ASTM E1765-16(2023)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E1765 − 16 (Reapproved 2023)
Standard Practice for
Applying Analytical Hierarchy Process (AHP) to
Multiattribute Decision Analysis of Investments Related to
Projects, Products, and Processes
This standard is issued under the fixed designation E1765; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
The analytical hierarchy process (AHP) is one of a set of multi-attribute decision analysis (MADA)
methods that considers nonmonetary attributes (qualitative and quantitative) in addition to common
economic evaluation measures (such as life-cycle costing or net benefits) when evaluating project,
product, and process alternatives. Investment decisions depend in part on how competing options
perform with respect to nonmonetary attributes. This practice complements existing ASTM standards
on building economics by incorporating the existing economic/monetary measures of worth described
in those standards into a more comprehensive standard method of evaluation that includes
nonmonetary (quantitative and nonquantitative) benefits and costs. The AHP is the MADA method
described in this practice. It has three significant strengths: an efficient attribute weighting process of
pairwise comparisons; hierarchical descriptions of attributes, which keep the number of pairwise
comparisons manageable; and available software to facilitate its use.
1. Scope and equipment. Processes include procurement, materials
management, work flow, fabrication and assembly, quality
1.1 This practice presents a procedure for calculating and
control, and services.
interpreting AHP scores of a project’s/product’s/process’ total
1.2 In addition to monetary benefits and costs, the procedure
overall desirability when making capital investment decisions.
allows for the consideration of characteristics or attributes
Projects include design, construction, operation, and disposal
which decision makers regard as important, but which are not
of commercial and residential buildings and other engineered
readily expressed in monetary terms. Examples of such attri-
structures. Products include materials, components, systems,
butes that pertain to the selection among project/product/
process alternatives are: a construction projects’s building
This practice is under the jurisdiction of ASTM Committee E06 on Perfor-
alternatives whose nonmonetary attributes are location/
mance of Buildings and is the direct responsibility of Subcommittee E06.81 on
accessibility, site security, maintainability, quality of the sound
Building Economics.
and visual environment, and image to the public and occu-
Current edition approved May 1, 2023. Published May 2023. Originally
ɛ1
approved in 1995. Last previous edition approved in 2016 as E1765 – 16 . DOI: pants; building products based on their economic and environ-
10.1520/E1765-16R23.
mental performance; and sustainability-related issues for key
For an extensive overview of MADA methods and a detailed treatment of how
construction processes that address environmental needs, while
to apply two MADA methods (one of which is AHP) to building-related decisions,
considering project safety, cost, and schedule.
see Norris, G A., and Marshall, H.E., Multiattribute Decision Analysis: Recom-
mended Method for Evaluating Buildings and Building Systems, National Institute
1.3 This standard does not purport to address all of the
of Standards and Technology, 1995.
safety concerns, if any, associated with its use. It is the
This practice presents a stand-alone procedure for performing an AHP analysis.
responsibility of the user of this standard to establish appro-
In addition, an ASTM software product for performing AHP analyses has been
developed to support and facilitate use of this practice. Software to Support ASTM
priate safety, health, and environmental practices and deter-
E1765: Standard Practice for Applying Analytical Hierarchy Process (AHP) to
mine the applicability of regulatory limitations prior to use.
Multiattribute Decision Analysis of Investments Related to Buildings and Building
Systems, MNL 29, ASTM, 1998.
4 5
Projects also include analytical studies that identify alternative means for Typical construction-related products for each product type are: (1) materials—
achieving organizational objectives as well as research and development activities concrete; (2) components—structural steel members; (3) systems—heating,
that support the deployment of new products and processes. ventilating, and air-conditioning system; and (4) equipment—heat pump.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1765 − 16 (2023)
1.4 This international standard was developed in accor- E1692 Classification for Serviceability of an Office Facility
dance with internationally recognized principles on standard- for Change and Churn by Occupants
ization established in the Decision on Principles for the E1693 Classification for Serviceability of an Office Facility
Development of International Standards, Guides and Recom- for Protection of Occupant Assets
mendations issued by the World Trade Organization Technical E1694 Classification for Serviceability of an Office Facility
Barriers to Trade (TBT) Committee. for Special Facilities and Technologies
E1700 Classification for Serviceability of an Office Facility
2. Referenced Documents
for Structure and Building Envelope
6 E1701 Classification for Serviceability of an Office Facility
2.1 ASTM Standards:
for Manageability
E631 Terminology of Building Constructions
E2114 Terminology for Sustainability
E833 Terminology of Building Economics
E2320 Classification for Serviceability of an Office Facility
E917 Practice for Measuring Life-Cycle Costs of Buildings
for Thermal Environment and Indoor Air Conditions
and Building Systems
E2432 Guide for General Principles of Sustainability Rela-
E964 Practice for Measuring Benefit-to-Cost and Savings-
tive to the Built Environment
to-Investment Ratios for Buildings and Building Systems
2.2 ASTM Adjunct:
E1057 Practice for Measuring Internal Rate of Return and
Discount Factor Tables - Adjunct to E917 Practice for
Adjusted Internal Rate of Return for Investments in
Measuring Life-Cycle Costs of Buildings and Building
Buildings and Building Systems
Systems - Includes Excel and PDF Files
E1074 Practice for Measuring Net Benefits and Net Savings
2.3 ASTM Software Product:
for Investments in Buildings and Building Systems
MNL 29 Software to Support ASTM E1765: Standard
E1121 Practice for Measuring Payback for Investments in
Practice for Applying Analytical Hierarchy Process (AHP)
Buildings and Building Systems
E1480 Terminology of Facility Management (Building- to Multiattribute Decision Analysis of Investments Re-
lated to Buildings and Building Systems
Related)
E1557 Classification for Building Elements and Related
3. Terminology
Sitework—UNIFORMAT II
E1660 Classification for Serviceability of an Office Facility
3.1 Definitions—For definitions of general terms related to
for Support for Office Work
building construction used in this practice, refer to Terminol-
E1661 Classification for Serviceability of an Office Facility
ogy E631; for general terms related to building economics,
for Meetings and Group Effectiveness
refer to Terminology E833; and for general terms related to
E1662 Classification for Serviceability of an Office Facility
whole buildings and facilities, refer to Terminology E1480. For
for Sound and Visual Environment
definitions of general terms related to sustainability relative to
E1663 Classification for Serviceability of an Office Facility
the performance of buildings, refer to Terminology E2114.
for Typical Office Information Technology
4. Summary of Practice
E1664 Classification for Serviceability of an Office Facility
for Layout and Building Factors
4.1 This practice helps you identify a MADA application,
E1665 Classification for Serviceability of an Office Facility
describe the elements that make up a MADA problem, and
for Facility Protection
recognize the three types of problems that MADA can address:
E1666 Classification for Serviceability of an Office Facility
screening alternatives, ranking alternatives, and choosing a
for Work Outside Normal Hours or Conditions
final “best” alternative.
E1667 Classification for Serviceability of an Office Facility
4.2 A comprehensive list of selected attributes (monetary
for Image to the Public and Occupants
and nonmonetary) for evaluating building decisions provides a
E1668 Classification for Serviceability of an Office Facility
pick list for customizing an AHP model that best fits your
for Amenities to Attract and Retain Staff
building-related decision. Three types of building decisions to
E1669 Classification for Serviceability of an Office Facility
which the list applies are choosing among buildings, choosing
for Location, Access and Wayfinding
among building components, and choosing among building
E1670 Classification for Serviceability of an Office Facility
materials. Examples of these typical building-related decisions
for Management of Operations and Maintenance
are provided.
E1671 Classification for Serviceability of an Office Facility
for Cleanliness 4.3 A case illustration of a building choice decision shows
E1679 Practice for Setting the Requirements for the Service- how to structure a problem in a hierarchical fashion, describe
ability of a Building or Building-Related Facility, and for the attributes of each alternative in a decision matrix, compute
attribute weights, check for consistency in pairwise
Determining What Serviceability is Provided or Proposed
comparisons, and develop the final desirability scores of each
alternative.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on Available from ASTM International Headquarters. Order Adjunct No.
the ASTM website. ADJE091717-EA. Original adjunct produced in 1984. Adjunct last revised in 2017.
E1765 − 16 (2023)
4.4 A description of the applications and limitations of the 6. Procedure
AHP method concludes this practice.
6.1 To carry out a MADA analysis using AHP, follow this
procedure:
5. Significance and Use
6.1.1 Identify the elements of your problem to confirm that
a MADA analysis is appropriate (see 6.2);
5.1 The AHP method allows you to generate a single
6.1.2 Determine the goal or objective of the analysis, select
measure of desirability for project/product/process alternatives
the attributes on the basis of which you plan to choose an
with respect to multiple attributes (qualitative and quantita-
alternative, arrange the attributes in a hierarchy, identify the
tive). By contrast, life-cycle cost (Practice E917), net savings
attribute sets in the hierarchy, identify the leaf attributes in the
(Practice E1074), savings-to-investment ratio (Practice E964),
hierarchy, and identify alternatives to consider (see 6.3);
internal rate-of-return (Practice E1057), and payback (Practice
6.1.3 Construct a decision matrix summarizing available
E1121) methods all require you to put a monetary value on
data on the performance of each alternative with respect to
benefits and costs in order to include them in a measure of
each leaf attribute (see 6.4);
project/product/process worth.
6.1.4 Compare in pairwise fashion each alternative against
5.2 Use AHP to evaluate a finite and generally small set of
every other alternative as to how much better one is than the
discrete and predetermined options or alternatives. Specific other with respect to each leaf attribute (see 6.5);
AHP applications are ranking and choosing among alterna- 6.1.5 Make pairwise comparisons, starting from the bottom
tives. For example, rank alternative building locations with of the hierarchy, of the relative importance of each attribute in
AHP to see how they measure up to one another, or use AHP a given set with respect to the attribute or goal immediately
above that set in the hierarchy (see 6.6); and
to choose among building materials to see which is best for
your application. 6.1.6 Compute the final overall desirability score for each
alternative (see 6.7).
5.3 Use AHP if no single alternative exhibits the most
6.2 Confirm that a MADA analysis is appropriate. Three
preferred available value or performance for all attributes. This
elements are typically common to MADA problems.
is often the result of an underlying trade-off relationship among
6.2.1 MADA problems involve analysis of a finite and
attributes. An example is the trade-off between low desired
generally small set of discrete and predetermined options or
energy costs and large glass window areas (which may raise
alternatives. They do not involve the design of a “best”
heating and cooling costs while lowering lighting costs).
alternative from among a theoretically infinite set of possible
5.4 Use AHP to evaluate alternatives whose attributes are
designs where the decision maker considers trade-offs among
not all measurable in the same units. Also use AHP when
interacting continuous decision variables. Selecting a replace-
performance relative to some or all of the attributes is
ment HVAC system for an existing building is a MADA
impractical, impossible, or too costly to measure. For example,
problem. In contrast, the integrated design and sizing of a
while life-cycle costs are directly measured in monetary units,
future building and its HVAC system is not a MADA problem.
the number and size of offices are measured in other units, and
6.2.2 In MADA problems, no single alternative is dominant,
the public image of a building may not be practically measur-
that is, no alternative exhibits the most preferred value or
able in any unit. To help you choose among candidate buildings
performance for all attributes. If one alternative is dominant, a
with these diverse attributes, use AHP to evaluate your MADA analysis is not needed. You simply choose that alter-
alternatives.
native. The lack of a dominant alternative is often the result of
an underlying trade-off relationship among attributes. An
5.5 The AHP method is well-suited for application to a
example is the trade-off between proximity to the central
variety of sustainability-related topics. Guide E2432 states
business district for convenient meetings with business clients
when applying the concept of sustainability, it is necessary to
and the desire for a suburban location that is convenient for
assess and balance three dissimilar yet interrelated general
commuting to residential neighborhoods and relatively free of
principles—environment, economic, and social—based on the
street crime.
best information available at the time the decision is made. Use
6.2.3 The attributes in a MADA problem are not all mea-
AHP for pairwise comparisons among environmental
surable in the same units. Some attributes may be either
attributes, among economic attributes, and among social
impractical, impossible, or too costly to measure at all. For
attributes, and for establishing relative importance weights for
example, in an office building, energy costs are measurable in
each attribute and for each of the three general principles to
life-cycle cost terms. But the architectural statement of the
which the attributes are attached. Use the AHP-established
building may not be practically measurable in any unit. If all
relative importance weights to select the preferred project/
relevant attributes characterizing alternative buildings can be
product/process from among the competing alternatives.
expressed in terms of monetary costs or benefits scheduled to
occur at specifiable times, then the ranking and selection of a
5.6 Potential users of AHP include architects, developers,
building does not require the application of MADA.
owners, or lessors of buildings, real estate professionals
(commercial and residential), facility managers, building ma-
terial manufacturers, equipment manufacturers, product and
process engineers, life cycle assessment experts, and agencies 8
Paragraphs 6.1 – 6.4 are common to many MADA methods. Paragraphs 6.5 –
managing building portfolios. 6.7 pertain specifically to the AHP method.
E1765 − 16 (2023)
6.3 Identify the goal of the analysis, the attributes to be
considered, and the alternatives to evaluate. Display the goal
and attributes in a hierarchy.
6.3.1 The following case example of a search for public
office space illustrates how to organize and display the con-
stituents of a hierarchy.
6.3.1.1 A state agency needs, within the next 18 months,
office space for 300 workers. It seeks a location convenient to
the state capitol building by shuttle. The agency seeks to
minimize the travel time and will not accept travel times
greater than 10 min. It also has telecommunications and
computer infrastructure requirements that will exclude many
buildings. The goal of the analysis is to find the best building
for the agency.
FIG. 2 A Hierarchy Illustrating Attribute Sets and Leaf Attributes
6.3.1.2 The specification of a 10 min maximum travel time
from the site to the capitol eliminates all buildings outside a
TABLE 1 Heating System Decision Matrix
certain radius. Having up to 18 months to occupy allows either
Leaf Attributes
the construction of a new building or the retrofitting of an
Life-Cycle Cost, Duration of Warranty, Familiarity with
existing building, either of which could be rented or leased.
K$ years the Technology
Telecommunications and computer infrastructure requirements Alternative 1 10 3 high
Alternative 2 15 1 medium
will limit the search even more. These specifications help the
Alternative 3 20 10 low
analyst define the “attributes” and building “alternatives” for
the MADA analysis.
6.3.1.3 Attributes selected for the hierarchy, displayed in
being considered and a column corresponding to each leaf
Fig. 1, are occupancy availability (within 18 months); infor-
attribute being considered. Each element of the matrix contains
mation technology (available telecommunications and com-
the available information about that row’s alternative with
puter support infrastructure); economics (life-cycle costs of
respect to that column’s attribute. Put quantitative data in the
alternative buildings, owned or leased); and location (how
decision matrix if available; use nonquantitative data other-
convenient to capitol building). The analyst works with the
wise.
decision maker to make sure that all significant needs of the
6.4.2 Table 1 is a hypothetical and simplified decision
decision maker are covered by the hierarchy of attributes.
matrix for the problem of selecting the “best” heating system
6.3.2 Fig. 2 covers attribute sets and leaf attributes.
for a building. Note that the first column pertains to a monetary
6.3.2.1 A set of attributes refers to a complete group of
attribute: life-cycle costs. The next attribute, warranty period,
attributes in the hierarchy which is located under another
is measured quantitatively, but not in monetary terms. The last
attribute or under the problem goal. There are four separate sets
attribute, familiarity with the technology, is characterized only
of attributes in the hierarchy displayed in Fig. 2. Each set is
qualitatively.
enclosed by dashed lines.
6.4.3 Include in the decision matrix and analysis only those
6.3.2.2 A leaf attribute is an attribute which has no attributes
attributes which the decision maker considers important and
below it in the hierarchy. The eleven leaf attributes present in
which vary significantly among one or more alternatives. For
the hierarchy in Fig. 2 are shaded.
example, heating capacity is clearly an important attribute of
6.4 Construct a decision matrix with data on the perfor-
any heating system, but if the alternatives in Table 1 include
mance of each alternative with respect to each leaf attribute.
only systems which match the capacity requirements of the
6.4.1 Characterize your MADA problem with a decision
building in question, then capacity is not a distinguishing
matrix similar to Table 1. The decision matrix indicates both
attribute and is not to be included in the decision matrix or in
the set of alternatives and the set of leaf attributes being
the MADA analysis.
considered in a given problem, and it summarizes the “raw”
6.4.4 The MADA methods allow one to use the information
data available to the decision maker at the start of the analysis.
in a problem’s decision matrix together with additional infor-
A decision matrix has a row corresponding to each alternative
mation from the decision maker in determining a final ranking
or selection from among the alternatives. For example, the
decision matrix alone provides neither information about the
relative importance of the different attributes to the decision
maker, nor about any minimum acceptable, maximum
acceptable, or target values for particular attributes.
6.4.5 For analytical and procedural simplicity, it is common
practice when employing MADA to neglect both uncertainties
and imprecision inherent in the decision matrix data as well as
in the additional information about attributes and alternatives
FIG. 1 An Example Hierarchy for the Problem of Selecting a
Building elicited from the decision maker. While there are ways to
E1765 − 16 (2023)
incorporate uncertainty and imprecision in MADA analyses, 6.5.2 Note that the decision maker responds to questions
they are not addressed here. about how much more desirable one alternative is than another.
It helps responders if the question is framed this way, since all
6.5 Compare in pairwise fashion each alternative against
answers will result in a number greater than or equal to one. As
every other alternative as to how much better one is than the
shown in Fig. 3, however, the entries in the MPC always
other with respect to each leaf attribute. Repeat this process for
characterize the desirability of the row alternative versus the
each leaf attribute in the hierarchy. This and subsequent steps
column alternative. Therefore, in cases where the column
in the procedure describe the AHP method of performing
alternative is more desirable than the row alternative, the
MADA analysis.
6.5.1 The AHP summarizes the results of pairwise judg- decision maker must answer the question, “How much more
ments in a matrix of pairwise comparisons (MPC), as shown in desirable is the column alternative than the row alternative?” In
Fig. 3. For each pair of alternatives, the decision maker
such cases, enter the reciprocal of the resulting number into the
specifies a judgment about how much more desirable or how
MPC.
much better in terms of strength of preference one alternative
6.5.3 There are three types of approaches for specifying
is than the other with respect to the attribute in question. Each
pairwise comparison judgments in AHP: numerical, graphi-
pairwise comparison requires the decision maker to provide an
cally mediated, and verbally mediated. Each method requires
answer to the question, “Alternative 1 is how much more
the decision maker to answer a series of questions of the form,
desirable than Alternative 2, relative to the attribute of inter-
“How much more desirable is Alternative 1 than Alternative 2
est?” This procedure is repeated for each leaf attribute in the
with respect to the attribute of interest?”
hierarchy.
NOTE 1—A separate MPC comparing the alternatives is completed for each leaf attribute in the hierarchy. Within a given MPC, all comparisons of the
desirability of Alternative j versus Alternative k are made with respect to the given leaf attribute of interest.
NOTE 2—Only the n(n−1)/2 shaded elements of the matrix (those above the matrix’s diagonal) need to be filled in by the decision maker. The n diagonal
elements are all equal to 1 by definition because each alternative is “exactly as desirable as itself.” The n(n−1)/2 elements below the diagonal are equal
to the reciprocals of the corresponding elements above the diagonal. This is because, for example, if Alternative 1 is twice as desirable as Alternative
2, then Alternative 2 must be half as desirable as Alternative 1.
FIG. 3 A Matrix of Paired Comparisons (MPC) Among Alternatives
E1765 − 16 (2023)
A
TABLE 2 Verbal Expressions and Their Numerical Counterparts
bute is more important than the row attribute, the decision
maker shall answer the question, “How much more important
NOTE 1—Use numerical values that are intermediate between those
listed in the “numerical counterpart” column when preferences are is the column attribute than the row attribute?” In such cases,
intermediate between those listed in the “verbal expression” column of the
enter the reciprocal of the resulting number into the MPC.
table. For these intermediate numerical values, use either integers or
6.6.3 Use numerical, graphically mediated, or verbally me-
non-integers.
diated judgments.
Numerical
Verbal Expression
Counterpart
6.6.3.1 For example, in the numerical approach, have the
Equal importance of attributes/Equal desirability of alternatives 1 decision maker answer each question with a number, as in
Moderate importance of one attribute over another/Moderate de- 3
“Attribute 1 is 2 times as important as Attribute 2.”
sirability of one alternative over another
Strong importance of one attribute over another/Strong desirability 5 6.6.3.2 For graphical judgments, use an interactive software
of one alternative over another
display to help the decision maker establish the degree of
Very Strong importance of one attribute over another/Very Strong 7
preference.
desirability of one alternative over another
Extreme importance of one attribute over another/Extreme desir- 9
6.6.3.3 For verbally mediated judgments, have the decision
ability of one alternative over another
maker respond with a verbal expression selected from Table 2
A
This table comes from the Expert Choice User’s Guide, Decision Support
as in“ Attribute 1 is moderately more important than Attribute
Software, Inc., Pittsburgh, PA, 1993.
2.” Then convert the verbal expressions to their numerical
counterparts in Table 2. Again be aware, however, that with
verbal mediation the final desirability scores for the alterna-
6.5.3.1 For the numerical approach, have the decision
tives are sensitive to the underlying numerical scale underlying
maker answer each question with a number, as in “Alternative
the approach.
1 is 3 times as desirable as Alternative 2.”
6.6.4 Repeat the procedure for each set of attributes in the
6.5.3.2 For graphically mediated judgments, use an interac-
hierarchy.
tive software display to help the decision maker establish the
degree of preference. 6.7 Compute the final, overall desirability score for each
alternative.
6.5.3.3 For verbally mediated judgments, have the decision
maker answer each question with a verbal expression selected
6.7.1 Obtain a vector of weights for each MPC using the
from Table 2 as in “Alternative 1 is moderately more desirable
principal eigenvector method. Find the principal eigenvector
than Alternative 2.” Then convert the verbal expressions to
e* which solves Eq 1, where M is the MPC of interest and λ
max
their numerical counterparts in Table 2. Be aware, however,
is the principal eigenvalue of the matrix M.
that with verbal mediation, the final desirability scores for the
λ e* 5 Me* (1)
max
alternatives are sensitive to the numerical scale underlying the
approach.
6.7.2 Normalize the eigenvector so that its elements sum to
1.0. To solve for the normalized principle eigenvector p, divide
6.6 Make pairwise comparisons of the relative importance
each of the n elements of the principal eigenvector e* by the
of each attribute in a given set (starting with sets at the bottom
sum of the elements of e*, as shown in Eq 2. The elements of
of the hierarchy) with respect to the attribute or goal immedi-
the normalized principal eigenvector p are the weights derived
ately above that set. (Attribute sets are defined in 6.3.2.1.) Use
from the MPC using the principal eigenvector method.
the same MPC approach that was described in 6.5 for making
a series of pairwise comparisons.
p 5 e* (2)
n
6.6.1 Compare in pairwise fashion the relative importance
S D
e*
( i
of each attribute with respect to the attribute or goal above its
i51
set in the hierarchy. For each pair of attributes, the decision
Use the AHP/Expert Choice for ASTM Building Evaluation
maker specifies a judgment about how much more important
software product or similar commercially available software to
one attribute is than the other. Each pairwise comparison
compute the principal eigenvector of each MPC. Simpler hand
requires the decision maker to provide an answer to the
calculations which develop approximate solutions to Eq 1 do
question,“ Attribute 1 is how much more important than
not reliably provide an accurate solution to the principal
Attribute 2, relative to the attribute or goal above it in the
eigenvector problem.
hierarchy?”
6.7.3 Use the principal eigenvalue to calculate a heuristic
6.6.2 Note that the decision maker responds to questions
about how much more important one attribute is than another. check of consistency among the pairwise comparisons in a
given MPC. Do a consistency check for each MPC in the
It helps responders if the question is framed this way, since all
answers will result in a number greater than or equal to one. problem both on comparisons among alternatives and among
attributes.
Recall from Fig. 3, however, that the entries in an MPC always
characterize the importance of each row attribute versus each
6.7.3.1 Perfect consistency among pairwise comparisons is
column attribute. Therefore, in cases where the column attri-
equivalent to perfect cardinal transitivity among the compari-
sons. That is, if Attribute 1 is twice as important as Attribute 2,
and Attribute 2 is three times as important as Attribute 3, then
Integer answers are not required. For example, it is appropriate to say
perfect cardinal transitivity requires that Attribute 1 is six (two
Alternative 1 is 1.2 times as desirable as Alternative 2 if that is your best estimate
of relative desirability. times three) times as important as Attribute 3.
E1765 − 16 (2023)
6.7.3.2 Since the MPC has ones along its diagonal, then One in the hierarchy), and Col. 2 contains 21 subattributes
according to a theorem of linear algebra, its principal eigen- (Level Two in the hierarchy). The Level One attributes
value will be exactly equal to n if the pairwise comparisons are represent broad categories; they are designed to help decision
perfectly consistent, where n is the number of columns or rows makers shape their decision problem in a parsimonious fashion
in the square matrix. Also, if the pairwise comparisons deviate (that is, without introducing an overly large number of attri-
only slightly from perfect consistency, then the principal butes). Consequently, the Level One attributes help decision
eigenvalue will deviate only slightly from n. makers avoid unnecessary complexity which would make the
6.7.3.3 Use the difference between the principal eigenvalue decision hierarchy become unwieldy. The Level Two attributes
λ and the order n of the matrix as the measure of inconsis- provide traceability to one or more of ASTM’s reference
max
tency. Compare this difference with the average difference, as standards. The corresponding ASTM reference standard(s) for
shown in the second column of Table 3, which would arise each Level Two attribute is listed in Col. 3.
from purely random pairwise comparison values. The farther
7.2 The list of attributes is the product of a collaboration
the difference λ 2n is from zero (that is, the closer to the
? max ?
between two subcommittees of ASTM Committee E06 on
difference resulting from random comparison values), the more
Performance of Buildings. These subcommittees are ASTM
inconsistent is your set of pairwise comparisons.
Subcommittee E06.25 on Whole Buildings and Facilities and
6.7.4 Compute the final desirability scores for each ASTM Subcommittee E06.81 on Building Economics. The
alternative, using Eq 3. The alternative with the highest majority of the attributes are based on the 18 published
desirability score is the preferred alternative. standard classifications developed by Subcommittee E06.25.
These attributes focus on rating building serviceability and
L
D 5 r i w i (3)
~ ! ~ !
a a
(i51
performance (see Practice E1679). The remaining attributes are
drawn from the E06.81 Subcommittee standards and focus on
The quantity L is the number of leaf attributes in the
evaluating the economic performance of investments in build-
hierarchy. The quantity r (i) is the normalized “rating” of
a
ings and building systems. These economics standards include
Alternative a with respect to Leaf Attribute i, which is equal to
one standard classification, four standard practices, and one
the ath element of the normalized principal eigenvector of the
MPC from comparisons of the alternatives with respect to Leaf adjunct.
Attribute i. The quantity w(i) is the composite weight of Leaf
7.3 The list of attributes shown in Table 4 provides the basis
Attribute i. For simple hierarchies with only one set of
for a glossary of attributes in the ASTM software product,
attributes, w(i) is equal to the ith element of the normalized
AHP/Expert Choice for ASTM Building Evaluation. The
principal eigenvector of the MPC from comparisons of the
software product, designed to support this standard, provides a
attributes with respect to the goal. For hierarchies with more
model-building feature that allows the decision maker to
than one set of attributes, compute w(i) following the proce-
“slice” away those attributes not wanted to create a model of
dure described in Annex A1.
remaining attributes that best represent the decision maker’s
unique problem. The software product is quite flexible in that
7. List of Selected Attributes for Evaluating Office
any attribute important to the decision maker, whether or not it
Buildings
is included in the glossary, can be added to the model structure.
7.1 Table 4 contains a list of attributes and subattributes that
7.4 The attributes apply primarily to office or commercial
decision makers typically find important in making building-
buildings. With some minor modifications, however the attri-
related choices. The list gives building users a ready-made set
butes are appropriate for evaluating residential choices.
of building attributes to choose from when using an AHP
7.5 Some of the attributes, such as property management
model to compare building alternatives. Because the list is
and regulation and building economics are also appropriate
intended to be comprehensive, it is arranged in a hierarchical
when using AHP to evaluate constructed facilities other than
fashion. Column 1 of Table 4 contains seven attributes (Level
buildings. This includes dams, water supply and waste treat-
ment facilities, transportation infrastructure, and other public
TABLE 3 Values of λ 2n Resulting from Random
| max |
works type projects. Alter the attributes cited in Table 4 or add
A
Comparison Values
new attributes to make the decision model fit the type of
Value of λ 2n Resulting from
Order of the Matrix
| max |
facility being evaluated.
(number of columns or rows)
Random Comparison Values
3 1.16
8. Typical Building-Related AHP Applications
4 2.7
5 4.48
8.1 There are four common types of AHP building-related
6 6.2
choice decisions: (1) choosing among buildings, (2) choosing
7 7.92
among building components or elements, (3) choosing
8 9.87
9 11.6
among building materials, and (4) choosing the location for a
10 13.41
business or household. The following sections illustrate for
11 15.1
these four decision types how to identify the goal, select
A
The numbers in this table are adopted from results published in Saaty’s The
attributes, and display them in a hierarchy.
Analytic Hierarchy Process, 1988, p. 21. They were derived assuming equal
probability of integer comparison values over the closed interval from 1 to 9,
enforcing reciprocity.
See Classification E1557 for a classification of building elements.
E1765 − 16 (2023)
TABLE 4 Attributes for Building-Related Decisions
Attribute ASTM Reference
Level One Level Two Standard
(Col. 1) (Col. 2) (Col. 3)
Work Function Support for office Work E1660
Meetings and Group Effectiveness E1661
Typical Office Information Technology E1663
Special Facilities and Technologies E1694
Environmental/Ergonomic Support Sound and Visual Environment E1662
Thermal Environment and Indoor Air Conditions E2320
Flexibility and Space Planning Change and Churn by Occupants E1692
Layout and Building Factors E1664
Security and Continuity of Work Protection of Occupant Assets E1693
Facility Protection E1665
Work Outside Normal Hours or Conditions E1666
Image, Amenities and Access Image to Public and Occupants E1667
Amenities to Attract and Retain Staff E1668
Location, Access and Wayfindig E1669
Property Management and Regulation Structure, Envelope and Grounds E1700
Manageability E1701
Management of Operations and Maintenance E1670
Cleanliness E1671
Building Economics First Cost Considerations E1557
Operations and Maintenance Cost Considerations Discount Factor Tables
Economic Measures E917, E1074
E964, E1057
8.2 Residential Example —A real estate company special-
izing in residential properties wants a computer-based decision
tool to help clients select the “best” match between their
individual housing wants and what is available on the multiple
listing. An out-of-town client on a two-day house search comes
to the real estate office and asks to be shown houses. The client
wants a four-bedroom, three-bath, traditional home with a
two-car garage in the suburbs that is reasonably accessible to a
commuter train station on route to the central business district.
The client wants a highly respectable, safe neighborhood and is
FIG. 4 An Example Hierarchy for the Problem of Selecting a
willing to pay up to $200,000 for the house. An important
Residence
consideration to the client is the quality of the public schools.
Find the best house for the client.
8.2.1 An AHP analysis is appropriate here in two stages.
of equipment components, but at the same time it does not
First, the real estate salesperson uses AHP to help the client
want to appear to its constituency as being uneconomic in its
select that set of houses to visit. The client identified the
choice of a heating and cooling system. Furthermore, the
following significant attributes: building serviceability (num-
association does not want the equipment to impair the existing
ber of rooms and baths, capacity of garage); aesthetics (taste-
successful operation and maintenance of the building. Help the
fully designed traditional home); location (accessibility to
trade association identify the best alternative among the
commuter station, desirability of neighborhood, proximity of
candidate systems.
good public schools); security; and economics (budget con-
8.3.1 The association selects several attributes from Table 4
straint). Fig. 4 displays the hierarchy of attributes. The house-
in evaluating the systems. In seeking to show the state-of-the-
hunting client visits the houses with the highest AHP scores.
art in equipment, the association acknowledges that image to
8.2.2 The real estate salesperson does the AHP analysis a
the owner is important. Economics was also pointed out.
second time once the client has seen the selected houses and
Maintaining successful building functions, smooth operation
has additional information for constructing a more detailed
and maintenance, a high level of thermal environment and air
decision matrix. An AHP analysis with a graphical presentation
quality, and a high standard of sound and visual environment
of the score of each house helps satisfy homebuyers that they
are also important. Fig. 5 displays a hierarchy made up of these
are selecting the house that is best for them.
attributes.
8.3 Choosing Among Components—A trade association rep-
8.4 Choosing Among Materials—An architect is working
resenting the heating and cooling equipment industry is choos-
with clients to select materials for a large office building. The
ing among three high-technology systems for retrofitting its
clients tell the architect that they want a building made from
office building. It wants to show the state of the art in its choice
materials that are friendly to the environment. The clients
qualify their specifications, however, to say that they do not
want the building’s functions to be compromised by the design
The choice-among-buildings decision for a commercial office building is
illustrated in Section 9. or choice of materials. They go on to say that, while they are
E1765 − 16 (2023)
FIG. 5 An Example Hierarchy for the Problem of Selecting a
FIG. 7 An Example Hierarchy for the Problem of Selecting a
Building Component
Building Location
existing buildings. The company gives the following descrip-
tion of its needs to a commercial realtor engaged to find
appropriate space.
9.2 The company conducts business inside and outside the
United States. The headquarters building, which is too small
because of staff growth, is in a large metropolitan area.
FIG. 6 An Example Hierarchy for the Problem of Selecting a
Management wants to lease a building for the new corporate
Building Material
headquarters in a prominent location somewhere in the same
metropolitan area. They want the style and location of the
willing to spend more money on materials to achieve a “green building to portray an upscale public image of a company that
building,” cost is still a consideration. The architect decides to is modern and progressive. They also want a location that will
be an attractant to the existing headquarters staff whom they
use AHP to make the material choices that will best satisfy the
clients’ needs. hope will stay with the company after the move to the new
building. Time is important because the lease on the existing
8.4.1 Fig. 6 displays a hierarchy made up of the attributes
that the clients identified: environmental impacts, economics, headquarters building is up for renewal in six months.
building serviceability, and operation and maintenance.
9.3 To find the building that best suits the company’s needs,
8.5 Choosing the Location —A large corporation is seek- the search firm decides to apply the AHP method in collabo-
ration with the three-member property search committee of the
ing the best location in the United States for a new manufac-
turing plant. The search committee is seeking an area where company’s board of directors. The steps, in order, are as
follows:
there will be a continuing, abundant, sufficiently educated labor
pool to staff an assembly line employing state-of-the-art (1) Define the goal of the building search;
(2) Identify important attributes and subattributes;
technology. The company is looking for an area where the
demand for labor is low, the community will offer incentives to (3) Identify alternative buildings (called properties in the
analysis);
a new company, new hires are expected to be loyal to the
company, and where management can likely operate a non- (4) Construct a decision matrix containing available data
union plant. Convenient and centrally located transportation on the performance of each alternative with respect to each leaf
nodes are also important. The major objective is to hold down attribute (see Fig. 8 and Fig. 9);
costs and remain competitive with foreign manufacturers. (5) Construct the hierarchy;
Environmental and cultural amenities are also important, (6) Make pairwise comparisons of each alternative against
however, to attract a high-quality management team. The every other alternative as to how much preferable one is over
the other with respect to each leaf attribute;
search committee uses AHP to find th
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