1. Example 7.4 Selecting the Best Marketing Strategy at the Acme Company
Multistage Decision Problems

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

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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 formula P(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)

11. Conditional Probabilities - continued
These equivalent equations are sometimes called the law of probabilities.
We determine the probabilities as for a great market, 0.37 for a fair market and 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.

12. 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.

13. Inputs

15. 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.

16. 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.

17. 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.