part © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in Business Analytics: Data Analysis and Chapter Decision Making 16 Simulation Models Introduction  Simulation can be used to analyze a wide variety of problems  The applications can be grouped into four general areas: Operations models Financial models Marketing models Games of chance  Simulation models can yield important insights in all of these areas © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Operations Models  In the operations of both manufacturing and service companies, there is likely to be uncertainty that can be modeled with simulation  Examples include:  Bidding for a government contract (uncertainty in the bids by competitors)  Warranty costs (uncertainty in the time until failure of an appliance)  Drug production (uncertainty in the yield and timing) © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Bidding for Contracts  In situations where a company must bid against competitors, simulation can often be used to determine the company’s optimal bid  Usually the company does not know what its competitors will bid, but it might have an idea about the range of the bids its competitors will choose  Simulation can be used to determine a bid that maximizes the company’s expected profit © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.1: Contract Bidding.xlsx (slide of 3)  Objective: To simulate the profit to Miller from any particular bid, and to see which bid amount is best  Solution: Miller Construction Company must decide whether to make a bid on a construction project  Miller assesses that the cost to complete the project has a triangular distribution with minimum, most likely, and maximum values $9000, $10,000, and $15,000  Miller also assesses that the cost to prepare the bid has a triangular distribution with parameters $300, $350, and $500  Four potential competitors are going to bid against Miller, and the lowest bid wins the contract  Miller believes that each potential competitor will bid, independently of the others, with probability 0.5  Miller also believes that each competitor’s bid will be a multiple of Miller’s most likely cost to complete the project, where this multiple has a triangular distribution with minimum, most likely, and maximum values 0.9, 1.3, and 1.8, respectively  If Miller decides to prepare a bid, its bid amount will be a multiple of $500 in the range $10,500 to $15,000 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.1: Contract Bidding.xlsx (slide of 3)  First, simulate the number of competitors who will bid and then simulate their bids  Then for any bid Miller makes, see whether Miller wins the contract, and if so, what its profit is  The simulation model is shown below © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.1: Contract Bidding.xlsx (slide of 3)  To run the simulation, set the number of iterations to 1000, and set the number of simulations to 10 because there are 10 bid amounts Miller wants to test  The summary results and a histogram of profit with a $13,000 bid are shown below © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Warranty Costs  When you buy a new product, it usually carries a warranty  A typical warranty might state that if the product fails within a certain period such as one year, you will receive a new product at no cost, and it will carry the same warranty  If the product fails after the warranty period, you have to bear the cost of replacing the product  Due to random lifetimes of products, the manufacturer needs a way to estimate the warranty costs of a product © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.2: Warranty Costs.xlsx (slide of 4)  Objective: To use simulation to estimate the number of replacements under warranty and the total NPV of profit from a given sale, using a discount rate of 8%  Solution: Yakkon Company sells a popular camera for $400  This camera carries a warranty such that if the camera fails within 1.5 years, the company gives the customer a new camera for free  If the camera fails after 1.5 years, the warranty is no longer in effect  Every replacement camera carries exactly the same warranty as the original camera, and the cost to the company of supplying a new camera is always $225 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.2: Warranty Costs.xlsx (slide of 4)  Yakkon estimates the distribution of time until failure from historical data, which indicates a rightskewed distribution, as shown in the figure to the right  This is a commonly used distribution called the gamma distribution  It is characterized by two parameters, α and β These determine its shape and location © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.8: Free Maintenance.xlsx (slide of 3)  Jamesons is hoping that the decrease in unit profit from the free maintenance agreement will be more than offset by the higher loyalty percentage Using a 15-year planning horizon, does the NPV of profits with a 10% discount rate confirm the company’s hopes?  Compare two simulations, one without free maintenance and one with it Because they are so similar, you can use RISKSIMTABLE to run both simulations  The completed simulation model is shown below © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.8: Free Maintenance.xlsx (slide of 3)  Set up @ RISK to run 1000 iterations and simulations, one for each maintenance decision to be tested Then run the simulation as usual  The summary measures for the two simulations are shown below © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Marketing and Sales Models  The next example is a model for marketing and selling condos  In this model, the main issue is the timing of sales  A deterministic model of this timing can provide very misleading results © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.9: Selling Condos.xlsx (slide of 4)  Objective: To develop a simulation model that allows us to see how the uncertain timing affects the monetary outcomes for Pletcher, and to compare this simulation model to a deterministic model with no uncertainty about the timing of sales  Solution: Blackstone Development Company has just finished building 12 high-end condos, each priced at $300,000  Blackstone has hired Pletcher Marketing to market and sell these condos  Pletcher will incur all of the marketing and maintenance costs, assumed to be $800 per unsold condo per month, and it will receive a 10% commission ($30,000) from Blackstone at the time of each condo sale  Because Blackstone wants these condos to be sold in a timely manner, it has offered Pletcher a $200,000 bonus at the end of the first year if at least half of the condos have been sold, and an extra $500,000 bonus at the end of the second year if all of the condos have been sold  Pletcher estimates that it can sell five condos per month on average, so it should be able to collect the bonuses However, it also realizes that there is uncertainty about the number of sales per month © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.9: Selling Condos.xlsx (slide of 4)  To make a fair comparison between a deterministic model with five sales per month and a simulation model with uncertainty in the timing of sales, we need a discrete distribution for monthly sales that has mean  Use the Poisson distribution, which is discrete and has only one parameter, the mean  As shown below, the Poisson distribution with mean has virtually no probability of values larger than 15 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.9: Selling Condos.xlsx (slide of 4)  The deterministic model (not shown) sells all condos by the end of year 2, receives both bonuses, and realizes an NPV (including bonuses) of $2,824,333—but it is not very realistic  The simulation model, modeled through 40 months, is shown below © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.9: Selling Condos.xlsx (slide of 4)  Set @RISK to run 1000 iterations for a single simulation Then run the simulation in the usual way  Distributions of the three outputs are shown below © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Simulating Games of Chance  It is instructive to see how simulation can be used to analyze games of chance, including sports contests  Many analysts refer to Monte Carlo simulation, which comes from the gambling casinos of Monte Carlo © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Simulating the Game of Craps  Most games of chance are great candidates for simulation because they are driven by randomness  One such game is the game of craps, which is played as follows:  A player rolls two dice and observes the sum of the two sides turned up  If the sum is or 11, the player wins immediately  If the sum is 2, 3, or 12, the plays loses immediately  If the sum is any other number, that number becomes the player’s point  Then the dice are thrown repeatedly until the sum is the player’s point or  If the player’s point occurs before a 7, the player wins  If a occurs before the point, the player loses © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.10: Craps.xlsx  Objective: To use simulation to find the probability of winning a single game of craps  Solution: There are no input numbers, only the rules of the game  The simulation model, shown below, is for a single game  Simulate 40 tosses and use only those that are necessary to determine the outcome of a single game  Set the number of iterations to 10,000 (to obtain a very accurate answer) and the number of simulations to Then run the simulation as usual  The estimate of the probability of winning is shown in cell J8 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.11: March Madness Men 2009.xlsm (slide of 3)  Objective: To simulate the NCAA basketball tournament and keep a tally on the number of times each team wins the tournament  Solution: At the time this example was written, the most recent NCAA Basketball Tournament was the 2013 tournament  On the Sunday evening when the 68-team field was announced, all that was known were the pairings (which teams would play which other teams) and the team ratings, based on Jeff Sagarin’s rating system, portions of which are shown to the right  Sagarin predicts that the actual point differential in a game will be the difference between the ratings of the two teams  Assume that the actual point differential is normally distributed with mean equal to Sagarin’s prediction and standard deviation 10  If the actual point differential is positive, team A wins If it is negative, team B wins © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.11: March Madness Men 2009.xlsm (slide of 3)  A portion of the simulation model sheet is shown below (Of course, Florida did not win the tournament; this figure just shows one possible scenario.) © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Example 16.11: March Madness Men 2009.xlsm (slide of 3)  Some of the results based on 1000 iterations are shown below © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part An Automated Template for @RISK Models (slide of 2)  The macro language for Excel®, VBA, can be used to automate @RISK  An automated template that can be used for any simulation is shown below (See the file Simulation Template.xlsm.) © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part An Automated Template for @RISK Models (slide of 2)  The text boxes provide the motivation and instructions, but there are two basic ideas:  First, you often have particular inputs you would like to vary in a sensitivity analysis  Once you specify these in the Inputs section, the program will run a separate simulation for each combination of the input values  Second, you typically have outputs that you want to summarize in certain ways  The Outputs section lets you specify the summary measures you want for each of your outputs  The program then lists the results on separate worksheets  It is still up to you to develop the logic of the simulation, but you no longer need to worry about RISKSIMTABLE functions or statistical functions © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part ... potential competitor will bid, independently of the others, with probability 0.5  Miller also believes that each competitor’s bid will be a multiple of Miller’s most likely cost to complete the project,... this multiple has a triangular distribution with minimum, most likely, and maximum values 0.9, 1.3, and 1.8, respectively  If Miller decides to prepare a bid, its bid amount will be a multiple of... duplicated, or posted to a publicly accessible website, in whole or in part Example 16. 2: Warranty Costs.xlsx (slide of 4)  The simulation model is shown below © 2015 Cengage Learning All Rights