Decision maker 1 Decision maker 2 Decision maker 3 Decision maker n-2 Decision maker n-1 Decision maker ndecision makerJointDecision maker 1 Decision maker 2 Decision maker 3 Decision maker n-2 Decision maker n-1 Decision maker nTransfer of income and resources over generations of decision makersdecision makerJointTransfer of costs and resources over generations of decision makersDecision maker 1 Decision maker 2 Decision maker 3 Decision maker n-2 Decision maker n-1 Decision maker ndecision makerJointDecision maker 1 Decision maker 2 Decision maker 3 Decision maker n-2 Decision maker n-1 Decision maker nTransfer of income and resources over generations of decision makersdecision makerJointTransfer of costs and resources over generations of decision makersFigure 13.11: Illustration of the interaction between present and future decision makers.
Following this principle the benefits have to be summed up over the present and future
decision makers as they are seen from their perspective (e.g. in accordance with the state of
the world at their point in time and capitalized to their point in time). The interest rate ( ) 6 t to
be considered for the present and future decision makers should represent all the prevailing
reasons for discounting, such as purely subjective preferences as well macro-economical
factors such as the growth of the wealth of society. The societal growth of wealth can and
should, however, also be taken into account to compensate for the improved economical
capabilities of future decision makers. The benefits of future decision makers must thus be
weighed (reduced) in the overall decision problem with the discounting factor ( )A t.
The benefit function for the joint decision maker (see Figure 13.11) can then be written as:
11(( )) () (, (), )( )
8
(^89)
aT a
i
i
i
n t
iG ii i
i t
UtttAT3 633td 9 (13.21)
where T3Gii(, (), )atti
is the benefit rate function for generation i and
aT( ) > tt t 12 , ,..,n??
t
aT();ttii
i
are the possible decision alternatives for the decision maker
at time.
Based on Equation (13.21) optimization of decisions may now be undertaken considering to
the best of knowledge the preferences of future decision makers as well as the way resources
and economical means might be transferred over time. In Rackwitz et al. (2005), Faber and
Nishijima (2004) and Nishijima et al. (2005) studies are performed to assess the impact of the
use of Equation (13.21) for engineering decision making. The general observation from the
studies is that significant changes in optimal decision making result from the inclusion of
intergenerational aspects. In effect the application of Equation (13.21) leads to optimal design,
inspection and maintenance decisions which are identical to decisions as achieved by use of
Equation (13.13) if in Equation (13.12) an interest rate ( ) 6 ttA( ) is applied; i.e. using an
interest rate reflecting only the economic growth in society (at present around 2% per annum).
For consistent sustainable decision making this interest rate should be applied on all benefits
and investments into engineering project - also those related to life saving activities (Paté-
Cornell, 1984). This result is indeed interesting as it is consistent with results achieved
differently by economists; see e.g. Bayer (1999) and Rackwitz et al. (2005). Furthermore, the
result shows that differences in interest rates which may be observable for different types of