Introduction to management science 10e by bernard taylor chapter 14

Simulation Chapter 14 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14-1 Chapter Topics ■The Monte Carlo Process ■Computer Simulation with Excel Spreadsheets ■Simulation of a Queuing System ■Continuous Probability Distributions ■Statistical Analysis of Simulation Results ■Crystal Ball ■Verification of the Simulation Model ■Areas of Simulation Application Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14-2 Overview ■ Analogue simulation replaces a physical system with an analogous physical system that is easier to manipulate ■ In computer mathematical simulation a system is replaced with a mathematical model that is analyzed with the computer ■ Simulation offers a means of analyzing very complex systems that cannot be analyzed using the other management science techniques in the text Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14-3 Monte Carlo Process ■ A large proportion of the applications of simulations are for probabilistic models ■ The Monte Carlo technique is defined as a technique for selecting numbers randomly from a probability distribution for use in a trial (computer run) of a simulation model ■ The basic principle behind the process is the same as in the operation of gambling devices in casinos (such as those in Monte Carlo, Monaco) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14-4 Monte Carlo Process Use of Random Numbers (1 of 10)  In the Monte Carlo process, values for a random variable are generated by sampling from a probability distribution  Example: ComputerWorld demand data for laptops selling for $4,300 over a period of 100 weeks Table 14.1 Probability Distribution of Demand for Laptop PC’s Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14-5 Monte Carlo Process Use of Random Numbers (2 of 10)  The purpose of the Monte Carlo process is to generate the random variable, demand, by sampling from the probability distribution P(x)  The partitioned roulette wheel replicates the probability distribution for demand if the values of demand occur in a random manner  The segment at which the wheel stops Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14-6 Monte Carlo Process Use of Random Numbers (3 of 10) Figure 14.1 A Roulette Wheel for Demand Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14-7 Monte Carlo Process Use of Random Numbers (4 of 10) When the wheel is spun, the actual demand for PCs is determined by a number at rim of the wheel Figure 14.2 umbered Roulette Wheel Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14-8 Monte Carlo Process Use of Random Numbers (5 of 10) Table 14.2 Generating Demand from Random Numbers Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14-9 Monte Carlo Process Use of Random Numbers (6 of 10) Select number from a random number table: Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Table 14.3 Numbers Delightfully Random 14- Crystal Ball Simulation of Profit Analysis Model (11 of 15) Exhibit 14.19 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14- Crystal Ball Simulation of Profit Analysis Model (12 of 15) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Exhibit 14.20 14- Crystal Ball Simulation of Profit Analysis Model (13 of 15) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Exhibit 14.21 14- Crystal Ball Simulation of Profit Analysis Model (14 of 15) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Exhibit 14.22 14- Crystal Ball Simulation of Profit Analysis Model (15 of 15) Exhibit 14.23 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14- Verification of the Simulation Model (1 of 2) ■ Analyst wants to be certain that model is internally correct and that all operations are logical and mathematically correct ■ Testing procedures for validity:  Run a small number of trials of the model and compare with manually derived solutions  Divide the model into parts and run parts separately to reduce complexity of checking  Simplify mathematical relationships (if possible) for easier testing  Compare results with actual real-world Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14- Verification of the Simulation Model (2 of 2) ■ Analyst must determine if model starting conditions are correct (system empty, etc) ■ Must determine how long model should run to insure steady-state conditions ■ A standard, fool-proof procedure for validation is not available ■ Validity of the model rests ultimately on the expertise and experience of the model developer Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14- Some Areas of Simulation Application ■Queuing ■Inventory Control ■Production and Manufacturing ■Finance ■Marketing ■Public Service Operations ■Environmental and Resource Analysis Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14- Example Problem Solution (1 of 6) Willow Creek Emergency Rescue Squad Minor emergency requires two-person crew Regular emergency requires a three-person crew Major emergency requires a five-person crew Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14- Example Problem Solution (2 of 6) Distribution of number of calls per night and emergency type: Manually simulate 10 nights of calls Determine average number of calls each night Determine maximum number of crew members that might be needed on given night Copyright © 2010 Pearson Education, Inc Publishingany as Prentice Hall 14- Example Problem Solution (3 of 6) Step 1: Develop random number ranges for the probability distributions Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14- Example Problem Solution (4 of 6) Step 2: Set Up a Tabular Simulation (use second column of random numbers in Table 14.3) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14- Example Problem Solution (5 of 6) Step continued: Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14- Example Problem Solution (6 of 6) Step 3: Compute Results: average number of minor emergency calls per night = 10/10 =1.0 average number of regular emergency calls per night =14/10 = 1.4 average number of major emergency calls per night = 3/10 = 0.30 If calls of all types occurred on same night, maximum number of squad members required would be 14 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14- Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14- ... for laptops selling for $4,300 over a period of 100 weeks Table 14. 1 Probability Distribution of Demand for Laptop PC’s Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14- 5... Publishing as Prentice Hall Exhibit 14. 2 14- Simulation with Excel Spreadsheets (3 of 3) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Exhibit 14. 3 14- Computer Simulation with... two laptops each week (2 of 2) Exhibit 14. 5 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 14- Simulation of a Queuing System Burlingham Mills Example (1 of 3) Table 14. 5 Distribution