Business analytics data analysis and decision making 5th by wayne l winston chapter 16

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 1 of 3  Objective: To simulate the p

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Simulation Models 16

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 Simulation can be used to analyze a wide variety of problems.

 The applications can be grouped into four general areas:

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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)

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 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.

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Example 16.1:

Contract Bidding.xlsx (slide 1 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

 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.

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 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.

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Example 16.1:

 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.

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 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.

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Example 16.2:

Warranty Costs.xlsx (slide 1 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.

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 Yakkon estimates the distribution

of time until failure from historical

data, which indicates a

right-skewed 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.

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Example 16.2:

 The simulation model is shown below.

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 The @RISK setup is typical Run 1000 iterations of a single simulation (because

there is no RISKSIMTABLE function).

 The @RISK summary statistics and histograms for the two outputs are shown below.

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Drug Production with Uncertain Yield

 In many manufacturing settings, products are produced in batches, and

the usable yields from these batches are uncertain

 This is particularly true in the drug industry.

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Drug Production.xlsx (slide 1 of 3)

 Objective: To use simulation to determine when Wozac should begin production

for this order so that there is a high probability of completing it by the due date.

 Solution: Wozac Company has recently accepted an order from its best

customer for 8000 ounces of a new miracle drug, and Wozac wants to plan its production schedule to meet the customer’s promised delivery date of

December 1.

 The drug must be produced in batches, and there is uncertainty in the time

required to produce a batch, which could be anywhere from 5 to 11 days This uncertainty is described by the discrete distribution in the table below.

 Wozac believes the yield can be modeled by a triangular distribution with

minimum, most likely, and maximum values equal to 600, 1000, and 1100

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Example 16.3:

 Simulate successive batches and keep a running total of the usable ounces

obtained so far IF functions can then be used to check whether the order is

complete or another batch is required.

 Keep track of the days required to produce all of the batches needed to meet the order and then “back up” to see when production must begin to meet the due date.

 The completed model appears below.

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 Set the number of iterations to 1000 and the number of simulations to

1, and then run the simulation as usual.

 After running the simulation, obtain the histograms of the number of batches required and the number of days required, as shown below.

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Financial Models

 There are many financial applications where simulation can be

applied.

 Future cash flows, future stock prices, and future interest rates are some of

the many uncertain variables financial analysts must deal with.

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 Many companies use simulation in their capital budgeting and financial planning processes

 Simulation can be used to model the uncertainty associated with future cash flows, including questions such as:

 What are the mean and variance of a project’s net present value (NPV)?

 What is the probability that a project will have a negative NPV?

 What are the mean and variance of a company’s profit during the next fiscal year?

 What is the probability that a company will have to borrow more than $2 million during the next year?

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Example 16.4:

New Car Development.xlsx (slide 1 of 3)

 Objective: To simulate the cash flows from the new car model, from

the development time to the end of its life cycle, so that GF can

estimate the NPV of after-tax cash flows from this car.

 Solution: General Ford (GF) Auto Corporation is developing a new

model of compact car.

 This car is assumed to generate sales for the next five years.

 GF has gathered the following information about the car:

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 The model is like most financial multiyear spreadsheet models

 The completed model extends several years to the right, but most of the work is for the first year or two.

 From that point, copy to the other years to complete the model.

 The completed model for GF appears below.

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Example 16.4:

New Car Development.xlsx (slide 3 of 3)

 Set the number of iterations to 1000 and the number of

simulations to 1, and then run the simulation as usual.

 After running @RISK, obtain the histogram shown below.

 The second slider has been positioned at its default 5th percentile setting Financial analysts often call this percentile the value at risk at the 5% level , or VaR 5% , because it indicates nearly the worst possible outcome.

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 All companies track their cash balance over time

 As specific payments come due, companies sometimes need to take out short-term loans to keep a minimal cash balance.

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Example 16.5:

Cash Balance.xlsx (slide 1 of 3)

 Objective: To simulate Entson’s cash flows and the loans the company must

take out to meet a minimum cash balance.

 Solution: Entson Company believes that its monthly sales from November of

the current year to July of next year are normally distributed with the means and standard deviations given in the table below.

 Each month Entson incurs fixed costs of $250,000.

 In March, taxes of $150,000 and in June taxes of $50,000 must be paid.

 Dividends of $50,000 must also be paid in June.

 Entson estimates that its receipts in a given month are a weighted sum of sales from the current month, the previous month, and two months ago, with weights 0.2, 0.6, and 0.2:

 Materials and labor needed to produce a month’s sales must be purchased one month in advance, and the cost of these averages to 80% of the product’s sales.

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 At the beginning of January,

Entson has $250,000 in

cash, and the company

wants to ensure that each

month’s ending cash

balance never falls below

$250,000

 This means that Entson

might have to take out

short-term (one-month)

loans The interest rate on a

short-term loan is 1% per

month.

 At the beginning of each

month, Entson earns

interest of 0.5% on its cash

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Example 16.5:

 Set the number of iterations to 1000 and the number of simulations to 1 Then run the simulation in the usual way.

 After running the simulation, obtain the summary results and the summary trend chart shown below.

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 Individual investors typically want to choose investment strategies that meet some pre-specified goal, such as a retirement goal.

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Example 16.6:

Retirement Planning.xlsx (slide 1 of 3)

 Objective: To use simulation to estimate the value of Sally’s future investments, in

today’s dollars, from several investment strategies in T-bills, T-bonds, and stocks.

 Solution: At age 25, Sally Evans has 40 years until retirement She plans to invest

$1000 at the beginning of each of the next 40 years.

 Each year, she plans to put fixed percentages—the same each year—of this $1000 into stocks, Treasury bonds (T-bonds), and Treasury bills (T-bills) These

percentages are called investment weights.

 She has the historical data shown in the table below (with some rows hidden).

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 Think of each historical year as

a possible scenario, where the

scenario specifies the returns

and inflation factor for that

year.

 Then for any future year,

randomly choose one of these

scenarios.

 Because more recent scenarios

should have a greater chance

of being chosen, give a weight

to each scenario, starting with

1 for 2007.

 Then the weight for any year is

a damping factor multiplied by

the weight from the next year.

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Example 16.6:

Retirement Planning.xlsx (slide 3 of 3)

 Set the number of iterations to 1000 and the number of simulations to 3 (one for each set of investment weights to be tested) Then run the simulation as usual.

 Summary results and the histogram for simulation 1 (put 80% in stocks) is shown below.

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 There are plenty of opportunities for marketing departments to use simulation.

 They face uncertainty in the brand-switching behavior of customers, the

entry of new brands into the market, customer preferences for different attributes of products, the effects of advertising on sales, and so on.

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Models of Customer Loyalty

 What is a loyal customer worth to a company? This is an extremely important question for companies.

 Companies know that if customers become dissatisfied with the

company’s product, they are likely to switch and never return.

 Marketers refer to this customer loss as churn .

 The loss in profit from churn can be large, particularly because

long-standing customers tend to be more profitable in any given year than new customers.

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Customer Loyalty.xlsx (slide 1 of 3)

 Objective: To use simulation to find the

NPV of a customer and to see how this

varies with the retention rate.

 Solution: CCAmerica is a credit card

company.

 The first year a customer signs up for

service typically results in a loss to the

company because of various administrative

expenses.

 However, after the first year, the profit from

a customer is typically positive, and this

profit tends to increase through the years.

 The company has estimated the mean profit

from a typical customer to be as shown in

column B to the right.

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Example 16.7:

Customer Loyalty.xlsx (slide 2 of 3)

 At the end of each year, the customer leaves the company, never to return, with

probability 0.15, the churn rate, or stays with probability 0.85, the retention rate.

 The company wants to estimate the NPV of the net profit from any such

customer who has just signed up for service at the beginning of year 1, at a

discount rate of 15%, assuming that the cash flow occurs in the middle of the year It also wants to see how sensitive this NPV is to the retention rate.

 Keep simulating profits for the customer until the customer churns

 The simulation model is shown below It simulates 30 years of potential profits, but this could be varied.

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