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Building and Environment 44 (2009) 1162–1170
Contents lists available at ScienceDirect
Building and Environment
journal homepage: www.elsevier.com/locate/buildenv
Optimization model for the selection of materials using a LEED-based
green building rating system in Colombia
Daniel Castro-Lacouture a, *, Jorge A. Sefair b, Laura Flórez b, Andrés L. Medaglia b
a
b
Building Construction Program, College of Architecture, Georgia Institute of Technology, 280 Ferst Drive, Atlanta, GA 30332, USA
Centro de Optimización y Probabilidad Aplicada (COPA), Departamento de Ingenierı́a Industrial, Universidad de los Andes, Bogotá D.C., Colombia
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 16 May 2008
Received in revised form 6 August 2008
Accepted 19 August 2008
Buildings have a significant and continuously increasing impact on the environment because they are
responsible for a large portion of carbon emissions and use a considerable number of resources and
energy. The green building movement emerged to mitigate these effects and to improve the building
construction process. This paradigm shift should bring significant environmental, economic, financial,
and social benefits. However, to realize such benefits, efforts are required not only in the selection of
appropriate technologies but also in the choice of proper materials. Selecting inappropriate materials can
be expensive, but more importantly, it may preclude the achievement of the desired environmental
goals. In order to help decision-makers with the selection of the right materials, this study proposes
a mixed integer optimization model that incorporates design and budget constraints while maximizing
the number of credits reached under the Leadership in Energy and Environmental Design (LEED) rating
system. To illustrate this model, this paper presents a case study of a building in Colombia in which
a modified version of LEED is proposed.
2008 Elsevier Ltd. All rights reserved.
Keywords:
Green building
Material selection
Sustainable building rating systems
Building design
Mixed integer linear programming
1. Introduction
Buildings have an enormous and continuously increasing
impact on the environment, using about 40% of natural resources
extracted in industrialized countries [1], consuming nearly 70% of
electricity and 12% of potable water [2], and producing between 45
and 65% of the waste disposed in landfills [3]. Moreover, they are
responsible for a large amount of harmful emissions, accounting for
30% of greenhouse gases, due to their operation, and an additional
18% caused indirectly by material exploitation and transportation
[3–5]. At the same time, the bad quality of indoor environments
may cause health problems to employees in office buildings, thus,
decreasing productivity [6].
1.1. Emergence of green buildings
In order to mitigate the impact of buildings along their life cycle,
Green Building (GB) has emerged as a new building philosophy,
encouraging the use of more environmentally friendly materials,
the implementation of techniques to save resources and reduce
* Corresponding author. Tel.: þ1 404 385 6964; fax: þ1 404 894 1641.
E-mail addresses: daniel.castro@coa.gatech.edu (D. Castro-Lacouture), j-sefair@
uniandes.edu.co (J.A. Sefair), l.florez403@egresados.uniandes.edu.co (L. Flórez),
amedagli@uniandes.edu.co (A.L. Medaglia).
0360-1323/$ – see front matter 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.buildenv.2008.08.009
waste consumption, and the improvement of indoor environmental
quality, among others [2,7]. This would result in environmental,
financial, economic, and social benefits. As an illustration, savings
in operation and maintenance costs in GBs can be realized through
the installation of high-efficiency illumination and insulation
systems [8] or through an appropriate material selection process
that considers, for instance, the daylight roof reflection [2,9]. Other
benefits of GBs related to indoor environmental quality improvements are the reduction on health costs and the increase on
employees’ productivity [8,10,11] through their perceived satisfaction towards work areas [6]. Furthermore, intangible benefits, such
as the building and builder’s goodwill, and perceived added value
must also be considered [8,12,13] because they could guide the
decisions of investors and future owners [10,13].
Despite their demonstrated benefits, GBs are not yet perceived
as attractive projects because most builders associate green
features with expensive technologies that add cost (e.g., photovoltaic panels, grey water reuse systems) [14,15]. However, a careful
design process and a comprehensive material selection method,
rather than an elevated investment in technology, may be enough
to achieve desired environmental goals at a lower cost. In fact, some
evidence supports the lack of difference between the average
investment cost per square foot for some GBs, such as academic
buildings, laboratories, community centers, and ambulatory care
facilities, and that of non-green buildings with the same characteristics [14]. Moreover, GBs provide better returns in the long run
D. Castro-Lacouture et al. / Building and Environment 44 (2009) 1162–1170
[8,10,11], recovering up to 10 times the green premium through the
realization of expected benefits [11].
The success of a GB depends on the quality and efficiency of the
installed green systems. If the building lacks these essential
features, it will neither accomplish the environmental goals nor
generate the estimated benefits. Thus, the market requires
a common way to differentiate GBs from traditional buildings
through the use of standard, transparent, objective, and verifiable
measures of green, which assure that the minimum green
requirements have been reached.
1.2. Green building rating systems
Many methodologies have been developed to establish the degree
of accomplishment of environmental goals, guiding the planning and
design processes. In these earlier stages of the construction process,
planners can make decisions to improve building performance at
very little or no cost, following the recommendations of the decisionmaking tool. The first of such tools was the Building Research
Establishment Environmental Assessment Method (BREEAM) [16].
After that, other methodologies, such as Green Star from Australia
[17], the Comprehensive Assessment System for Building Environmental Efficiency (CASBEE) from Japan [18], the Building and Environmental Performance Assessment Criteria (BEPAC) from Canada
[19], and the Leadership in Energy and Environmental Design (LEED)
from the United States [20] were developed and are currently widely
applied. Very comprehensive inventories of available tools for environmental assessment methods can be found in Ding [21], the Whole
Building Design Guide [22], and the World Green Building Council
[23].
Although the existing methods and tools have an extended use,
LEED has established strong credibility among the experts [1,21],
increasing its affiliates. According to Bowyer [24], in April of 2007,
the LEED system was comprised of 7500 companies and organization members, validating its importance as the standard environmental performance measure of a building [3,8] and becoming
a reference system for the design, construction, and operation of
GBs beyond the U.S. [1,12,15,25]. Adaptations of the LEED system
have been applied or are in the process of implementation in Brazil
and Mexico [26], two of the largest developing economies in the
Western hemisphere. Furthermore, the LEED system is being
proposed as a reference framework for countries in which there is
no current method of building environmental assessment, such as
the case of Colombia [27], where a national council for sustainable
construction is being formed to start operations in 2008 [23,28].
Like many of the available rating systems, the LEED rating
system is based on credits and points [29]. Through each credit, the
system evaluates the performance of the candidate building and
awards points if the requirements are reached in a variety of areas
such as sustainable sites, indoor environmental quality, and
materials and resources. Although these categories should not be
treated separately, but rather as a whole, it has been stated that
materials are the most-significant topic in a building study [30],
reducing the environmental footprint through the correct choice
and substitution of materials [7]. According to the LEED rating
system [29], the selection of environmentally responsible materials
considers material accessibility by encouraging the use of materials
extracted, processed, and manufactured regionally, and, at the
same time, promoting the development of regional economies. The
LEED system also encourages the use of high recycled content, rapid
renewable cycle, and low-emitting contaminant materials which
aim to reduce their impact on the environment and indoor air
quality of the building. As a result, the design of a GB requires
a comprehensive process for material selection that considers not
only the previously described standards but also design and budget
requirements that are key factors for the success of the building.
1163
1.3. Selection of materials
The material selection problem has been treated extensively in
the literature through many approaches, such as multiobjective
optimization [31,32], ranking methods [33,34], index-based
methods [35,36], and other quantitative methods like cost–benefit
analysis [37]. However, current literature in the building domain
lacks a standard method that may help the decision-maker select
the more-appropriate materials while at the same time looking at
the accomplishment of environmental goals and meeting design
and budgetary requirements. This gap is observed in spite of cost
being a common reason for the bankruptcy of many GB projects
[15,21] given that materials reach up to 20–30% of the total building
cost [8].
This article proposes a mixed integer linear program (MILP) that
improves green construction decision-making through the selection of materials. The model considers both design and budget
constraints to address realistic scenarios experienced by the decision-maker. In addition, the model includes soft constraints that
describe the LEED requirements pertaining to the selection of
materials, which may or may not be satisfied. The number of
satisfied constraints constitutes the objective function to maximize.
In other words, the model attempts to maximize the number of
satisfied LEED constraints while also satisfying design and budget
constraints. To illustrate the operation of the model, a case study of
an office building construction project in Colombia is discussed.
This article is organized as follows. Section 2 describes the LEED
credits considered. Section 3 presents the optimization model.
Section 4 addresses the case study of a building in Colombia,
describing the data sources used, and presenting the results and
sensitivity analysis of the case study. Finally, Section 5 concludes
the paper and outlines the future research.
2. LEED-based rating system for material selection
Credits in the proposed LEED-based rating system are based on
those credits in the existing LEED rating system for new construction and major renovations that are related to material selection
[29]. Through each credit, the proposed rating system evaluates the
performance of the candidate building in terms of the characteristics of the materials, such as the contribution to the heat island
effect, proportion of recycled content, distance from the supplier or
producer to the project site, and emissions of indoor pollutants (see
Table 1). For each criterion, the rating system awards points if the
requirements are reached, accounting a number of 11 available
points.
The requirements of the proposed LEED-based rating system are
adapted for the specific situation of the Colombian market. For
instance, in Colombia, because specifications on available materials
state only the total recycled content, those credits related to recycled content do not differentiate between pre-consumer or postconsumer recycled content. Thus, credits 4.1 and 4.2 in the area of
materials and resources (see Table 1) state that, in order to award
points, the total recycled content should constitute a minimum
portion of the total cost of the materials for the project, requiring
a minimum 10% for credit 4.1 and 20% for credit 4.2. Credits
regarding regional materials (credits 5.1 and 5.2 in the area of
materials and resources) are also adapted to take into account
a more-convenient distance from the place where materials are
extracted, harvested, recovered, or manufactured to the project
site. However, it is not possible to track the origin of the components for most available materials, manufacturing requirements do
not consider the proportion of the final product manufactured in
the region, but only that at least one process has been conducted in
the same region of the project. As LEED states, the aim of these
credits is not only to reduce the environmental effects caused by
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D. Castro-Lacouture et al. / Building and Environment 44 (2009) 1162–1170
Table 1
LEED-based credits considered in the materials selection problem
Credit
Area
Name
Intent
7.2 (Points: 1)
Sustainable sites
Heat island effect, roof
Reduce heat islands
4.1 (Points: 1)
Materials and resources
Recycled content – 10%
4.2 (Points: 1)
Recycled content – 20%
5.1 (Points: 1)
Regional materials, 10%
extracted, processed &
manufactured regionally
5.2 (Points: 1)
Regional materials, 20%
extracted, processed &
manufactured regionally
6 (Points: 1)
Rapidly renewable materials
7 (Points: 1)
Certified wood
4.1 (Points: 1)
Indoor environmental quality Low-emitting materials,
adhesives & sealants
4.2 (Points: 1)
Low-emitting materials, paints
& coatings
4.3 (Points: 1)
Low-emitting materials, carpet
systems
4.4 (Points: 1)
Low-emitting materials,
composite wood & agrifiber
products
Description
Use roofing materials having a solar reflectance
index (SRI) equal to or greater than 78 for lowsloped roofs (2:12) or 29 for steep-sloped
roofs (>2:12). These values must be used for
a minimum of 75% of the roof surface.
Increase demand for building
Use materials with recycled content such that
products that incorporate recycled the content constitutes at least 10% (based on
content materials, reducing impacts cost) of the total value of the materials in the
from extraction and processing of
project. Only include materials permanently
virgin materials.
installed in the project, except mechanical,
electrical, plumbing components and specialty
items such as elevators. The recycled fraction of
the assembly (by weight) is multiplied by the
cost of assembly to determine the recycled
content value.
Use materials with recycled content such that
content constitutes an additional 10% beyond
Credit 4.1 (total of 20%, based on cost) of the
total value of the materials in the project.
Increase demand for building
Use building materials or products that have
materials and products that are
been extracted, harvested or recovered, as well
extracted and manufactured within as manufactured, within the same region of the
the region, supporting local
project site for a minimum of 10% (based on
economies and reducing the
cost) of the total materials value. Only include
environmental impacts resulting
materials permanently installed in the project,
from transportation.
except mechanical, electrical, plumbing
components and specialty items such as
elevators.
Use building materials or products that have
been extracted, harvested or recovered, as well
as manufactured, within the same region of the
project site for an additional 10% beyond Credit
5.1 (total of 20%, based on cost) of the total
materials value.
Reduce the use and depletion of
Use rapidly renewable building materials and
finite raw materials and long-cycle products (made from plants that are typically
renewable materials by replacing
harvested within a ten-year cycle or shorter) for
them with rapidly renewable
2.5% of the total value of all building materials
materials.
and products used in the project, based on cost.
Encourage environmentally
Use a minimum of 50% (based on cost) of woodresponsible forest management.
based materials and products, which are
certified (e.g., Forest Stewardship Council’s
-FSC), for wood building components (e.g.,
structural framing and general dimensional
framing, flooring, sub-flooring, wood doors, and
finishes). Only include materials permanently
installed in the project.
Reduce the quantity of indoor air
All adhesives and sealants used on the interior
contaminants that are odorous,
of the building shall comply with the volatile
irritating and/or harmful to the
organic compounds (VOC) limits provided in
comfort and well-being of installers USGBC (2005) page 65.
and occupants.
Paints and coatings used on the interior of the
building shall comply with the volatile organic
compounds (VOC) limits provided in USGBC
(2005) page 67.
All carpet installed in the building interior shall
meet the product requirements of the Carpet
and Rug Institute’s Green Label Plus program.
Composite wood and agrifiber products used on
the interior of the building shall contain no
added urea-formaldehyde resins. Laminating
adhesives used to fabricate on-site and shopapplied composite wood and agrifiber
assemblies shall contain no added ureaformaldehyde resins.
Source: Adapted from USGBC [29].
transportation, but also to support regional economies. Credits
promoting the use of rapidly renewable materials (credit 6 in the
area of materials and resources), certified wood (credit 7 in the area
of materials and resources), and low-emitting materials (credits 4.1,
4.2, 4.3, and 4.4 in the area of indoor environmental quality) are
considered as stated in the LEED system for new construction and
major renovations [29]. Credit 7.2 in the area of sustainable sites
considers the solar reflectance index as the only criteria for roofing
materials.
3. Mixed integer optimization model for material selection
This section presents the proposed mixed integer model for
material selection. Let S be the set of building systems (e.g., wood
D. Castro-Lacouture et al. / Building and Environment 44 (2009) 1162–1170
finishes, floors, walls, roofs), T the set of types of materials, and Jj the
subset of materials that are used in system j˛S. Let
F ¼ MA WMP WMC WMW WMW WMR be a partition based on the
types of materials, where MA represents the set of adhesives and
sealants, MP the set of paints and coatings, MC the set of carpet
systems, MW the set of composite wood and agrifiber products
permanently installed in the building, MW the set of composite
wood and agrifiber products temporally installed in the building
during the construction process, and MR the set of roofing materials.
Note that F ¼ W Mt , where Mt1 XMt2 ¼ B for t1 st2 ; t1 ; t2 ˛T.
t˛T
j
Let Qn be a category of materials such that one or more of these
materials can be selected to complete a fraction or the whole system
NðjÞ
j
j. Consequently, Jj ¼ Wn ¼ 1 Qn , where N(j) is the maximum number
of categories in the system j. Finally, the set of credits under the
proposed LEED-based system, according to Section 2, is expressed by
L.
The available budget for materials in the building systems in S is
denoted by the parameter b. The dimension (length, area, or
volume units) of system j is expressed by dj and the cost per unit of
material is denoted by ci. The number of points earned if credit k˛L
is accomplished is pk. The recycled content of material i as
a percentage of the total weight is expressed by ri. Let vi be the
content of volatile organic compounds (VOC) of the material
i˛MA WMP measured in [g/L] for adhesives, sealants, and paints. Let
v_ i be the emission factor of volatile organic compounds (VOC) of the
material i˛MC measured in [mg/m2 h] for carpets. The maximum
allowed content of VOC (in [g/L]) of a material i˛MA WMP is denoted
by vui. The maximum allowed emission factor of VOC (in [mg/m2 h])
of a material i˛MC is denoted by v_ ui. The minimum and maximum
fraction of the system j˛S that can be built using one of the
materials from category Qnj , are denoted by lnj and
unj ð0 lnj unj 1Þ, allowing the designer to impose his/her
requirements. The maximum number of materials from category Qnj
that can be selected to build system j is Knj. The constant G takes
a value much greater than zero ðG[0Þ and it is used in some of the
constraints as a penalty term.
Binary parameters are also defined to describe some properties
of materials: ei takes the value of 1 if the material was extracted,
recovered, manufactured, or processed in the same region that the
project, it takes the value of 0, otherwise; hi takes the value of 1 if the
material i˛MW WMW is made by rapidly renewable materials (see
Table 1), it takes the value of 0, otherwise; fi takes the value of 1 if the
material i˛MW has a certification of responsible forest management
(e.g., Forest Stewardship Council’s – FSC), it takes the value of 0,
otherwise; mi takes the value of 1 if the material i˛MW WMA does not
contain urea–formaldehyde resins, it takes the value of 0, otherwise;
and si takes the value of 1 if material i˛MR accomplishes the required
minimum solar reflectance index according to the desired slope (see
Table 1), it takes the value of 0, otherwise.
The proposed model identifies the materials and their required
amount as a fraction of the system. Let xij ð 0Þ be the fraction of
system j˛S that is built using material i. The binary variable yi takes
the value of 1 if the material is used (in any building system); it
takes the value of 0, otherwise. Let zk be a binary variable that takes
the value of 1 if credit k˛L is accomplished, as is stated in the Table
1; it takes the value of 0, otherwise. The proposed mixed integer
program follows:
max
X
pk zk
i˛Qnj
xij unj ;
j˛S; n ¼ 1; 2; .; NðjÞ
(3)
i˛Qnj
j˛S; i˛Jj
xij yi ;
X
xij ¼ 1;
(4)
j˛S
(5)
ci dj xij b
(6)
i˛Jj
X X
j˛S i˛Jj
X
si xij 0:75z1 ;
j˛S
(7)
i˛Jj XMR
0
0:10@
XX
1
0
ci dj xij A @
j˛S i˛Jj
0
0:20@
XX
1
0
ci dj xij A @
j˛S i˛Jj
0
0:10@
X
X X
X
0:20@
X X
1
0
ci dj xij A @
0:025@
1
0
ci dj xij A @
0:5@
XX
X
1
X
ri ci dj xij A þGð1z3 Þ
(9)
X X
1
ei ci dj xij A þ Gð1 z4 Þ
(10)
X X
1
ei ci dj xij A þ Gð1 z5 Þ
(11)
j˛S i˛Jj
1
0
ci dj xij A @
j˛S i˛Jj
0
(8)
j˛S i˛Jj
j˛S i˛Jj
0
ri ci dj xij A þGð1z2 Þ
j˛S i˛JyMW
j˛S i˛Jj
0
1
X
j˛S i˛Jj yMW
X
XX
1
hi ci dj xij A þGð1z6 Þ
(12)
j˛S i˛Jj
1
0
ci dj xij A @
j˛S i˛Jj XMW
X
X
1
fi ci dj xij A þ Gð1 z7 Þ
j˛S i˛Jj XMW
(13)
vi yi vui þ ð1 z8 ÞG;
i˛MA
(14)
vi yi vui þ ð1 z9 ÞG;
i˛MP
(15)
v_ i yi v_ ui þ ð1 z10 ÞG;
subject to,
X
yi Knj ;
1165
(1)
k˛L
lnj X
j˛S; n ¼ 1; 2; .; NðjÞ
(2)
yi ð1 mi Þ ð1 z11 ÞG;
i˛MC
i˛MW
(16)
(17)
1166
xij 0;
D. Castro-Lacouture et al. / Building and Environment 44 (2009) 1162–1170
j˛S; i˛Jj
(18)
carpentry, and wood carpentry; 5) carpets used on floors of
common areas; 6) roofs; 7) glass; and 8) window assemblies.
Additionally, the building design specifies a low-sloped roof.
i˛F
(19)
4.1. Data sources
yi ˛f0; 1g;
zk ˛f0; 1g;
k˛L
(20)
As is shown in Eq. (1), the model seeks to maximize the number of
points awarded by the accomplishment of LEED-based credits. The
set of constraints (2) allows the decision-makers to impose lower
and upper limits on the fraction of each system built using materials from a specific category while constraints (3) allow the decision-makers to impose a maximum number of materials that can
be selected to build each system. If the decision-maker would like
to determine the fraction of system j that must be built using
j
materials from category Qn, then he/she could set lnj ¼ 0 and unj ¼ 1.
On the other hand, if the decision-maker sets lnj ¼ unj, then the
j
fraction of system j built using materials from category Qn is fixed.
Constraints (4) articulate the variables representing the fraction of
the materials used, with the corresponding binary variables that
specify that a given material is used. The set of constraints in Eq. (5)
states that the entire system (100%) must be completed. The budget
constraint shown in Eq. (6) limits the amount of money available to
purchase materials for the systems in S.
Constraints (7)–(17) consider the LEED-based requirements
stated in Table 1. The constraints shown in Eq. (7) represent credit
7.2 from the area of sustainable sites, which states that 75% of the
roof area must be built using materials complying with the required
solar reflectance index. Credit 4.1, from the area of materials and
resources, is considered in Eq. (8) and requires that at least 10% of
the total cost of materials in the project should be allocated to
materials with recycled content. Constraint (9) represents credit 4.2
from the area of materials and resources, and reflects an additional
10% of the cost invested in materials with recycled content. Notice
that if constraint (9) is satisfied, then constraint (8) is also satisfied.
Credits 5.1 and 5.2, promoting the purchase of regional materials,
are considered in constraints (10) and (11), respectively. Likewise, if
constraint (11) is satisfied, then constraint (10) is also satisfied.
Constraint (12) shows the requirements stated in credit 6 from the
area of materials and resources, motivating the use of rapidly
renewable materials. Credit 7, from the area of materials and
resources, is considered in Eq. (13) and encourages the use of
certified wood. Constraints (14) and (15) show the recommended
maximum VOC content for adhesives and sealants, paints, and
coatings, respectively, while constraint (16) shows the maximum
VOC emission factor for carpet systems. Constraint (17) contains the
requirements in credit 4.4 from the area of indoor environmental
quality. It discourages the use of materials containing urea–formaldehyde resins. Finally, constraints (18) enforce non-negativity
conditions on the fractions, while constraints (19) and (20) state the
binary nature of the decisions regarding material use and the
accomplishment of the LEED credits.
4. A numerical example based on a case study
The case study is based on the application of the model in an 11story office building with an area of 6000 m2 in Bogotá, Colombia.
The estimated total budget for materials is about USD 183,500. A
total of eight systems are considered: 1) wood carpentry used in the
building interior, including doors and wood finishes; 2) wood
temporally used during construction, such as slabs, timbers, rolls,
and laminates for walls and exterior finishes; 3) adhesives and
sealants; 4) paints, coatings, vinyl, and varnishes used in the
building interior for ceilings, walls, parking spaces, metallic
The environmental properties required by the LEED-based
system of Section 2 are mainly obtained using Building for Environmental and Economic Sustainability software – BEES [38].
Although BEES is not the only source available in the literature, it
provides reliable information for a wide range of construction
materials. However, some of the materials available in the Colombian market, as well as some material properties required by the
LEED system [39], are not included in BEES. Thus, we also use local
studies [40] to complement the main data source.
The information regarding systems and materials is shown in
Table 2. The recycled content for adhesives and sealants, carpets,
and paints is obtained from BEES software, while the same information for wood components, construction wood, glass, roof, and
windows is obtained from a study in Motta [40], which provides an
inventory of properties for local materials. Information regarding
regional materials, renewable time, urea–formaldehyde content,
and certified-wood labels comes directly from the suppliers. The
volatile organic compound (VOC) emissions for carpets are estimated using BEES software and, for similar products not available
in BEES, they are obtained from the California Indoor Air Quality
Program [41]. The maximum allowed emission of VOC for carpets is
obtained from the Carpet and Rug Institute [42]. The VOC content
for paints, adhesives, and sealants are obtained through BEES
software and free online databases. Maximum limits for VOC
content for adhesives and sealants, paints, and carpets are
considered as stated in USGBC [29]. The solar reflectance index
(SRI) for roofing materials is estimated using similar materials from
Energy Star [43]. Finally, the cost per unit of dimension for each
material is obtained from a local directory of prices.
4.2. Optimal selection of materials
Table 3 shows the results of the model, where the column
labeled xij indicates the fraction of each system to be built from the
selected materials. For instance, to build the wood components
system, the model suggests the use of 40% of wood component 2,
20% of wood component 3, and 40% of wood component 4.
Although these results show the fraction of the system that should
be built using a specific material, they can also be used to quantify
the required amount of each material. For instance, the model
suggests purchasing 67.59 m of wood component 2, 230.77 gal of
paint 3 and 91.34 m2 of glass 3. Furthermore, the results provided
by the model can also be used to obtain a detailed purchase plan. As
shown in Table 3, once the costs of all materials are estimated, the
total cost is USD 183,353.
Although the solution shown in Table 3 satisfies budget and
design constraints, it satisfies only 5 out of the 11 LEED-based
constraints. In other words, the solution awards 5 out of the 11
points available, but fails to achieve the points in credit 7.2 from
sustainable sites, credits 4.2 and 7 from materials and resources,
and those from credits 4.2, 4.3 and 4.4 related to indoor environmental quality. This number of awarded points may be insufficient
to obtain a green certification, so a further analysis to determine
how to award more points will add value to the decision-making
process.
As stated in the literature, a crucial factor that can preclude the
achievement of green goals is the available budget [15]. A scarce
budget may not allow the model to select more convenient materials to satisfy all LEED-based constraints, limiting the number of
awarded points. To determine the additional funding required for
D. Castro-Lacouture et al. / Building and Environment 44 (2009) 1162–1170
1167
Table 2
System and materials information
System (j)
dj
Wood components
Construction (wood)
168.97 (m)
8768.64 (m)
Adhesives and sealants
5.01 (gal)
Paint
288.46 (gal)
Carpet
17.22 (m2)
Roofs
542.9 (m2)
91.344 (m2)
Glass
Windows
1059.35 (m2)
Material (i)
lnj
unj
wood component 1
wood component 2
wood component 3
wood component 4
wood component 5
construction wood 2
construction wood 3
construction wood 4
construction wood 5
construction wood 1
sealant 1
sealant 2
sealant 3
sealant 4
sealant 5
paint 1
paint 2
paint 3
paint 4
paint 5
carpet 1
carpet 2
carpet 3
carpet 4
carpet 5
roof material 1
roof material 2
roof material 3
roof material 4
roof material 5
glass 1
glass 2
glass 3
glass 4
glass 5
window 1
window 2
window 3
window 4
window 5
20%
40%
10%
40%
20%
60%
20%
40%
10%
50%
20%
70%
0%
100%
60%
80%
10%
30%
0%
100%
10%
15%
75%
90%
0%
100%
30%
50%
30%
90%
10%
30%
ci (USD)
ri
ei
vi
v_ i
vui
v_ ui
hi
fi
mi
si
62.01
32.93
22.97
33.35
119.5
9.7
6.55
7.11
35.93
16.82
24.37
16.83
9.39
17.28
39.83
28.4
19.85
6.84
20.75
33.57
25.02
33.24
6.35
13.89
52.25
22.41
14.17
3.9
5.5
7.1
72.9
27.79
10.1
28.83
123.2
35.4
30.54
8.85
38.87
487.7
35%
0%
0%
0%
40%
–
–
–
–
–
0%
0%
0%
0%
0%
50%
0%
0%
0%
76%
6%
6%
0%
49%
66%
95%
75%
20%
70%
80%
95%
85%
75%
75%
100%
25%
10%
0%
0%
30%
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
–
–
–
–
–
–
–
–
–
–
700
850
550
300
25
0
150
250
100
0
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
215
180
700
605
0
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
750
750
250
250
250
150
100
150
250
50
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
500
500
500
500
500
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
0
0
1
1
1
1
0
1
0
1
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
1
0
0
0
1
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
1
0
1
0
1
–
–
–
–
–
1
0
0
0
1
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
1
1
0
0
1
–
–
–
–
–
–
–
–
–
–
obtaining extra LEED-based points, the model presented in Eqs.
(1)–(20) can be slightly modified as follows. First, let h be the
desired number of awarded points; then, the new constraint which
guarantees that at least a number of h points are awarded follows:
The objective function changes to account for the minimum
amount of money required to reach the desired number of points.
The new objective function follows:
X
min
pk zk h
(21)
k˛L
Table 3
Materials required in the optimal solution
System
Material
xij
Quantity
Cost
Wood components (m)
wood component 2
wood component 3
wood component 4
construction wood 3
construction wood 4
construction wood 1
sealant 1
paint 3
paint 4
carpet 3
roof material 2
roof material 3
glass 3
window 1
window 3
window 5
Total cost
40%
20%
40%
40%
10%
50%
100%
80%
20%
100%
10%
90%
100%
30%
60%
10%
67.59
33.79
67.59
3507.46
876.86
4384.32
5.01
230.77
57.69
17.22
54.29
488.61
91.34
317.81
635.61
105.94
2226
776
2254
22,974
6235
73,744
122
1578
1197
109
769
1906
923
11,250
5625
51,665
183,353
Construction (wood) (m)
Adhesives and sealants (gal)
Paints (gal)
Carpet (m2)
Roof (m2)
Glass (m2)
Windows (m2)
X X
ci dj xij
(22)
j˛S i˛Jj
In summary, the resulting model is comprised of objective function
(22) subject to constraints (2)–(21), except budget constraint (6),
which is no longer necessary.
The modified model determines the minimum amount of
money required to achieve the desired number of credits indicated
by h. To reveal the existing trade-off between money and LEED
points, we devise an iterative scheme to explore the complete
scope of all the combinations of LEED-based points subject to
a given budget. According to this scheme, the model is solved
several times, increasing the value of the parameter h one point at
a time, up to the maximum points available. In this case study, the
modified model is solved seven times, varying the parameter h
from 5 to 11, that is, from the maximum number of points achieved
with the original model up to the maximum number of points
available.
The compromise between awarded points and budget is shown
in Fig. 1. Points A, B, C, and D show an opportunity to gain extra
LEED points with a relatively low effort in terms of cost. On the
other hand, points E, F, and G require a higher increase in cost to
gain extra LEED points, suggesting a more careful analysis to
determine their convenience (e.g., cost–benefit). Each one of these
1168
D. Castro-Lacouture et al. / Building and Environment 44 (2009) 1162–1170
11
G
10
F
LEED-based points
9
H
E
8
D
7
C
6
B
5
A
4
180,000
185,000
190,000
195,000
200,000
205,000
210,000
The modified model unveils the non-dominated points (A, B, C,
and D in Fig. 1). These efficient points represent the cheapest
alternative for each level of LEED-based score. To illustrate the
concept of efficiency (non-domination), let us compare points H
and E in Fig. 1. Even though both points achieve a solution with
a LEED-based score of 9, point H is more expensive than point E,
thus based on cost, solution E dominates H. Although in this case
the cost criterion is used to select the best alternative, other criteria
such as material availability and material delivery time from the
supplier can be considered to break ties among a set of alternatives
with the same number of LEED-based points.
It is worthwhile to note that a scarce budget is not the only
reason why a low number of LEED points can be awarded. Material
constraints can restrict the capacity of the model to award points,
limiting its choice of alternatives. In the case in point, if none of the
available wood-based materials is certified, then credit 7 from the
materials and resources area will be impossible to comply with.
Design constraints can also affect the number of awarded points. To
illustrate this case, if the design constraints reduce the solution
space such that the model is forced to select some specific materials, then the model might not be able to substitute lower-quality
materials with higher-quality ones.
Budget (USD)
4.3. Sensitivity analysis
Fig. 1. Existing trade-off between LEED-based points and budget.
points represents a given set of materials and their extent of use.
For instance, point A corresponds to the results presented in Table
3, while point B represents a different choice of materials that adds
an extra LEED point to those awarded in point A. This increment
from 5 to 6 points implies the compliance with credit 4.3 from the
indoor environmental quality area, but demands an addition of just
USD 321 to the current budget. In contrast, moving from a solution
represented by point F to that of point G (from 10 to 11 LEED
points), implies the compliance with credit 4.2 from the materials
and resource area, which requires a significant addition to the
budget of USD 11,291. These results show the general rule that as
more points are awarded, it is more expensive to add a marginal
point.
The amount required of each material at point G is shown in
Table 4. Note that this solution differs widely from that suggested
in Table 3. For instance, the use of new materials, such as wood
component 1, paint 1, and carpet 1, helps to award the total
number of available points, but requires a significant addition to
the budget.
The primary goal of the proposed model is to maximize the
number of earned LEED-based points, selecting the best materials
and determining their extent of use. However, changes in market
conditions such as government policies, material prices, and
material availability, can affect the optimal solution. The study of
the effect of these external changes will provide the decisionmaker with valuable information to take better decisions under
a constantly changing environment.
In recent years, the forest policy in Colombia is receiving ever
increasing attention given that certified timber production has
become an alternative economic activity for small producers of
illicit crops [44]. According to the Colombian Ministry of Environment, Housing and Territorial Development, more than USD 1M has
been assigned to support sustainable forest plans in some regions
in Colombia [45]. Given those policies it is reasonable to assume
that the LEED-based rating system will double the points awarded
to credit 7 from the materials and resources area, motivating the
use of certified wood while contributing to alleviate a deep social
problem.
Let us assume an available budget of USD 186,000 which is
enough to reach the point C presented in Fig. 1, where seven LEEDbased points are earned (see Table 5). After running the model
with the new budget under the new forest policy, there are some
Table 4
Materials required in the eleven-LEED point solution (point G)
System
Material
xij
Quantity
Cost
Wood components (m)
wood component 1
wood component 3
wood component 5
construction wood 3
construction wood 4
construction wood 1
sealant 1
paint 1
paint 5
carpet 1
roof material 2
roof material 5
glass 5
window 1
window 3
window 5
Total cost
40%
20%
40%
40%
10%
50%
100%
80%
20%
100%
10%
90%
100%
30%
60%
10%
67.59
33.79
67.59
3507.46
876.86
4384.32
5.01
230.77
57.69
17.22
54.29
488.61
91.34
317.81
635.61
105.94
4191
776
8077
22,974
6235
73,744
122
6554
1937
431
769
3469
11,254
11,250
5625
51,665
209,072
Construction (wood) (m)
Adhesives and sealants (gal)
Paints (gal)
Carpet (m2)
Roof (m2)
Glass (m2)
Windows (m2)
Table 5
LEED-based points awarded given changes in model parameters
Credit
Area
7.2
Sustainable sites
4.1
Materials and
4.2
resources
5.1
5.2
6
7
4.1
Indoor
4.2
environmental
4.3
quality
4.4
Total LEED-based points
Points
awarded
at point C
(Fig. 1)
Points awarded
motivating the use
of certified wood
Points awarded
increasing material
prices by 1%
1
1
1
1
1
1
1
1
1
2
1
1
1
1
7
8
6
1
1
1
1
1
1
D. Castro-Lacouture et al. / Building and Environment 44 (2009) 1162–1170
1169
Table 6
Comparison of optimal solutions given a change in the LEED-based points
System
Optimal solution at point C (Fig. 1)
Optimal solution motivating the use of certified wood Optimal solution increasing material prices by 1%
Material
Material
Quantity
Cost
Material
Quantity
Cost
wood component 1
wood component 3
wood component 4
construction wood 3
construction wood 4
construction wood 1
sealant 1
paint 3
paint 4
carpet 1
roof material 2
roof material 3
glass 3
window 1
window 3
window 5
Total cost
67.59
33.79
67.59
3507.46
876.86
4384.32
5.01
230.77
57.69
17.22
54.29
488.61
91.34
317.81
635.61
105.94
4191
776
2254
22,974
6235
73,744
122
1578
1197
431
769
1906
923
11,250
5625
51,665
185,640
wood component 2
wood component 3
wood component 4
construction wood 3
construction wood 4
construction wood 1
sealant 1
paint 3
paint 4
carpet 1
roof material 2
roof material 3
glass 3
window 1
window 3
window 5
Total cost
67.59
33.79
67.59
3507.46
876.86
4384.32
5.01
230.77
57.69
17.22
54.29
488.61
91.34
317.81
635.61
105.94
2248
784
2277
23,204
6,297
74,482
123
1594
1209
435
777
1925
932
11,363
5681
52,181
185,511
Wood components
Quantity Cost
wood component 2
67.59
2226
wood component 3
33.79
776
wood component 4
67.59
2254
Construction (wood)
construction wood 3 3507.46
22,974
construction wood 4 876.86
6235
construction wood 1 4384.32
73,744
Adhesives and sealants sealant 1
5.01
122
Paint
paint 3
230.77
1578
paint 4
57.69
1197
Carpet
carpet 1
17.22
431
Roofs
roof material 2
54.29
769
roof material 5
488.61
3469
Glass
glass 3
91.34
923
Windows
window 1
317.81
11,250
window 3
635.61
5625
window 5
105.94
51,665
Total cost
185,238
changes in the accomplished credits. Credit 7.2 from the sustainable sites area is replaced by credit 7 from the materials and
resources area (see Table 5). The comparison between the optimal
solutions (see Table 6) shows that roof material 5 is substituted by
roof material 3, which is cheaper and does not comply with the
solar reflectance index requirements. Conversely, the wood
component 2, which does not comply with the certified forest
requirement, is substituted by wood component 1. These
exchanges help the model to comply with credit 7 from the
materials and resources area within the same budget. That is, most
of the savings generated by the roof materials exchange are used to
buy a more expensive yet certified wood component. It is worth
mentioning that under lower budget levels the model is not able to
exchange materials.
The availability and price of materials can also affect the
optimal solution. For instance, if certified wood components
(1 and 5) are unavailable in the market, it is impossible to
comply with credit 7 from the materials and resources area.
Moreover, if the price of the materials increases by 1%, which
seems to be a slight change, the number of LEED-based credits
decreases from seven (point C in Fig. 1) to six. Table 5 shows
how under this scenario, the model output fails to comply with
credits 7.2 from the sustainable sites area and credit 7 from the
materials and resources area. The optimal solution is shown in
Table 6, where roof material 5 is replaced by roof material 3,
which is cheaper but does not comply with the solar reflectance index requirement. Although the optimal quantities are
the same, the total cost of each material (except for roofs) is 1%
higher, consuming a bigger portion of the budget. As a result,
a material substitution is needed, buying a cheaper material
and consequently losing a LEED-based credit.
5. Concluding remarks
Although many approximations to the material selection
problem have been proposed in the literature, the outlined model is
the only one that incorporates design, budget, and environmental
requirements simultaneously to determine a better set of materials
and their extent of use in green buildings. The model allows the
user to freely include preferred materials and design parameters
through design constraints, without enforcing a restrictive (even
costly) environmental solution. A widely applied rating system is
used to determine the level of accomplishment of environmental
goals. However, the rating system is adapted to the specific situation in Colombia to reflect the situation of its construction market.
The reality-based case study illustrates the application of the
model in a building in Colombia. The decision-makers can obtain
a detailed purchase plan that describes the materials that should be
used and their extent of use. The solution of the model also
provides the total cost of the materials. Moreover, the model can be
adapted to show the amount of additional money required to
obtain extra LEED credits, providing decision-makers with the
necessary steps to improve the green performance of building
projects.
The results of the case study show the importance of the
availability of green materials. If materials with desirable properties
are not available, LEED-based requirements are nearly impossible
to meet. In the case of the Colombian market, the LEED-based
system is highly dependent on the use of materials with a low
content or emission factor of volatile organic composites (VOC) and
a high content of recycled constituents. Materials with these
characteristics are scarce and expensive. Similarly, other materials,
such as certified wood, are not widely available, nor do they come
with information about their origin and properties. As no regulations currently require manufacturers to report data, the lack of
information about materials – some characteristics are unknown
even to the manufacturers – will continue to challenge LEED-based
systems.
The case study shows that the budget can determine the success
of green building projects, many of which are abandoned due to
insufficient funds [15]. The results demonstrate that sometimes
a slight budget addition may lead to a significant increment of
earned points. Finally, the trade-off analysis also shows that the
marginal cost of an additional LEED point may be expensive,
depending on the price of the materials involved in the extra credit.
The proposed model is based on a modified LEED rating system
for building evaluation in Colombia, where the GB movement is at
its birth and still emerging. Given the limitations of the Colombian
construction market, a LEED-based rating system was selected as
the more realistic first step towards green building evaluation. The
booming GB culture will attract builders and designers to improve
their early green practices by using tools like the proposed LEEDbased rating system. Although this method is easy to adopt by
builders due to the transparency of its requirements and the
reduced data complexity, its application must be considered as
a first phase towards a more robust environmental building design.
The maturity of the GB market in Colombia will improve data
availability and quality, helping designers apply not only green
rating systems, but more sophisticated assessment methods of
environmental impact such as life cycle analysis (LCA).
1170
D. Castro-Lacouture et al. / Building and Environment 44 (2009) 1162–1170
Acknowledgments
This work was partially funded by the Industrial Engineering
Department and the Masters Internship Fund of the School of
Engineering at Universidad de los Andes. We also thank Fair Isaac
Corporation for providing us with access to Xpress-MP’s optimization products under the Academic Partner Program subscribed
with Universidad de los Andes. Finally, we express our deep
appreciation to the construction company Pérez Arciniegas S.A.
(Payc S.A.) for sharing with us valuable information related to the
case study.
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