A utility function is stated using a well-ordered metric scale. On this scale, the
numbers have no absolute physical significance, but the scale is assembled by
allocating numbers to any two points at its limits. Normally these points represent
the worst and the best possible outcomes for the relevant attribute. Usually, the worst
outcome is allocated a utility of 0, while the best possible outcome is assigned a
utility of 1.
During decision-making periods, when looking at the performance of any two
alternatives on a given utility function, the decision maker, will either:
(1) prefer one to the other, thus one outscoring the other, or
(2) be indifferent between them, with both options obtaining the same score.
These are the only conceivable results. The utility function will grow monotonically from 0 to 1. This increase can be either linear or non-linear.
In most assessments concerning complex engineering projects, the decision
maker must consider the high number of different attributes or types of results.
These resulting impacts concern the technical, economic, social and environmental
performance of the various alternatives under scrutiny. In principle, the same Utility
Theory developed for the single decision attribute can be developed directly to
consider such cases. All the distinct utility functions for the specific criteria are
assembled within one mathematical formulation, known as a multi-attribute utility
function.
Any decision maker will indirectly try to maximise some function, U, that
aggregates all the different perspectives to be considered. Thus, when the decision
maker is queried about a range of alternatives, his reply will be comprehensible,
consistent and compatible with a certain unknown function U. This function is,
however, articulated in terms of a variety of relevant criteria. Estimating or developing the form of this function is the starting point for the problem-solving procedure within MAUT.
In its simplest form, if each criterion’s utility is independent from that of the
others (this property is called ‘utility independence’), then the multi-attribute utility
function can be expressed as a weighted average combination of each individual
(consequence) attribute’s utility functions, i.e.:
U X
ð Þ ¼
X
i
w i U x i
ð Þ
ð15:1Þ
where X is a vector of containing the n criteria:
X ¼ x 1 , x 2 , x 3 , . . . x n
ð
Þ
ð 15:2Þ
and w i is the weightage coefficient for criterion i specifying the relative influence of
each criterion in the final decision.
In certain situations, the utility of certain criteria can be influenced by other
criteria, and utility independence cannot be assumed. Say, for example, two highway
15.2 The Simple Additive Weighting (SAW) Model
415
numbers have no absolute physical significance, but the scale is assembled by
allocating numbers to any two points at its limits. Normally these points represent
the worst and the best possible outcomes for the relevant attribute. Usually, the worst
outcome is allocated a utility of 0, while the best possible outcome is assigned a
utility of 1.
During decision-making periods, when looking at the performance of any two
alternatives on a given utility function, the decision maker, will either:
(1) prefer one to the other, thus one outscoring the other, or
(2) be indifferent between them, with both options obtaining the same score.
These are the only conceivable results. The utility function will grow monotonically from 0 to 1. This increase can be either linear or non-linear.
In most assessments concerning complex engineering projects, the decision
maker must consider the high number of different attributes or types of results.
These resulting impacts concern the technical, economic, social and environmental
performance of the various alternatives under scrutiny. In principle, the same Utility
Theory developed for the single decision attribute can be developed directly to
consider such cases. All the distinct utility functions for the specific criteria are
assembled within one mathematical formulation, known as a multi-attribute utility
function.
Any decision maker will indirectly try to maximise some function, U, that
aggregates all the different perspectives to be considered. Thus, when the decision
maker is queried about a range of alternatives, his reply will be comprehensible,
consistent and compatible with a certain unknown function U. This function is,
however, articulated in terms of a variety of relevant criteria. Estimating or developing the form of this function is the starting point for the problem-solving procedure within MAUT.
In its simplest form, if each criterion’s utility is independent from that of the
others (this property is called ‘utility independence’), then the multi-attribute utility
function can be expressed as a weighted average combination of each individual
(consequence) attribute’s utility functions, i.e.:
U X
ð Þ ¼
X
i
w i U x i
ð Þ
ð15:1Þ
where X is a vector of containing the n criteria:
X ¼ x 1 , x 2 , x 3 , . . . x n
ð
Þ
ð 15:2Þ
and w i is the weightage coefficient for criterion i specifying the relative influence of
each criterion in the final decision.
In certain situations, the utility of certain criteria can be influenced by other
criteria, and utility independence cannot be assumed. Say, for example, two highway
15.2 The Simple Additive Weighting (SAW) Model
415