61 21 46 01 14 82 87 88 02 28 49 36 87 21 95 50 24 18 62 32 78 74 82 01 53 74 05 71 06 49 11 13 62 69 85 69 13 82 27 93 74 30 35 94 99 78 56 60 44 57 82 23 64 49 74 76 09 11 10 24 03 32 23 59 95 34 51 08 48 66 97 03 96 46 47 03 11 10 67 23 89 62 56 74 54 31 62 37 33 82 99 29 27 75 89 78 68 64 62 30 17 12 74 45 11 52 59 37 60 79 21 85 71 48 39 31 35 12 73 41 31 97 78 94 66 74 90 95 29 72 17 55 15 36 80 02 86 94 59 13 25 91 85 87 90 21 90 89 29 40 85 69 68 98 99 81 06 34 35 90 92 94 25 57 34 30 90 01 24 00 92 42 72 28 32 73 41 38 73 01 09 64 34 55 84 16 98 49 00 30 23 00 59 09 97 69 98 93 49 51 92 16 84 27 64 94 17 84 55 25 71 34 57 50 44 95 64 16 46 54 64 61 23 01 57 17 36 72 85 31 44 30 26 09 49 13 33 89 13 37 58 07 60 77 49 76 95 51 16 14 85 59 85 40 42 52 39 73 Harry’s Auto Tires: Monte Carlo Example (continued) Step 4: Generate random numbers.

17. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-17 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 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: Random number: 52 06 50 88 53 30 10 47 99 37 Simulated demand: 3 1 3 5 3 2 1 3 5 3 TiresInterval of DemandedRandom Numbers 001 - 05 106 - 15 216 - 35 336 - 65 466 - 85 586 - 100 1 2 3

18. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-18 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Three Hills Power Company: Monte Carlo Example Three Hills provides power to a large city. The company is concerned about generator failures because a breakdown costs about $75 per hour versus a $30 per hour salary for repairpersons who work 24 hours a day, seven days a week. Management wants to evaluate the service maintenance cost, simulated breakdown cost, and total cost. Let’s use Monte Carlo simulation to analyze Three Hills system costs.

19. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-19 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Three Hills Power Generator Breakdown Times: Monte Carlo (continued) ½50.05 01 - 05 160.060.1106 - 11 1 ½160.160.2712 - 27 2330.330.6028 - 60 2 ½210.210.8181 - 81 3190.191.00 82 - 00 Time Between Breakdowns (Hrs) Number of Times Observed Probability Cumulative Probability Random Number Interval Steps 1-3: Determine probability, cumulative probability, and random number interval - BREAKDOWNS. Total 100 1.00

20. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-20 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Three Hills Power Generator Repair Times 1280.28 01 - 28 2520.520.8029 - 80 3 200.201.0081 - 00 Repair Time Required (Hours) Number of Times Observed Probability Cumulative Probability Random Number Interval Steps 1-3: Determine probability, cumulative probability, and random number interval - REPAIRS.

21. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-21 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Three Hills Power Generator Breakdown Times: Monte Carlo (continued) 15722:00 713:001 2171.53:30 6025:302 33625:30 7727:302 4722.58:00 49210:002 585311:00 76213:002 ::::::::: 148934:006:004228:004 15131.55:308:0052210:004.5 Simulation Trial Random Number Time Repair Can Begin Random Number Time Repair Ends Repair TimeNo. of hrs. Machine is down Time b/t Breakdowns Time of Breakdown Steps 4 & 5: Generate random numbers and simulate.

22. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-22 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Three Hills Power Generator Breakdown Times: Monte Carlo (continued) Cost Analysis: Service maintenance: = 34 hrs of worker service X $30 per hr = $1,020 Simulate machine breakdown costs: = 44 total hrs of breakdown X $75 lost per hr of downtime = $3,300 Total simulated maintenance cost of the current system: = service cost + breakdown costs = $1,020 + $3,300 = $4,320

23. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-23 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Operational Gaming Simulation Model Operational gaming refers to simulation involving competing players. Examples: Military games Business games

24. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-24 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Systems Simulation Model Systems simulation is similar to business gaming because it allows users to test various managerial policies and decision. It models the dynamics of large systems. Examples:  Corporate operating system  Urban government  Economic systems

25. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-25 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Econometric Simulation Models Income Tax Levels Corporate Tax Rates Interest Rates Government Spending Foreign Trade Policy Economic Model GNP Inflation Rates Unemployment Rates Monetary Supplies Population Growth Rates

26. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-26 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Verification and Validation Verification of simulation models involves determining that the computer model is internally consistent and follows the logic of the conceptual model. Validation is the process of comparing a simulation model to a real system to assure accuracy.

27. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-27 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 The Role of Computers in Simulation  General-purpose languages Visual Basic, C++, Java  Special-purpose simulation languages GPSS/H, SLAM II, SIMSCRIPT II.5 1. require less programming 2. more efficient and easier to check for errors 3. have random number generators built in  Pre-written simulation programs Extend, AutoMod, ALPHA/Sim, SIMUL8,STELLA, Arena, AweSim!, SLX, etc.

28. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-28 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Harry’s Auto Tires: Excel Demonstration Create lookup table using cumulative probability Generate a random number and look it up in the table

29. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-29 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Harry’s Auto Tires: Excel Demonstration Results