Session 4a

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Session 4a
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Overview

• Marketing Simulation Models
• New Product Development Decision
• Uncertainty about competitor behavior
• Uncertainty about customer behavior
• Market Shares
• Modeling the dynamics of a 3-supplier market
• Customer loyalty
• Benefits of quality improvement
• Pricing Strategy
• Retailer game
• Integrating simulation with other tools

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Marketing Example New Product Development
Decision
Cavanaugh Pharmaceutical Company (CPC) has
enjoyed a monopoly on sales of its popular
antibiotic product, Cyclinol, for several years.
Unfortunately, the patent on Cyclinol is due to
expire. CPC is considering whether to develop a
new version of the product in anticipation that
one of CPCs competitors will enter the market
with their own offering. The decision as to
whether or not to develop the new antibiotic
(tentatively called Minothol) depends on several
assumptions about the behavior of customers and
potential competitors. CPC would like to make the
decision that is expected to maximize its profits
over a ten-year period, assuming a 15 cost of
capital.
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Customer Demand Analysts estimate that the
average annual demand over the next ten years
will be normally distributed with a mean of 40
million doses and a standard deviation of 10
million doses, as shown below. This demand is
believed to be independent of whether CPC
introduces Minothol or whether Cyclinol/Minothol
has a competitor.
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CPCs market share is expected to be 100 of
demand, as long as there is no competition from
AMI. In the event of competition, CPC will still
enjoy a dominant market position because of its
superior brand recognition. However, AMI is
likely to price its product lower than CPCs in
an effort to gain market share. CPCs best
analysis indicates that its share of total sales,
in the event of competition, will be a function
of the price it chooses to charge per dose, as
shown below. The Cyclinol product at
7.50 would only retain a 38.1 market share,
whereas the Minothol product at 6.00 would have
a 55.0 market share.
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Questions What is the best decision for CPC, in
terms of maximizing the expected value of its
profits over then next ten years? What is the
least risky decision, using the standard
deviation of the ten-year profit as a measure of
risk? What is the probability that introducing
Minothol will turn out to be the best decision?
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U(0, 1) (whether or not AMI enters market)
N(40, 10) (Total market demand)
Income statement-like calculations for each of
four scenarios
3 Forecasts NPV in millions for each
decision Yes/No New Product Better
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Example Market Shares
Suppose that each week every family in the United
States buys a gallon of orange juice from company
A, B, or C. Let PA denote the probability that
a gallon produced by company A is of
unsatisfactory quality, and define PB and PC
similarly for companies B and C.
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If the last gallon of juice purchased by a family
is satisfactory, then the next week they will
purchase a gallon of juice from the same company.
If the last gallon of juice purchased by a
family is not satisfactory, then the family will
purchase a gallon from a competitor. Consider a
week in which A families have purchased juice A,
B families have purchased juice B, and C families
have purchased juice C.
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Assume that families that switch brands during a
period are allocated to the remaining brands in a
manner that is proportional to the current market
shares of the other brands. Thus, if a customer
switches from brand A, there is probability B/(B
C) that he will switch to brand B and
probability C/(B C) that he will switch to
brand C. Suppose that 1,000,000 gallons of orange
juice are purchased each week. After a year, what
will the market share for each firm be? Assume PA
0.10, PB 0.15, and Pc 0.20.
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Now recall that a binomial random variable X is
an integer between 0 and n, viewed as the number
of successes out of n trials. The binomial
distribution assumes that there is a probability
p of a success on any one trial, and that all
trials are independent of each other. In this
case, X is the number of gallons that are bad,
n is the total number of gallons purchased of a
particular brand, and p is the probability that
any one gallon is bad.
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Note that we have used dollar signs in the cell
references, so this can be copied
down to the rest of the assumption cells in
column H.

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We can use the binomial distribution again here.
The number of people who switch from Brand A to
Brand B in any given week will be a binomial
random variable, with n equal to the total number
of people who abandon Brand A in that week, and p
equal to the proportion of the non-Brand A market
held by Brand B in that week, or B/(B C).
(Recall that the problem asks us to Assume
that families that switch brands during a period
are allocated to the remaining brands in a manner
that is proportional to the current market shares
of the other brands.)
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Well set up the ns for these binomial random
variables in columns K, L, and M, using MAX
functions as before to make sure that they never
go below 1. In column N we calculate the
proportion of non-A customers who buy B in the
current week, once again using a MAX function to
make sure this is never zero.
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The number of A customers who switch from A to
Brand C is calculated in column P it is simply
the difference between K7 and O7. We model the
switching behavior of former B customers in
columns Q, R, and S, and former C customers in
columns T, U, and V. Finally, the various
numbers of switchers are taken into account for
the start of the next week in columns B, C, and
D. All of the binomial assumptions (columns H,
I, J, O, R, and U) get copied down through row
58, so we can model a 52-week year.
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Suppose a 1 increase in market share is worth
10,000 per week to company A. Company A
believes that for a cost of 1 million per year
it can cut the percentage of unsatisfactory juice
cartons in half. Is this worthwhile? (Use the
same values of PA, PB, and PC as in part a.)
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There are a number of ways to approach this kind
of issue. One elegant way is to run two
simulations simultaneously, in which the only
difference is (in this case) the different value
for PA. Well run the same model as before, but
add to it, in parallel, a second model in which
PA 0.05 instead of 0.10. The old model is in a
worksheet called Part (a) and the new model is in
a worksheet called Part (b).
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Retailer
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Retailer

• Statistical analysis of historical data
• Optimization with respect to expected value
• Fine-tuning of a simple strategy

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Statistical Analysis

• What have been the historical patterns?
• Sales in the first week
• Sales in subsequent weeks
• Customer responses to price cuts
• How stable have these patterns been?

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Sales in the First Week
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1st-week sales Maybe a normal distribution
(69.7, 21.6) Subsequent weeks 3-factor model
to forecast expected sales assume errors are
normal (0, 46.0)These are random factors what
about the pricing decisions?
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Optimization

• A quick introduction to Solver
• Formulation
• Decision Variables
• Objective Function
• Constraints
• Solving the problem
• Interpreting the results

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Decision Variables

• The key choices to be made
• In this case how many weeks at each price point
• Four price points four decision variables

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Objective Function

• Some quantitative measure we want to maximize or
  minimize
• In this case maximize revenue
• Revenue here is the sum of regular sales at
  various prices over 15 weeks, plus any salvage
  value at the end of the season

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Constraints

• Factors that prevent us from earning infinite
  revenue
• In this case
• A limited season of 15 weeks
• A limit of 2000 units we can sell
• Must start out at 60 for at least one week
• Decision variables are integers (can only change
  prices once per week

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The initial sales level in C6 is arbitrary well
eventually try a wide range of values Notice that
this is based on expected values no randomness
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Solver finds a solution that says If initial
sales are 125 units at 60, then the best
strategy is to sell for 12 weeks at 60 and 3
weeks at 54
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Repeated runs of Solver give us strategies for a
range of demand levels. Notice that we never cut
the price to 36. Why? What about randomness?
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Fine-tuning a Simple Strategy

• A simulation of the strategy in action
• Using a multipier
• Choosing the best multiplier
• Testing the strategy

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Fine-tuning a Simple Strategy

• A simulation of the strategy in action
• Using a multipier
• Choosing the best multiplier
• Testing the strategy

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Simulated 15-week Retailer game
Choice of strategy (big IF statement)
Score-keeping
Parameters for 1st-week sales
Using the multiplier to fine-tune the Solver
results
Strategies
Regression results used to calculate expected
values in F2F16
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These simulation results seem to suggest the 0.9
multiplier gives the best strategy on the
average, in the long run. In other words, the
expected value optimal solutions from Solver
are slightly different from the optimal
stochastic solutions. Why?
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• Takeaways from this analysis
• A simple strategy that a manager can implement
  based on week one demand to plan the rest of the
  season
• A tool for exploring possible strategies and for
  management training
• Use of multiple quantitative tools statistics,
  optimization, simulation (both Crystal Ball and
  Retailer)
• Timing of price cuts (is it better to cut too
  early, or too late?)
• Identification of price levels that are never
  optimal

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Summary

• Marketing Simulation Models
• New Product Development Decision
• Uncertainty about competitor behavior
• Uncertainty about customer behavior
• Market Shares
• Modeling the dynamics of a 3-supplier market
• Customer loyalty
• Benefits of quality improvement
• Pricing Strategy
• Retailer game
• Integrating simulation with other tools