## Utility Value Analysis

Description of the method

This method seeks to analyse a number of complex alternatives, with the aim of ordering them according to the preferences of the decision-maker in a multidimensional target system. The ordering is carried out by calculating so-called utility values for the alternatives.

In utility value analysis, multiple target criteria are weighted according to their importance to the decision-maker. The ability of the different alternatives (here, the investment projects) to fulfil each target is measured and a corresponding partial utility value is given. The weighted partial utility values are summed to obtain a total value for every alternative - the utility value. For any one alternative, the aggregation of (weighted) partial utility values allows unfavourable results on one target measure to be compensated by better results on others. If certain criteria have minimum requirements, those must be fulfilled before carrying out a utility value analysis.

The utility value analysis consists of the following steps:

1. Determination of target criteria.

2. Weighting of each target criterion.

3. Calculation of partial utility values.

4. Calculation of (total) utility values.

### 5. Assessment of profitability.

In the first step of the utility value analysis, the determination of target criteria, a measurement scale (which may be nominal, ordinal or cardinal) is required for every criterion. The consideration of project attributes should not be duplicated by applying more than one criterion per attribute, and the extent to which an investment project fulfils one target criterion should be measured independently of the assessments made for other criteria. Monetary criteria are not normally included in a utility value analysis, since cash inflows and outflows, or yields and expenditures, are typically affected by many characteristics of investment projects that fall under some of the other criteria. Determining the target criteria requires a careful structuring and analysis of the target system. In complex decision problems, it is often worthwhile to split target measures into a multi-level hierarchy.

In the second step of the utility value analysis, a weighting wc is determined for each criterion c in order to rank its importance to the decision-maker. The weightings should total 1 or 100 in order to simplify the interpretation of analysis results.

In the third step, the alternative projects are evaluated with respect to each criterion using, as appropriate, a nominal, ordinal or cardinal scale. Then, the results are transformed into partial utility values uic for each alternative i and for each criterion. The partial utility values are measured using a uniform cardinal scale, preferably with a range of 0 to 1, or 0 to 100.

In the fourth step, a (total) utility value Uui, is calculated as follows:

Finally, an assessment of profitability is made using the following definitions:

Key Concept:

Absolute profitability is achieved if an investment project's utility value is higher than a given target value.

Relative profitability: an investment project is preferred if its utility value is higher than that of any alternative project.

In some situations the utility value is not the only result of model analyses used for profitability assessment. As mentioned above, monetary target measures (e.g. net present value) should not be included in a utility value analysis, but considered separately. In such situations, goal conflicts are possible and a new multi-criteria problem can arise.

### Example 6-1

In the following example, a utility value analysis is carried out in order to assess the relative profitability of three location alternatives: A1, A2 and A3.

As a first step, the targets shown in Figure 6-2 have been determined. The main target, selection of the optimum location, is split into sub-targets as illustrated. The weightings, which are determined in the second step, also appear in Figure 6-2. The third step, the calculation of partial utility values is illustrated using the criterion 'size of land' in Figure 6-3. The alternatives under consideration have sizes of 60,000 m2 (A1), 42,500 m2 (A2) and 35,000 m2 (A3A3).

2nd level:

Sub-

targets

3rd level:

Target criteria Size Price Develop Labour Labour Traffic of of ment potential market con land land competition nection (S) (P) (D) (LP) (LC) (T) Partial utility value

40,000 45,000 50,000 55,000 60,000 m2

Fig. 6-3: Transformation function for the criterion 'size of land'

In accordance with this function, the partial utility values of the alternatives for this criterion are: 1 (Aj), 0.2 (A2) and 0 (A3). For the other criteria, partial utility values have been determined as follows:

 Target criteria Alternative S P D LP LC T FC DP FS AA MF-TT A1 1 0.4 1 0.2 0.4 0.6 0.4 0.6 0.8 0.4 0.6 a2 0.2 0.4 0.2 0.6 0.8 0.4 0 1 0.8 0.8 1 a3 0 0.6 0.8 0.9 1 0.8 1 0.2 0.8 0.4 0.4

Tab. 6-1: Partial utility values of the alternatives Aj, A2 and A3

In the fourth step, the total utility values are calculated. The weighted partial utility values are determined by multiplying the partial utility values by the weightings of the associated criterion and sub-target. For alternative A1 and the criterion 'size of land', for example, it is: 1 ■ 0.3 ■ 0.2 = 0.06

This value indicates the contribution of the criterion 'size of land' to the fulfilment of the highest-level target. By multiplying other partial values by their weightings, and adding the resulting weighted partial utility values, (total) utility values Uui for the three alternatives Ai can be determined:

It can be concluded, that Alternative A3 is relatively profitable because it has the highest utility value.

### Assessment of the method

Utility value analysis is a comparatively simple method for multi-criteria decision-making. It is easily comprehended and requires only minor computational effort. Also, its application encourages systematic structuring of the underlying problem.

The results of a utility value analysis can be easily interpreted, especially if standardised scales are used for the weightings and partial utility values, as proposed above. Then, a utility value of 1 or 100 is the maximum attainable and the utility value of an alternative can be interpreted as a proportion or percentage of this maximum value. Perhaps for these reasons, utility value analysis is a popular method in practice.

However, data collection can be problematic as target criteria, weightings and partial utility values must be determined and, for the latter two, cardinal measuring scales are required. The target criteria, target weightings and transformation into partial utility values must be based on personal, subjective judgements and estimates, often requiring extensive effort. It might also be questionable whether these criteria, weightings and transformations fully reflect the preferences of the decision-maker, whether target criteria are completely independent, and whether each project characteristic is examined under only one criterion. Effects caused by uncertainty and subjectivity of data, and deviations from assumptions, may by analysed by combining utility value analysis with appropriate procedures for investment methods under uncertainty (especially sensitivity analysis and risk analysis, as described in Chapter 8).

Some other reservations concern the weightings used. These represent overall statements about the relative importance of targets only, i.e. the relationship between two weightings must not be interpreted as a substitution rate for the outcomes of these two targets. Therefore, the utility function is not necessarily additive as this method implies. These aspects are reconsidered in Section 6.4, in the context of multi-attribute utility theory.

Another method for multi-criteria decision-making is now described: the analytic hierarchy process. 