EXAMPLE 11.2 WARRANTY COSTS FOR A CAMERA The 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 If the camera fails after 1.5 years, the warranty is no longer in effect.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. Use simulation to esti- mate, for a given sale, the number of replacements under warranty and the NPV of profit from the sale, using a discount rate of 8%. Objective To use simulation to estimate the number of replacements under warranty and the total NPV of profit from a given sale. Where Do the Numbers Come From? The warranty information is a policy decision made by the company. The hardest input to estimate is the probability distribution of the lifetime of the product. We discuss this next. Solution The gamma distribution is a The only randomness in this problem concerns the time until failure of a new camera. Yakkon could estimate the distribution of time until failure from historical data. This popular distribution, especially when you want a right-skewed distribution of a nonnegative quantity. would probably indicate a right-skewed distribution, as shown in Figure 11.5. If you look through the list of distributions available in @RISK under Define Distributions, you will see several with this same basic shape. The one shown in Figure 11.5 is a commonly used distribution called the gamma distribution. We will use a gamma

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 65P

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Question

See how sensitive the results in Example 11.2 are to
the following changes. For each part, make the change
indicated, run the simulation, and comment on any
differences between your outputs and the outputs in
the example.
a. The cost of a new camera is increased to $500.
b. The warranty period is decreased to one year.
c. The terms of the warranty are changed. If the camera fails within one year, the customer gets
a new camera for free. However, if the camera
fails between 1 year and 1.5 years, the customer
pays a pro rata share of the new camera, increasing
linearly from 0 to full price. For example, if it fails at 1.2 years, which is 40% of the way
from 1 to 1.5, the customer pays 40% of the
full price.
d. The customer pays $50 up front for an extended
warranty. This extends the warranty to three years.
This extended warranty is just like the original,
so that if the camera fails within three years, the
customer gets a new camera for free.

EXAMPLE
11.2 WARRANTY COSTS FOR A CAMERA
The 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. Use simulation to esti-
mate, for a given sale, the number of replacements under warranty and the NPV of profit
from the sale, using a discount rate of 8%.
Objective To use simulation to estimate the number of replacements under warranty and
the total NPV of profit from a given sale.
Where Do the Numbers Come From?
The warranty information is a policy decision made by the company. The hardest input
to estimate is the probability distribution of the lifetime of the product. We discuss
this next.
Solution
The gamma
distribution is a
The only randomness in this problem concerns the time until failure of a new camera.
Yakkon could estimate the distribution of time until failure from historical data. This
popular distribution,
especially when you
want a right-skewed
distribution of a
nonnegative quantity.
would probably indicate a right-skewed distribution, as shown in Figure 11.5. If you
look through the list of distributions available in @RISK under Define Distributions,
you will see several with this same basic shape. The one shown in Figure 11.5 is
a commonly used distribution called the gamma distribution. We will use a gamma

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