IIBMS MMS CASE STUDY ANSWER SHEETS – XYZ paint company identified the attributes which are important to their customers and also classified each of the attributes into their levels.
IIBMS MMS CASE STUDY ANSWER SHEETS – XYZ paint company identified the attributes which are important to their customers and also classified each of the attributes into their levels.
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CASE – 5 Conjoint Analysis
Problem
XYZ paint company identified the attributes which are important to their customers and also classified each of the attributes into their levels. Based on this, they want to use the technique of conjoint analysis to determine from a potential customer’s point of view, how important each attribute is to him. They also want to know how much utility the customer derives from a given combination of these levels of attributes. It also helps to understand the feasible offerings from the marketer’s point of view. The three important attributes identified for the paint are:
-
Life—this is the number of years the paint coat lasts.
-
Price—the price of one litre of paint.
-
Colour—the colour of paint.
The levels of the above mentioned attributes are as follows:
-
Life—3 years, 4 years, 5 years
-
Price—Rs. 50 per litre, Rs. 60 per litre, Rs. 70 per litre
-
Colour—Green, Blue, Cream
Input data
After the attributes and their levels are decided, the next stage is to collect from the respondent, the ranking of all 27 combinations of levels. This can be seen from Table 1.1.
TABLE 1.1 Input Data for Conjoint Analysis
S.No. |
Life (in years) |
Price (Rs/Litre) |
Colour |
Rating (27 to 10 |
1 |
5 |
50 |
Green |
27 |
2 |
4 |
50 |
Green |
26 |
3 |
5 |
50 |
Cream |
25 |
4 |
5 |
50 |
Blue |
24 |
5 |
5 |
60 |
Green |
23 |
6 |
4 |
60 |
Green |
22 |
7 |
5 |
70 |
Green |
21 |
8 |
5 |
60 |
Blue |
20 |
9 |
5 |
60 |
Cream |
19 |
10 |
4 |
50 |
Blue |
18 |
11 |
4 |
50 |
Cream |
17 |
12 |
5 |
70 |
Blue |
16 |
13 |
3 |
50 |
Green |
15 |
14 |
5 |
70 |
Cream |
14 |
15 |
3 |
50 |
Blue |
13 |
16 |
4 |
60 |
Blue |
12 |
17 |
4 |
60 |
Cream |
11 |
18 |
3 |
50 |
Cream |
10 |
19 |
4 |
70 |
Green |
9 |
20 |
3 |
60 |
Green |
8 |
21 |
4 |
70 |
Blue |
7 |
22 |
3 |
60 |
Blue |
6 |
23 |
4 |
70 |
Cream |
5 |
24 |
3 |
60 |
Cream |
4 |
25 |
3 |
70 |
Green |
3 |
26 |
3 |
70 |
Blue |
2 |
27 |
3 |
70 |
Cream |
1 |
Table 1.2 Shows different codes assumed for various levels of attributes for a regression run. The coding of the attribute levels for this purpose is known as ‘effects coding’. In this table, which is similar to the coding of dummy variables, the three levels of life are coded as follows:
Life in years |
Var 1 |
Var 2 |
3 |
1 |
0 |
4 |
0 |
1 |
5 |
─1 |
─1 |
Thus, the two variables, Var 1 and Var 2 are used to indicate the 3 levels of life, as per the coding scheme mentioned above.
Similarly the coding scheme for the three levels of the price is as shown as follows:
Price(Rs. Per liter) |
Var 3 |
Var 4 |
50 |
1 |
0 |
60 |
0 |
1 |
70 |
─1 |
─1 |
Finally, the coding scheme for colour is as shown below:
Colour |
Var 3 |
Var 4 |
Green |
1 |
0 |
Blue |
0 |
1 |
Cream |
─1 |
─1 |
Thus, 6 variables, that is Var 1 ─ Var 6 are used to represent the 3 levels of life of the paint (3, 4, 5), 3 levels of price per litre (50, 60 & 70) and 3 levels of colour (green, blue and cream). All the six variables are independent variables in the regression run. Var 7 is the rating of each combination given by the respondent, and forms the dependent variable for the regression curve. The recoded input data are shown in Table 1.3.
If the conjoint analysis is run as a regression model, the rating (which is the reverse of ranking) is used as a dependent variable. All combinations from the first to the twenty-seventh are ranked by the respondent. Rank 1 can be considered as the highest rating and given a rating of 27. Rank 2 can be given a rating of 26 and so on. This is not an interval-scaled rating, and should have only ordinal interpretation.
Table 1.3 Conjoint Problem Input Data Coded for Regression
Var 1 |
Var 2 |
Var 3 |
Var 4 |
Var 5 |
Var 6 |
Var 7 |
─1.00 |
─1.00 |
1.00 |
0.00 |
1.00 |
0.00 |
27.00 |
0.00 |
1.00 |
1.00 |
0.00 |
1.00 |
0.00 |
26.00 |
─1.00 |
─1.00 |
1.00 |
0.00 |
─1.00 |
─1.00 |
25.00 |
─1.00 |
─1.00 |
1.00 |
0.00 |
0.00 |
1.00 |
24.00 |
─1.00 |
─1.00 |
0.00 |
1.00 |
1.00 |
0.00 |
23.00 |
0.00 |
1.00 |
0.00 |
1.00 |
1.00 |
0.00 |
22.00 |
─1.00 |
─1.00 |
─1.00 |
─1.00 |
1.00 |
0.00 |
21.00 |
─1.00 |
─1.00 |
0.00 |
1.00 |
0.00 |
1.00 |
20.00 |
─1.00 |
─1.00 |
0.00 |
1.00 |
─1.00 |
─1.00 |
19.00 |
0.00 |
1.00 |
1.00 |
0.00 |
0.00 |
1.00 |
18.00 |
0.00 |
1.00 |
1.00 |
0.00 |
─1.00 |
─1.00 |
17.00 |
─1.00 |
─1.00 |
─1.00 |
─1.00 |
0.00 |
1.00 |
16.00 |
1.00 |
0.00 |
1.00 |
0.00 |
1.00 |
0.00 |
15.00 |
─1.00 |
─1.00 |
─1.00 |
─1.00 |
─1.00 |
─1.00 |
14.00 |
1.00 |
0.00 |
1.00 |
0.00 |
0.00 |
1.00 |
13.00 |
0.00 |
1.00 |
0.00 |
1.00 |
0.00 |
1.00 |
12.00 |
0.00 |
1.00 |
0.00 |
1.00 |
─1.00 |
─1.00 |
11.00 |
1.00 |
0.00 |
1.00 |
0.00 |
─1.00 |
─1.00 |
10.00 |
0.00 |
1.00 |
─1.00 |
─1.00 |
1.00 |
0.00 |
9.00 |
1.00 |
0.00 |
0.00 |
1.00 |
1.00 |
0.00 |
8.00 |
0.00 |
1.00 |
─1.00 |
─1.00 |
0.00 |
1.00 |
7.00 |
1.00 |
0.00 |
0.00 |
1.00 |
0.00 |
1.00 |
6.00 |
0.00 |
1.00 |
─1.00 |
─1.00 |
─1.00 |
─1.00 |
5.00 |
1.00 |
0.00 |
0.00 |
1.00 |
─1.00 |
─1.00 |
4.00 |
1.00 |
0.00 |
─1.00 |
─1.00 |
1.00 |
0.00 |
3.00 |
1.00 |
0.00 |
─1.00 |
─1.00 |
0.00 |
1.00 |
2.00 |
1.00 |
0.00 |
─1.00 |
─1.00 |
─1.00 |
─1.00 |
1.00 |
IIBMS MMS CASE STUDY ANSWER SHEETS – XYZ paint company identified the attributes which are important to their customers and also classified each of the attributes into their levels.
OUTPUT AND ITS INTERPRETATION
The output of the regression model is shown in Table 1.4. Variables 1 to 6 are treated as independent variables. The column titled ‘B’ (the regression coefficient column) provides the part utility of each level of attributes.
Table 1.4 Multiple regression output for conjoint problem (partial output shown)
Variables in the regression equation |
|
VARIABLE |
B |
Var 1 |
─7.00 |
Var 2 |
0.11 |
Var 3 |
5.44 |
Var 4 |
─0.11 |
Var 5 |
3.11 |
Var 6 |
─0.88 |
For example, the life of 3 years is represented by variable 1 as per our coding scheme. Its utility is equal to ─7.11 (looking under column ‘B’ of Table 1.4 for variable 1). Similarly the utility for variable 2, representing life of 4 years is 0.11. The utility for the 3rd level of life, is not in the table, but is derived from the property of this coding, that all the utilities for a given attributes should sum to 0. Thus, utility for life of 5 years should be equal to 7 (─7.11 + 0.11).
Similarly for price, the utilities of Rs. 50/litre and Rs. 70/litre are given by the numbers 5.44 and ─0.11, as shown against 3 and 4 in Table 1.4 in Table 1.4 but the utility for Rs. 80/litre is derived from the same property, that the sum of the utilities for different levels of price should sum to 0. Therefore the price Rs. 80/litre has the utility of 5.33 (5.44 + (─0.11).
Finally for colour, green has the utility of 3.11 and blue has the utility of ─0.88. Cream has a derived utility of 2.23 (3.11 + (─0.88).
TABLE 1.5 Utilities Table for Conjoint Analysis
Attributes |
Levels |
Part Utility |
Range of Utility(Max ─ Min) |
|
Life |
3 years |
─7.11 |
= 7.00 ─ (─7.11) |
|
4 years |
0.11 |
= 14.11 |
||
5 years |
7.00 |
|||
Price |
Rs. 50/litre |
5.44 |
||
Rs. 60/litre |
─0.11 |
= 5.44 ─ (─0.11) |
||
Rs. 70/litre |
5.33 |
= 5.55 |
||
Colour |
Green |
3.11 |
= 3.11 ─ (─0.88) |
|
Blue |
─0.88 |
= 3.99 |
||
Cream |
2.23 |
From the Table 1.5 we can conclude that the life or the number of years the paint lasts is the most important attribute for the customer. There are two indicators for this.
-
The range of utility value is highest (14.11) for the life. (From Range of Utility column)
-
The highest individual value of this attributes is at its 3rd level that is, i.e., 7.00.
Both these figures indicate that the number of years the paint lasts is the most important attribute at given levels of attributes. The price/litre seems to be the second most important attribute, as its range of utilities is 5.55. The last attribute in relative importance is the colour, with the utility range of 3.99.
Combination Utilities
The total utility of any combination can be calculated by picking the attribute levels of our choice. For example, the combined utility of the combination 4 years of life, Rs. 70/litre, and cream colour is 0.11 + 5.33 + 2.33 = 7.67. If we want to know the best combination, it is advisable to pick the highest utilities from each attribute, and add them. The possible combination is 5 years of life, Rs. 50/litre, and green colour, that is, 7.00 + 5.44 + 3.11 = 15.55. The next best combination is 5 years of life, Rs. 70/litre, and green colour, with the combined utility of 7 + 5.33 + 3.11 = 15.44.
Individual Attribute
The difference in utility with the change of one level in one attribute can also be checked. For the life of 3 years to 4 years, there is increase in utility value of 7.22 units, but the next level, that is, 4 years to 5 years has an increase in utility of 6.89.
Similarly, increase in price from Rs. 50/litre to Rs. 60/litre induces a utility drop of 5.55, whereas from Rs. 60/litre to Rs. 70/litre there is an increase in utility of 5.44.
Finally, colour green to colour blue induces 3.99 drop in utility. Next, from colour blue to colour cream there is an increase in utility of 3.11.
Question:
Case 5: Use conjoint analysis to determine from a potential customer’s point of view, how important each attribute is to him. Also determine how much utility the customer derives from a given combination of these levels of attributes. The attributes are life, price and colour.
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