Kroft Food Products
Case Study
Kroft Food Products
is attempting to decide whether it should introduce a new line of salad
dressings called Special Choices.
The company can test
market the salad dressings in selected geographic areas or bypass the test market
and introduce the product nationally.
·
The cost of the test market is $150,000.
·
Cost of Begin Market $550000.
·
Revenue $2300000.
If the company
conducts the test market, it must wait to see the results before deciding whether
to introduce the salad dressings nationally.
·
The probability of a positive test market
result is estimated to be 0.6
·
The probability of a negative test market
result is estimated to be 0.4
Alternatively, the
company can decide not to conduct the test market and go ahead and make the
decision to introduce the dressings or not.
·
The probability of success 0.50 without the
test market
·
The probability of success 0.80 with the test
market and it is positive.
·
The test market is negative, the probability of
success drops to 0.30.
Using decision tree
analysis, determine whether the company should conduct the test market?
Solution:-
- 1st calculate posterior probabilities
(Success | Positive) =0.8
(Success | Negative) =0.3
(Fail | Positive) =0.2
(Fail | Negative) =0.7
Posterior Given Success:-
|
States of Nature
|
Prior
|
Conditional
|
Join
|
Posterior
|
|
Positive
|
0.6
|
0.8
|
0.48
|
0.8
|
|
Negative
|
0.4
|
0.3
|
0.12
|
0.2
|
Posterior Given Fail:-
|
States of Nature
|
Prior
|
Conditional
|
Join
|
Posterior
|
|
Positive
|
0.6
|
0.2
|
0.12
|
0.3
|
|
Negative
|
0.4
|
0.7
|
0.28
|
0.7
|
The decision tree for the problem is shown below:-
Step 1:-
---> involves working out the total profit for each of the
paths from the initial node to the terminal node
1-path to reach node 9, we choose to test market (cost 150000), if
the result of testing was positive and begin in market, this will cost 550000,
if we success we will win (2300000), then total profit will be
(-150000 -550000+2300000)
=1600000
2-path to reach node 10, we choose to test market (cost 150000), if
the result of testing was positive and begin in market, this will cost 550000,
then if we failure then total profit will be
(-150000 -550000) =-700000
3-path to reach node 11, we choose to test market (cost 150000), if
the result of testing was positive and then we abandon then the total profit
will be -150000
4-path to reach node 12, we choose to test market (cost 150000), if
the result of testing was negative and begin in market, this will cost 550000,
if we success we will win (2300000), then total profit will be
(-150000-550000+2300000) =1600000
5-path to reach node 13, we choose to test market (cost 150000), if
the result of testing was negative and begin in market, this will cost 550000,
then if we failure then total profit will be
Total profit = (-150000-550000) =-700000
6-path to reach node 14, we choose to test market (cost 150000), if
the result of testing was negative and then we abandon then the total profit
will be -150000
7-path to reach node 15, we don’t choose to test market (cost 0),
and begin in market, this will cost 550000, if we success we will win
(2300000), then total profit will be
(-550000+2300000) =1750000
8-path to reach node 16, we don’t choose to test market (cost 0),
and begin in market, this will cost 550000, if we failure the total profit = -550000
9-path to
reach node 17, we don’t choose to test market (cost 0), and then abandon then
the cost will be = 0
|
Terminal node
|
Total profit
|
|
9
|
1600000
|
|
10
|
-700000
|
|
11
|
-150000
|
|
12
|
1600000
|
|
13
|
-700000
|
|
14
|
-150000
|
|
15
|
1750000
|
|
16
|
-550000
|
|
17
|
0
|
--------------------------------------------------------------------------------------------------------
Step 2- background
- For chance node 7 the EMV is 0.8(1600000) + 0.2(-700000) = 1140000
- For chance node 8 the EMV is 0.7(1600000) + 0.3(-700000) = 910000
- For chance node 6 the EMV is 0.5(1750000) + 0.5(-550000) = 600000
- For decision node 4 the EMV is the biggest (1140000,-150000) = 1140000
- For decision node 5 the EMV is the biggest (910000, -150000) = 910000
- For chance node 2 the EMV is 0.6(1140000) + 0.4(910000) = 1048000
- For decision node 3 the EMV is the biggest (600000, 0)= 600000
- For
decision node 1 the EMV is the biggest (1048000, 600000)=
1048000
----> So the best decision is to test market and wait for the result and
begin in market
