Example 1: Decision Analysis Example

A household consisting of two parents (Paul and Laura) and three small daughters decides to search for a new dwelling because their current dwelling doesn’t have enough room since the birth of their third daughter. The couple requires an owner-occupied home with a backyard for their small children. After a thorough search with the use of some internet sites proposing available dwellings, the couple finds out that there are six available dwellings within their selected region that satisfy their requirements. These dwellings differ with respect to their characteristics (so-called attributes).

The couple decides to examine which alternative they should choose using a Multi-Attribute Utility method. Firstly, they decide which attributes are important to them. After some deliberation, they come up with the following ones: dwelling type, costs, size of the living room, number of rooms, size of the backyard, archi-tectural style and residential environment. The six available dwellings can be described in terms of their attribute levels. These descriptions are termed dwelling profiles. They are presented in Table 5.2.

Next, they determine the values of the attributes of each alternative using a rating scale with two anchors. On the left side the rating scale is anchored by “extremely unattractive” (0) and on the right side by “extremely attractive” (100). Paul and Laura’s individual values, as well as their mean values, are presented in Table 5.3.

For example, Laura has provided a value of 50 for a ground floor apartment and feels more attracted to a semi-detached house, which she has given a value of 90.

In contrary, Paul likes the ground floor apartment most (value of 90) and finds the semi-detached house the least attractive (a value of 40). The table shows that the couple each assigns quite different values. They do agree about the least preferred and most preferred characteristics with regard to size of the living room, number of rooms and residential environment. But their evaluation differs with regard to the other attributes. This justifies a decision-analysis method.

Next, the couple decides to assign a score to each of the attributes according to their importance. They use a rating scale with numerically scaled endpoints of 0 (not important at all) and 100 (extremely important). Thus, the higher the impor-tance, the higher the score for that particular attribute. The importance scores are

Table 5.2 Six dwelling profiles on the basis of their attribute levels Dwelling A Semi-detached € 220,000 20 m² 2 rooms 5 m Innovative Rural B Semi-detached € 140,000 20 m² 4 rooms 15 m Traditional Sub-urban C Terraced/corner € 300,000 40 m² 4 rooms 10 m Traditional Rural D Terraced/corner € 140,000 40 m² 2 rooms 15 m Innovative Urban E Apartment € 220,000 20 m² 3 rooms 10 m Traditional Rural F Semi-detached € 220,000 30 m² 2 rooms 10 m Modern Urban

Table 5.3 Attribute values

Laura Paul Couple

Dwelling type

Apartment (ground floor) 50 90 70

Terraced house/corner house 70 60 65

Semi-detached house 90 40 65

Purchase costs

presented in Table 5.4. After that, they normalize the importance ratings into weights by dividing the rating of each attribute by the sum of all the ratings. The weights obtained in this way sum up to one. For example, for Laura the importance score for dwelling type is 95 and the sum of all importance scores is 625. The weight for dwelling type thus becomes 95/625 = 0.15. The weights are provided in Table 5.4.

For Laura, all attributes are almost equally important; they range from 0.13 to 0.16. The weights assigned by Paul show more variation, he finds the size of the backyard relatively unimportant (weight = 0.08), but the costs and number of rooms are very important to him (weight = 0.22).

Finally, the couple multiplies the values with the weights for every attribute level to calculate single-attribute utilities. The results are presented in Table 5.5. A higher single-attribute utility indicates that the particular attribute level is valued highly and deemed to be important. A lower utility indicates that the particular attribute level is relatively unimportant, lowly valued, or both. For Laura a backyard with a

Table 5.4 Importance scores and weights

Importance scores Weights

Laura Paul Couple Laura Paul Couple

Dwelling type 95 55 75 0.15 0.12 0.14

Purchase costs 100 100 100 0.16 0.22 0.19

Size living room 80 55 67.5 0.13 0.12 0.12

Number of rooms 95 100 97.5 0.15 0.22 0.19

Backyard size 95 35 65 0.15 0.08 0.11

Architectural style 80 55 67.5 0.13 0.12 0.12

Residential

Apartment (ground floor) 7.6 10.9 9.6

Terraced house/corner house 10.6 7.3 8.9

Semi-detached house 13.7 4.8 8.9

size of 15 m, a semi-detached house and a backyard with a size of 10 m obtain the most utility. For Paul, purchase costs of € 220,000 and a dwelling with four rooms yield the most utility. For the couple, most utility is obtained from the attribute level of four rooms, directly followed by the attribute level of three rooms. An innovative

Table 5.6 Multi-attribute utilities aggregated with the use of two different weighting methods Dwelling Profile

Weighted additive method Equal weights method

Laura Paul Couple Laura Paul Couple

A 71.5 58.2 65.2 71.5 60.1 65.8

B 76.9 61.5 66.6 77.2 55.8 66.5

C 80.6 73.6 76.4 81.5 75.1 78.2

D 68.2 39.1 52.3 68.6 38.6 53.6

E 73.8 82.1 76.9 74.4 78.6 76.5

F 77.1 53.2 64.1 77.2 51.5 64.3

architectural design and an urban residential environment provide the least single-attribute utility.

Finally, the couple uses the weighted linear additive preference function to cal-culate multi-attribute utilities. This means that the single-attribute utilities are sim-ply aggregated according to the combination of attribute levels in the dwelling profiles. Table 5.6 shows the multi-attribute utilities for the six available dwellings in the column labeled “Weighted additive method”. For the couple, the highest util-ity score is obtained for dwelling E, indicating that they should choose this dwelling.

The couple decides to carry out a sensitivity analysis to evaluate the robustness of the results. Firstly, they examine their individual multi-attribute utilities.

Table 5.6 shows that dwelling E is the best choice for Paul, but not for Laura. For Laura, this dwelling is only fourth in preference ranking based on multi-attribute utilities. A further exploration shows that dwelling C might also be a good choice;

it is the option with the highest multi-attribute utility for Laura and the second high-est utility for Paul. As a second sensitivity analysis, they calculate multi-attribute utilities using the equal weights method. This means that every attribute has the same importance (in this case 0.143) and that multi-attribute utilities are calculated using these weights. The results are presented in Table 5.6 in the column labeled

“Equal weights method”. Dwelling C now has the highest multi-attribute utility for the couple. It is the best option for Laura and the second best option for Paul. This sensitivity analysis teaches the couple that besides dwelling E, dwelling C might also be a good alternative. It also shows the potential impact that the importance of attributes can have on the calculated best choice alternative.

5.4.2 Example Two: Calculating Single-Attribute Utilities