Example 7.4Selecting the Best Marketing Strategy at the Acme Company

Multistage Decision Problems

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Objective

To construct a multistage decision tree model to identify the marketing contingency plan that maximizes Acme’s expected profit.

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Background Information

Acme Company is trying to decide whether to market a new product.

As in many new-product situations, there is much uncertainty about whether the product will “catch-on”.

Acme believes that it would be prudent to introduce the product to a test market first.

Thus the first decision is whether to conduct the test market.

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Background Information -- continued Acme has determined that the fixed cost of the test

market is $3 million.

If they proceed with the test, they must then wait for the results to decide if they will market the product nationally at a fixed cost of $90 million.

If the decision is not to conduct the test market, then the product can be marketed nationally with no delay.

Acme’s unit margin, the difference between its selling price and its unit variable cost, is $18 in both markets.

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Background Information -- continued

Acme classifies the results in either market as great, fair or awful.

Each of these has a forecasted total units sold as (in 1000s of units) 200, 100 and 30 in the test market and 6000, 3000 and 900 for the national market.

Based on previous test markets for similar products, it estimates that probabilities of the three test market outcomes are 0.3, 0.6 and 0.1.

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Background Information -- continued Then based on historical data on products that were

tested then marketed nationally, it assesses the probabilities of the national market outcomes given each test market outcome.

– If the test market is great, the probabilities for the national market are 0.8, 0.15, and 0.05.

– If the test market is fair. then the probabilities are 0.3, 0.5, 0.2.

– If the test market is awful, then the probabilities are 0.05, 0.25, and 0.7.

Note how the probabilities of the national market mirrors those of the test market.

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Elements of Decision Problem

The three basic elements of this decision problem are:

– the possible strategies

– the possible outcomes and their probabilities

– the value model

The possible strategies are clear:

– Acme must first decide whether to conduct the test market.

– Then it must decide whether to introduce the product nationally.

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Contingency Plan

If Acme decides to conduct a test market they will base the decision to market nationally on the test market results.

In this case its final strategy will be a contingency plan, where it conducts the test market, then introduces the product nationally if it receives sufficiently positive test market results and abandons the product if it receives negative test market results.

The optimal strategies from many multistage decision problems involve similar contingency plans.

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Conditional Probabilities - continued The probabilities of the test market outcomes and

conditional probabilities of national market outcomes given the test market outcomes are exactly the ones we need in the decision tree.

However, suppose Acme decides not to run a test market and then decides to market nationally. Then what are the probabilities of the national market outcomes? We cannot simply assess three new probabilities.

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Conditional Probabilities - continued These probabilities are implied by the given

probabilities. They are implied by the given probabilities. This follows from the rule of conditional probability.

If we let T1, T2, and T3 be the test market outcomes and N be any national market outcomes, then by the addition rule of probability and the conditional probability formulaP(N) = P(N and T1) + P(N and T2) and P(N and T3) =P(N|T1)P(T1) + P(N|T2)P(T2) + P(N|T3)P(T3)

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Conditional Probabilities - continued These equivalent equations are sometimes called the

law of probabilities.

We determine the probabilities as 0.425 for a great market, 0.37 for a fair market and 0.205 for an awful market.

The monetary values are the fixed costs of test marketing or marketing nationally and these are incurred as soon as the “go ahead” decisions are made.

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ACME.XLS

This file contains the inputs for the decision tree.

The only calculated values in this spreadsheet are in row 28, which follow from the equation. The formula in cell B28 is =SUMPRODUCT(B22:B24,$B$16:$B$18)then it is copied across row 28.

The creation of the tree is then straightforward to build and label.

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Inputs

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Interpreting the Tree

The interpretation of the tree is fairly straightforward if we realize that each value just below each node name is an EMV.

Each of these EMVs have been calculated with the folding back procedure.

We can also see Acme’s optimal strategy by following the “TRUE” branches from left to right.

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Optimal Strategy

Acme should first run a test market and if the results are great then they should market it nationally.

If the test results are fair or awful they should abandon the product.

The risk profile (created by clicking on PreceisionTree’s “staircase” button and selecting Statistics and Risk Profile options) that there is a small chance of two possible large losses, there is a 70% chance of a moderate loss and there is a 24% chance of a smaller loss.

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Optimal Strategy -- continued

One might argue that the large potential (70%) chance of some loss should persuade Acme to abandon the product right away - without a test market.

This is what “playing the averages” with EMV is all about.

Since the EMV of this optimal strategy is greater than 0, Acme should go ahead with this strategy if it is an EMV maximizer.

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Expected Value of Sample Information The role of the test market in this example is to provide

Acme with information.

Information usually costs, in this case its fixed cost is $3 million.

From the decision tree we can see that the EMV from test marketing is $807,000 better than the decision not to test market. The most Acme would be willing to pay for the test marketing is $3.807 million.

This value is called the expected value of sample information or EVSI.

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Expected Value of Sample Information -- continued In general we can write the following expression:

EVSI=EMV with free information - EMV without information

For the Acme example the EVSI is $3.807 million.

The reason for the term sample is that the information does not remove all uncertainty about the future.

That is, even after the test market results are in, there is still uncertainty about the national market.

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Expected Value of Perfect Information We can go one step further and ask how much perfect information is worth.

Perfect could be imagined as an envelope containing the final outcome.

No such envelope exists but if it did how much would Acme be willing to pay for it?

This question can be answered with a decision tree.

Folding back produces an EMV of $7.65 million.

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Expected Value of Perfect Information -- continued This value is called the expected value of perfect

information, or EVPI.

The EVPI may appear to be irrelevant because perfect information is almost never available - at any price.

However, it is often used as an upper bound on EVSI for any potential sample information.

That is, no sample information can ever be worth more than the EVPI.