Sustainable Construction A Life Cycle Approach in Engineering

2 MULTI-CRITERIA DECISION MAKING METHODS
In this section a brief description of multi-criteria decision making methods (MCDM) which are
most commonly used in retrofitting, deconstruction and demolition of buildings is presented .
MCDM can be divided into multi-objective decision making (MODM) and multi-attribute
decision making (MADM) (Triantaphyllou, 2000). In the first case the decision space is continuous,
as for example in mathematical programming problems with multiple objective functions,
while in MADM the decision space is discrete.
A multi-criteria decision problem consists of determining the optimal alternative A * among a
set of solutions A i which are evaluated with respect to a set of criteria C j .
Criteria can be expressed with different units of measure and may be qualitative or quantitative.
As a consequence, the application of MCDM methods involve the normalization of variables,
the quantification of qualitative data and determination of criteria weights. Criteria can
be classified as benefit-type or cost-type, according to the interest of decision maker in maximizing
or minimizing their evaluation.
In general, MCDM problems can be formulated in a matrix format. Let a ij be the performance
of each alternative A i with respect to different criteria C j whose weights are w j . Weights are
generally expressed in relative terms, that is
w j j
=1. The typical decision matrix is then:
A
m x n
A
A
A
1
2
m
C C C C C
1 2 3 4 n
a a ... ... ... a
a21
am1
a
11 12 1n
mn
(1)
Any decision-making technique can be divided in three steps: l) Determination of the relevant
criteria and alternatives; 2) Attachment of numerical measures to the relative importance
of the criteria and to the impacts of the alternatives on these criteria; 3) Processing of numerical
values to determine a ranking of each alternative.
In the following, a brief description of most common MCDM methods and most used approaches
in demolition, deconstruction and retrofitting of existing structures is reported. In particular,
details on weighted sum model, weighted product model, analytic hierarchy process and
TOPSIS method are provided. Concerning other approaches as ELECTRE, MAUT, VIKOR
and PROMETHEE methods the reader is referred to existing literature.
The WSM and WPM methods
In the weighted sum model (WSM) the best alternative is selected according to the following
espression:
n
*
WSM-score
max
i
j1
ij j
A a ×w for i=1,...., m.
(2)
In general, this method is suitable for single-dimensional problems while in multidimensional
cases difficulties occur. Moreover, involving the maximization or minimization of
different performances, the WSM method is applicable to problems with criteria all of the same
type, that is benefit or cost-type criteria, while it is clear that in some cases their value can conflict
each other.
The weighted product model (WPM) is similar to the WSM. Each alternative is compared
with the others according to the following product:
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