Accounting for decision variable dependent preferences

When we maximise the number of affordable houses we basically end up on a corner point of the solution space. This is labeled Alternative 1. Maximising the profit, in essence, changing the objective function, we end up on a completely different corner point. This outcome is labeled Alternative 2. In order to choose between both we can use preference function modelling. Because we need at least three alternatives to measure we also add a third point on the boundary of the solution space. This point lies between both before mentioned corner points and is labeled Alternative 3.

The numerical output from running the LP model for each alternative is illustrated in Table 6.1

We can then measure the overall preference of each of these alternatives using the preference measurement software. Both stakeholders have to state their preference for each alternative regarding the criteria 'amount of profit' (project developer) and 'number of affordable houses' (municipality). The in-

Alternative

Ai

a2

A3

Profit

0

100

83

Number of affordable houses

100

0

50

Table 6.2 Numerical input for pfm software put is given in Table 6.2.

The output yields the following ranking:

1. Alternative 3 (midpoint) with an overall preference of 68;

2. Alternative 1 and 2 both with an overall preference of 50;

As this example illustrates, it can be very useful to explore the edges of the solution space to establish a group optimum. In this example adding more alternatives on the boundary of the solution space between both corner points may yield an alternative with a better overall preference than the corner point solutions.

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