## Nonlinear optimisation for exponential preference behaviour

In both the Open Design methodology of Chapter 1 and the preference measurement as described in Chapter 5, linearity is implied. For instance, a finance-oriented stakeholder can specify the price per square meter he or she is prepared to pay for a parking lot. The realistic case mentioned before, that the stakeholder is prepared to pay more per square meter for a small parking lot for VIPs only, cannot be taken into account. Non-linear stakeholder preference behaviour is quite common. For instance:

• Price to be paid for a location related to the distance from a noisy factory;

• Price to be paid for percentage green in an urban area;

• Price to be paid for energy savings;

• Price to be paid for an airport island related to the distance to the shore;

• Unsupported length of buildings over the railways of a station related to the number of railway tracks;

• Price to be paid for shape, volume and area to enable the architect to create interesting architecture.

Figure 7.1 The price a decision maker is prepared to pay for a location at some distance from a noisy factory follows an exponential curve

CD O

Distance from noisy factory

Figure 7.1 The price a decision maker is prepared to pay for a location at some distance from a noisy factory follows an exponential curve

Non-linear preference behaviour tends to follow an exponential pattern (see Lootsma, 1999). For instance, the extra price the decision maker is prepared to pay for having a location at some distance from a noisy factory will be as indicated by the exponential curve in Figure 7.1 and not the linear one. The exponential curve can be expressed in the equation:

The unknown coefficients a, g and b can be determined if three points on the curve are given. The decision maker must, therefore, specify three instead of two equivalent alternatives. For the linear case, we could write:

from which the ratio wilw2 could be obtained. For the non-linear case, this becomes:

## Best Investment Tips and Ideas

The dynamics of investing can be very emotional and stressful if not properly managed. When you are aware of what is all involved you give yourself the power to avoid those situations or at least manage them effectively. That will make your investments more exciting, rewarding, and enjoyable. Those positive factors will only lead to greater success in all that achieve with investments and life.

Get My Free Ebook