Prepared by Lee Revere and John Large Chapter 15 Simulation Modeling Prepared by Lee Revere and John Large To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-1

Learning Objectives Students will be able to: Tackle a wide variety of problems by simulation. Understand the seven steps of conducting a simulation. Explain the advantages and disadvantages of simulation. Develop random number intervals and use them to generate outcomes. Understand the alternative simulation packages available commercially. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-2

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 To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-3

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 To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-4

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

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 Action To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-6

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 To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-7

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 for Management, 9e by Render/Stair/Hanna 15-8

Simulation Models Categories Monte Carlo consumer demand inventory analysis queuing problems maintenance policy Operational Gaming Systems Simulation To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-9

Monte Carlo Simulation The Monte Carlo simulation is applicable to business problems that exhibit chance, or uncertainty. For example: Inventory demand Lead time for inventory Times between machine breakdowns Times between arrivals Service times Times to complete project activities Number of employees absent To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-10

Monte Carlo Simulation (continued) The basis of the Monte Carlo simulation is experimentation on the probabilistic elements through random sampling. It is used 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 trials To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-11

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… 10 0.05 1 20 0.10 2 40 0.20 3 60 0.30 4 5 30 0.15 Demand Frequency Probability for Tires = 10/200 200 1.00 To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-12

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% To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-13

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% To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-14

Harry’s Auto Tires: Monte Carlo Example (continued) Step 3: Establish an interval of random numbers. Demand Frequency Probability Cumulative Probability Random Number Interval 10 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 0.85 66 - 85 5 30 1.00 86 - 00 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 To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-15

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

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 36 - 65 4 66 - 85 5 86 - 100 2 3 1 Random number: 52 06 50 88 53 30 10 47 99 37 Simulated demand: 3 1 3 5 3 2 1 3 5 3 To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-17

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. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-18

Three Hills Power Generator Breakdown Times: Monte Carlo (continued) Steps 1-3: Determine probability, cumulative probability, and random number interval - BREAKDOWNS. ½ 5 0.05 01 - 05 1 6 0.06 0.11 06 - 11 1 ½ 16 0.16 0.27 12 - 27 2 33 0.33 0.60 28 - 60 2 ½ 21 0.21 0.81 81 - 81 3 19 0.19 1.00 82 - 00 Time Between Breakdowns (Hrs) Number of Times Observed Probability Cumulative Probability Random Number Interval Total 100 1.00 To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-19

Three Hills Power Generator Repair Times Steps 1-3: Determine probability, cumulative probability, and random number interval - REPAIRS. 1 28 0.28 01 - 28 2 52 0.52 0.80 29 - 80 3 20 0.20 1.00 81 - 00 Repair Time Required (Hours) Number of Times Observed Probability Cumulative Probability Random Number Interval To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-20

Three Hills Power Generator Breakdown Times: Monte Carlo (continued) Steps 4 & 5: Generate random numbers and simulate. Machine is down No. of hrs. Breakdowns Time b/t Breakdown Time of Time Repair Can Begin Time Repair Ends Simulation Trial Random Number Random Number Repair Time 1 57 2 2:00 7 3:00 17 1.5 3:30 60 5:30 3 36 77 7:30 4 72 2.5 8:00 49 10:00 5 85 11:00 76 13:00 : 14 89 4:00 6:00 42 15 13 52 4.5 To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-21

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 To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-22

Operational Gaming Simulation Model Operational gaming refers to simulation involving competing players. Examples: Military games Business games To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-23

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 To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-24

Econometric Simulation Models Foreign Trade Policy Government Spending Corporate Tax Rates Income Tax Levels Interest Rates Economic Model GNP Inflation Rates Unemployment Rates Monetary Supplies Population Growth Rates To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-25

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. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-26

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. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-27

Harry’s Auto Tires: Excel Demonstration Create lookup table using cumulative probability Generate a random number and look it up in the table To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-28

Harry’s Auto Tires: Excel Demonstration Results To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-29