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

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-2 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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.

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-3 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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 15-4 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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 15-5 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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:

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-6 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-7 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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 15-8 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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 15-9 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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

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

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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… Demand Frequency Probability for Tires = 10/200

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Harry’s Auto Tires: Monte Carlo Example ( continued) Demand Frequency Probability Cumulative Probability Random Number Interval 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

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Harry’s Auto Tires: Monte Carlo Example (continued) Step 4: Generate random numbers.

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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: Simulated demand: TiresInterval of DemandedRandom Numbers

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 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 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Three Hills Power Generator Breakdown Times: Monte Carlo (continued) ½ ½ ½ 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

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Three Hills Power Generator Repair Times 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.

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Three Hills Power Generator Breakdown Times: Monte Carlo (continued) 15722:00 713: : : : : : : : :002 ::::::::: :006:004228: :308: :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.

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

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