Int J Life Cycle AssessDOI 10.1007/s11367-010-0227-9

INPUT-OUTPUT AND HYBRID LCA

An input-output approach for the efficientdesign of sustainable goods and services

Elaine Croft McKenzie · Pablo Luis Durango-Cohen

Received: 20 July 2009 / Accepted: 24 July 2010© Springer-Verlag 2010

AbstractPurpose We propose a prescriptive framework to sup-port environmentally conscious decision making in thedesign of goods and services. The framework bridgesrecent applications of input-output analysis to conductenvironmental life cycle assessment (LCA), with semi-nal work in production economics. In the latter, productdesign, production planning, and scheduling problemsare frequently formulated as input-output models withsubstitution, and subsequently analyzed and solved aslinear programs. The use of linear programming pro-vides an appealing theory and computational frame-work to support decision making, as well as to conductsensitivity analysisMethods In this paper, we explore the benefits of inte-grating LCA within a linear programming (LP) frame-work and present a case study where we consider a hy-pothetical advertiser located in the Chicago Metropol-itan Area, who wishes to allocate a predeterminedbudget to place ads in either the print or online versionsof a high-circulation, local newspaper. We formulatethe problem of finding an advertising strategy thatminimizes global warming potential (GWP), subject

Responsible Editor: Seungdo Suh

E. Croft McKenzie · P. L. Durango-Cohen (B)Department of Civil and Environmental Engineering,Northwestern University, 2145 Sheridan Road,A332 Evanston, IL 60208-3109, USAe-mail: pdc@northwestern.edu

E. Croft McKenziee-mail: e-croft@northwestern.edu

to demand and budget constraints. We then solve theproblem and evaluate the optimal strategy in termsof discharges of component greenhouse gases, andin terms of requirements imposed on various energysources. We also analyze the sensitivity of the optimaladvertising strategy (and associated global warming po-tential) to perturbations in the model parameters andconstraints.Results and discussion By embedding LCA within anLP formulation, we are able to examine the relation-ships between economic and environmental factorsinherent within decisions to use specific products orservices. Specifically, the advertiser finds that eachstrategy contains tradeoffs among and between envi-ronmental and monetary costs. A disaggregate compar-ison of greenhouse gas release and energy consumptionamong strategies highlights the variation between thesefactors and the potential dangers of aggregation. Sensi-tivity analysis gives us marginal costs (per dollar andper person) of GWP in the optimal solution. These andother managerial insights presented highlight the com-plex tradeoffs necessary for environmentally conscious,sustainable decision making.

Keywords Product design · Environmental life cycleassessment · Production planning and scheduling ·Input-output analysis · Linear programming ·Print vs. online advertising

1 Introduction

Input-output (IO) analysis has been used extensively toconduct life cycle assessments (LCAs) of the environ-mental impact, e.g., greenhouse gas emissions, energy

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and water consumption, associated with various in-dustrial/commercial/government processes, goods, ser-vices, resources, and policies. The approach was con-ceived by Leontief (1970). Miller and Blair (1985),Joshi (2000), and Hendrickson et al. (2006) provide anoverview of the methodological approach and describeseveral recent applications of IO analysis in engineer-ing, management, and policy.

Overall, the IO approach involves specifying thedirect requirements, i.e., a bill of materials, of goods,and services in terms of demand imposed on sectorsof the economy. The IO model, in turn, is used tocompute the direct and indirect requirements that sat-isfying an exogenous demand imposes on the economyas a whole. Subsequently, the model is used to calcu-late the environmental repercussions associated withthe economic activity that is needed to meet the de-mand. The flexibility, transparency, and accuracy of themethodology explain its broad appeal in the scientificand engineering community, and why it is has becomean accepted method for conducting LCA, especiallyamong products or services that are not well served bymore resource intensive LCA methods (Hendricksonet al. 2006; Lenzen 2001).

Although they have provided much insight, eco-nomic IO life cycle assessments (EIO-LCAs) have beenused almost exclusively as descriptive tools. That is,EIO-LCA models have not been integrated into a pre-scriptive framework to support decisions that arise dur-ing product/process design or (production) planning.Furthermore, LCAs in general lack the ability to reflectthe preference structure or value systems of differentstakeholders (Zhou and Schoenung 2007). To addressthese limitations, we build on literature in productioneconomics, where process/product design, productionplanning, and scheduling problems are often formu-lated as IO models with substitution, and subsequently,analyzed and solved as linear programs (cf. Shephard1953; Hackman and Leachman 1989). Indeed, and asdescribed in Koopmans (1951), these types of problemsare among the first applications of linear programming.From a managerial perspective, one of the appealingfeatures of the proposed framework is that linear pro-gramming provides a well-established theory, as well asa systematic approach, to conduct sensitivity analysis,i.e., to evaluate the effect of perturbations in the inputson the results.

The contribution of our work is, therefore, (1) tocombine the two literature streams of environmentallife cycle assessment and production economics, and(2) to provide a practical, prescriptive framework tosupport the design of environmentally conscious goodsand services. To illustrate the proposed framework,

we analyze the problem of designing an advertisingstrategy. In particular, we consider an environmentallyconscious advertiser in the Chicago Metropolitan Area,wishing to allocate a predetermined budget to place adsin either of two media outlets: print vs. online versionsof a high-circulation, local newspaper. We assume thatthe advertiser’s objective is to minimize environmentalimpact, i.e., global warming potential, while reaching atarget population.1 We use the proposed framework tofind an optimal advertising strategy, and then evaluateand compare the strategy to two benchmarks in termsof discharges of component greenhouse gases, and re-quirements imposed on various energy sources. Finally,we analyze the sensitivity of the optimal advertisingstrategy and associated environmental impact to per-turbations in the budget, size of the target population,relative costs to place ads, and relative environmentalimpact associated with each medium.

The remainder of the paper is organized as follows:Section 2 reviews approaches to carry out environmen-tal LCAs, as well as frameworks to optimize the designof goods, services, or processes while accounting for en-vironmental impact metrics. In Section 3, we provide anoverview of the use of IO analysis to address problemsrelated to design and production of goods or services.In Section 4, we apply the proposed framework tothe problem of designing an environmentally friendlyadvertising strategy. Concluding remarks appear inSection 5.

2 Related work

In this section, we position the proposed frameworkin relation to alternative methods of environmentalLCAs. We also consider approaches to optimize thedesign of goods, services, or processes that explicitlyaccount for environmental impact metrics, e.g., thatinclude restrictions that limit pollution.

In the early 1990s, sustainable development emergedas an all-encompassing, integrative concept/philosophyto simultaneously capture and address economic, social,and environmental concerns that began to dominatethe world-wide political landscape. As defined by theWorld Commission on Environment and Development,

1We recognize that a single advertising campaign does not havea significant effect on the environmental footprint of differentmedia types. However, because ad revenue is one of the mainsources of income for many media types, an increase or decreaseof advertising dollars could affect their long-term viability, andthus their environmental impact.

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sustainable development refers to “development thatmeets the needs of the present without compromisingthe ability of the future to meet its needs” (Mihelcicet al. 2003). These concerns spearheaded significantwork in the development, adaptation, and applicationof numerous methodologies to conduct environmentalLCAs, i.e., to quantitatively evaluate the environmen-tal impact of a variety of goods and services overtheir life cycle and over their supply chain. Finkbeineret al. (2006) summarizes the series of internationalstandards in place to consolidate procedures and meth-ods of LCA throughout businesses and organizations(ISO 14040:1997, ISO 14041:1999, ISO 14042:2000, ISO14043:2000, ISO 14040:2006, ISO 14044:2006).

Over the past two decades, different types of LCAshave emerged. Hertwich (2005) reviewed different ap-proaches to conduct LCAs, and classified them aseither “classical product/process models” or as “eco-nomic IO models”. In process models, the objectiveis to establish a causal link between activities thattake place over a product’s life cycle, i.e., raw materialextraction, fabrication, distribution, sales, utilization,disposal, and the associated environmental stresses. Intheir purest form, the specification and application ofsuch models requires detailed descriptions of the afore-mentioned activities, and relies on identification andunderstanding of the physical/chemical/engineeringprocesses that take place during their execution, i.e.,chemical reactions, mass/energy/heat transfer, etc. Thebroad adoption of process models stems from the thor-oughness of the analysis, coupled with the fact that theUS government spells out standards for the develop-ment of such models under a framework created by theSociety of Environmental Toxicology and Chemistryand the Environmental Protection Agency.

The main limitations of process models also relateto the thoroughness of the analysis and comparabilitybetween studies. In particular, following Hendricksonet al. (2006) and others, we note that because they aredata and analysis driven, process models are extraordi-narily resource intensive. This may render the approachinefficient or impractical in many situations. Further-more the data sources and variations in methodologynecessary to conduct a process analysis by differentfirms or organizations may in some cases limit thecomparability of products or services. Finally, definingthe scope of a process model places an artificial andsubjective boundary on the supply chain impact of thegood, service, or process being analyzed, which, in turn,can lead to significant errors (Lenzen 2001; Suh et al.2004).

Economic IO models constitute an alternative ap-proach to conduct LCAs, while addressing the afore-

mentioned difficulties. Rather than mapping processesin detail, the IO approach involves specifying the directrequirements, i.e., a bill of materials, of a product interms of demand for economic sectors, e.g., transporta-tion, construction, financial services, etc. This demandis (usually) expressed in monetary value, i.e., US dol-lars. The model, in turn, is used to compute the level ofeconomic activity and environmental repercussions as-sociated with satisfying the given demand for the prod-uct. Because all sectors represented in the economyare linked, there is no effective boundary on the scopeof the analysis. The number and diversity of LCAsemploying IO analysis has greatly increased since thelate 1990s as a result of the methodology’s flexibility,simplicity, and, importantly, the availability of onlinetools to support the analysis (cf. The Green DesignInstitute 2008). Examples can be found in the fieldsof waste disposal (Kondo and Nakamura 2004), trans-portation (Facanha and Horvath 2007) urban studies(Norman et al. 2006), energy (Hendrickson et al. 2006),and service industries (Rosenblum et al. 2000).

The main criticisms of the Economic IO-based LCAs(EIO-LCAs) are related to estimation biases intro-duced by aggregation and linearity. Suh and Nakamura(2007) lists the most common limitations of EIO-LCAsalong with relevant work to overcome these limitations.One of the main arguments by critics is that monetaryvalues used to represent demands and flows in theeconomy are not a good representation of (physical)processes or their environmental repercussions. Also,the use of flows across the national economy, as wellas nation-wide, average discharges per economic sectormay not be representative of a process taking place in aspecific location using a particular technology.

While research to validate the use of EIO-LCAmodels has shown that the results are comparable tothose using process models (see Hendrickson et al. 2006and the references therein), the aforementioned weak-nesses have motivated work to improve the precisionof EIO-LCAs. Yi et al. (2007), for example, describethe development of a regional IO LCA model. Wealso note the work of Joshi (2000), who describes anumber of techniques to exploit the flexibility of IOmodels, leading to more detailed representations/mapsof goods, services or processes. The ensuing models arereferred to as hybrid LCA models.

Hybrid type models which incorporate elementsfrom both process-based and IO-based LCA models.Although hybrid LCA models can still include errorinherent in IO models, such as aggregation and lin-earity, Lenzen (2001) demonstrates that these errorsare often significantly lower than errors caused bythe subjective boundaries in process LCAs. Similar in

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function to the hybrid model is the ecological-economicmodel proposed by Suh (2004), which interconnectsphysical and commodity based systems in order to re-duce the error for subjective boundaries and improvethe ability to conduct analysis and supply chain man-agement. The approach used by the authors in thispaper (see Section 3) is also similar in function to hybridLCA models.

Much of the work on LCA has focused on improvingthe data sources and the modeling structures needed toproduce more precise measurements of the life cycleimpacts of a product. Less work has been done tointegrate environmental LCA models with quantita-tive frameworks to optimize the design of sustainablegoods, services, or processes. However some researchhas been done to develop integrated frameworks. Zhouand Schoenung (2007) proposed an Integrated Indus-trial Ecology Function Deployment model to incorpo-rate environmental impact assessment within industrialmanagement tools and focus on incorporating the pref-erences of different stakeholders into the analysis.Within the chemical engineering system design litera-ture, Azapagic and Clift (1995, 1999), and related worksprovide a good starting point in the context of genericapproaches to study the tradeoffs between environmen-tal, economic, and social factors in product/process de-sign. In Azapagic and Clift (1999), they propose a multi-objective optimization model to identify Pareto optimalpolicies that satisfy both economic and environmentalcriteria for sustainable performance of a system overits life cycle. Similar to other (earlier) works, they takea process model perspective to assess impact.

In contrast, we propose to integrate optimization andanalysis methods with a (hybrid) economic IO modelperspective. Using this modeling structure allows us tonot only avoid the limitations of process LCAs, butalso exploit synergies with models of product/processdesign from the production economics literature. Thisperspective is more in line with the work of Kondoand Nakamura (2005), who propose a LP extensionof their Waste-IO model. Both the model presentedherein and the model in Kondo and Nakamura (2005)exploit the ability of IO models to be integrated intoLP, and subsequently examine optimal solutions andtradeoffs. However, the research differs in scope. Thefocus of the cited research is optimal strategies us-ing IO models where waste management options areintegrated into the matrix structure and subsequentlysolved as a LPs. Our focus is to use EIO-LCA as atool to integrate the concepts of environmental impactsand sustainability into a traditionally economic decisionmaking framework that can be used in a wide variety ofapplications.

3 Proposed framework: application of IO analysisto support the design of sustainable goodsand services

In this section we provide an overview of the method-ological tools used in the framework for environmentaldecision making. First, we describe the use of IO analy-sis and linear programming to support decisions thatarise in the design of goods, services, and processes. Todo so we adopt terminology and conventions appearingin references such as Hackman and Leachman (1989)and Hopp and Spearman (2000). We then describe howthe approach is used to calculate the environmentalrepercussions associated with satisfying a demand fora given product or process.

We define a product or process as a collection ofn items/steps that are associated in order to delivera functional purpose. For example, we consider anend-product or process, labeled “A”, that consists ofcomponents/sub-assemblies labeled “B–E”. The rela-tionships and requirements between the n = 5 itemsare captured in the product structure trees presented inFig. 1.

In this case, we consider two alternative designs of Acaptured in the product structure trees. The root nodein each of the trees corresponds to the end-product.The components are represented as nodes on the tree.The numbers that appear next to the arcs represent thenumber of components that are needed to manufacturethe preceding item/assembly. For example, product Arequires three B’s and each B requires one D, under ei-ther of the product structure trees. These requirementscan also be represented in matrix form as follows:

B1 =

⎡⎢⎢⎢⎢⎣

0 0 0 0 03 0 0 0 02 0 0 0 00 1 2 0 00 0 0 0 0

⎤⎥⎥⎥⎥⎦

; B2 =

⎡⎢⎢⎢⎢⎣

0 0 0 0 03 0 0 0 00 0 0 0 00 1 0 0 04 0 0 0 0

⎤⎥⎥⎥⎥⎦

(1)

3 2 3 4

1 2 1

Product Structure Tree 1 Product Structure Tree 2

CB

DD

A

EB

D

A

Fig. 1 Product structure trees for product A

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The matrices, Br, r = 1, 2 are the Bills of Material(or IO matrices) corresponding to the product structuretrees presented above. Entry i − j in the above matri-ces, denoted br

ij for r = 1, 2, represents the amount ofinput i needed to produce one unit of output j under billof materials r. In our example, the rows and columnsare for items A–E. They are arranged in alphabeticalorder; that is, row 1 (and column 1) is for item A, row 2is for item B, etc.

3.1 Calculating the gross requirements to satisfydemand for a product or process: an example

Prior to describing the approach to calculate the grossrequirements associated with a product or process, weconsider a scheme to classify a product’s componentsinto various levels. The scheme uses the product struc-ture trees, where end-products are classified as Level0 items. The direct requirements for end-products areclassified as Level 1 items. For example, items B andC are the Level 1 items in product structure tree 1.This scheme is applied iteratively by assigning the directrequirements of Level k products to Level k + 1.2

For a given product structure tree, r, we addressthe issue of calculating the gross requirements neededto satisfy an exogenous demand. The exogenous de-mand is represented as a vector y with componentsthat correspond to the demand for each of the items.We may, for example, be interested in calculating thegross requirements associated with a demand for itemA of 5 units, i.e., y′ = [5, 0, 0, 0, 0]. (The notation y′represents the transpose of vector y.) The gross require-ments of all level k items that are needed to deliver y,under bill of materials r, are obtained by consideringthe expression [Br]k y. Under bill of materials 1, thegross requirements to deliver y are as follows:

Level 0 Requirements: [B1]0 y = Iy = [5, 0, 0, 0, 0]′ (2)

Level 1 Requirements: [B1]1 y = [0, 15, 10, 0, 0]′ (3)

Level 2 Requirements: [B1]2 y = [0, 0, 0, 35, 0]′ (4)

For k = 3, 4, . . .,

Level k Requirements: [B1]k y = [0, 0, 0, 0, 0]′ (5)

where I is an n × n identity matrix.The total gross requirements associated with satisfy-

ing y under r are obtained by adding the gross require-ments across all levels. Letting xr ≡ [

xr1, xr

2, . . . , xrn

]′ de-

2In general, product structure trees can be cyclic, and thereforean item can be assigned to multiple levels.

note the total gross requirements for the n items underr, we have that:

xr =∞∑

k=1

[Br]k y = (I − Br)−1 y (6)

where vector component xri represents the total gross

requirements for item i that are needed in order tomeet the exogenous demand y.3 In the example, x1 =[5, 15, 10, 35, 0]′.

Allowing for substitution, as is done in the con-text of product/process design or of production plan-ning/scheduling, implies the existence of alternatives tomeet the exogenous demand, y. In the example, there isflexibility to meet the demand for end-product A undereither of the two product structure trees presentedearlier. Letting τr be the number of units producedusing each product structure, we have:

xr = (I − Br)−1 τr (7)

where:2∑

r=1

τr = y (8)

We define x ≡ ∑2r=1 xr, i.e., as the total gross

requirements to meet y. In the example, ifτ1 = [3, 0, 0, 0, 0]′ and τ2 = [2, 0, 0, 0, 0]′, thenx = [3, 9, 6, 21, 0]′ + [2, 6, 0, 6, 8]′ = [5, 15, 6, 27, 8]′.

A key observation of Dantzig (1949), Koopmans(1951), Wagner (1957) is that demand met under eachproduct structure can be obtained by solving a linearprogram, thereby providing an analytical and compu-tational approach to support the optimal design of aproduction strategy (to satisfy the demand for end-product A). The approach is widely used to addressvarious problems that arise in production economics.For example, Hackman and Leachman (1989) considerthe problem of satisfying demand over a finite set ofperiods, and formulate a linear program to find a pro-duction schedule that minimizes the total discountedinventory-holding costs. In this problem, referred toas Material Requirements Planning or MRP, the sub-stitution alternatives are related to feasible productionschedules. As described below, the methodology can beeasily adapted to address problems related to the designand production of sustainable goods and services. Forexample, one could consider a problem to minimize(production and operation) costs subject to limiting

3Conditions that guarantee the result presented in Eq. (6)are not restrictive. For instance, the expression holds whenlimk→∞ [Br]k = 0, as is the case in the example.

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environmental discharges, or, as is done in Section 4,to minimize discharges subject to meeting requirementsand not exceeding available resources. In the remainderof this section, we explain how the above scheme isextended to account for the environmental repercus-sions associated with goods and services. We begin,however, by considering the application of IO analysisto characterize the structure of a nation’s economy.

Rather than describing the structure of a product,Leontief (1951, 1952) developed IO analysis as a tech-nique to characterize the overall structure of the USeconomy. Instead of items/sub-assemblies, the tech-nique relies on economic sectors, e.g., energy gen-eration, construction, transportation, mining, etc., asfundamental building blocks. The inputs in the analy-sis correspond to the annual flows between economicsectors. For consistency, the flows are measured interms of monetary value, and expressed in US dollars.In terms of notation, we consider an economy with Nsectors, and denote the economic IO table A, where:

A =

⎡⎢⎢⎢⎣

a11 a12 · · · a1N

a21 a22 · · · a2N...

. . ....

aN1 aN2 · · · aNN

⎤⎥⎥⎥⎦ (9)

and the coefficients, aij, correspond to the inputs (in $)from sector i needed to obtain $1 of output from sectorj. In the USA, the Department of Commerce generates“Benchmark” economic IO tables on a 5 year cycle thatcapture flows across nearly 600 economic sectors (seehttp://www.bea.gov/industry/io_benchmark.htm).

Integrating economic IO tables with the bill of mate-rials of a product/process provides a natural approachto calculate the gross, i.e., direct and indirect, economicactivity (across all sectors) that is needed to satisfy anexogenous demand. The approach involves expandingthe bill of materials to include the direct requirements(in $) for various economic sectors. Graphically, thisexpansion can be represented on a product structuretree where the leaves correspond to economic sectors.For illustration, in Fig. 2, we return to the example, andexpand Product Structure Tree 1 for end-product A.Only 2 economic sectors, S1 and S2, appear explicitly inthe expanded product structure tree. The coefficients,a1, b1, c2, d1, and d2, correspond to the inputs (in $)from the economic sectors needed to produce one unitof output.

Even though only sectors S1 and S2, appear explic-itly in the expanded product structure tree, it shouldbe noted that these sectors require inputs from theN sectors that comprise the national economy. Theserelationships are given in the IO table, A, and are repre-

A

S1 B C

D DS1 S2

S1 S1S2 S2

a1 3 2

1 b1 2 c2

d1 d2 d1 d2

Fig. 2 Expanded product structure tree 1 for product A

sented in the expanded bill of materials, B̂1, presentedbelow:

B̂1 =

⎡⎢⎢⎣

B1 O5×N

a1 b1 0 d1 00 0 c2 d2 0 A

O(N−2)×5

⎤⎥⎥⎦ (10)

where Op×q is a Zero Matrix of dimensions p × q.Again, for an exogenous demand of y, the total as-

sociated gross requirements, x, can be calculated usingEq. (7)—replacing Br with the associated matrix B̂r,which is equivalent in form to the matrix in (10). Wealso note that the vector x can be partitioned as follows:x = [x1, . . . , xn|xn+1, . . . , xn+N]′, where the first n com-ponents correspond to the gross requirements for theitems/sub-assemblies being considered, while the otherN components correspond to the gross requirementsfor each economic sector represented in the economy.

In the USA, the Department of Energy, among otherorganizations, has done extensive research to quantifythe environmental impact associated with economicactivity in various economic sectors. These estimatesare presented as a set of coefficients, denoted f jk, rep-resenting the (national average) discharge rate of pol-lutant k per dollar of output in economic sector j. Theset of discharge rates can be collected in an environ-mental impact matrix, F ≡ [

f jk]. We note that the gross

environmental impact to satisfy y is given by the vector[xn+1, . . . , xn+N]F, where

∑n+Nj=n+1 x j f jk corresponds to

the total output of pollutant k. Single dimensional en-vironmental impact measures, such as global warmingpotential, can be calculated by constructing weighted

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averages of the components of the aforementionedvector, e.g.,

∑Mk=1 wk

∑n+Nj=n+1 x j f jk, where M pollutants

are considered and wk is the weight assigned to therepercussions of pollutant k.

4 Case study: print vs. online advertising in theChicago Metropolitan Area

Historically, newspapers have been the major target ofadvertising spending. Although more money is spenton newspaper ads than on any other media outlet,recently more people are turning to online sourcesfor news and advertising. Not surprisingly, the pro-portion of dollars spent by advertisers on online adsis increasing (Pricewaterhouse-Coopers 2009). In thissection, we illustrate the flexibility and usefulness ofthe proposed framework to support decision makingapplications by considering a Chicago-based companywishing to design/run an environmentally friendly ad-vertising campaign. Our work builds upon the casestudy presented in Toffel and Horvath (2004), whocompare the environmental impact of a consumer inBerkeley, California, reading the print version of theNew York Times, versus reading the newspaper onlineusing a PDA device. Both case studies use data fromthe EIO-LCA tool (Carnegie Mellon University GreenDesign Institute 2008) and other sources to calculateenvironmental impacts. In this section, we present aprescriptive model based on the 2004 case study for de-signing an environmentally friendly advertising strategy.

In particular, we consider an advertiser who is look-ing to reach a target audience of D consumers byallocating a budget of $B across a set of P mediatypes. In this context, an advertising campaign specifiesthe number of ads to be placed in each medium, andis represented by the set of decision variables τi, i =1, . . . , P, where τi corresponds to the advertising expo-sure through medium i. The environmental impact ofthe campaign is measured in terms of the dischargesof M greenhouse gas pollutants. These pollutants arethen aggregated by their Global Warming Potential(GWP), i.e. the amount that the different gases con-tribute to global warming. The environmental outcomemeasure in this research is total GWP, measured inEquivalent Metric Tons (EMTs) of CO2. We formulatethe problem of designing an advertising campaign thatminimizes environmental impact as follows:

Minimize:M∑

k=1

wk

N∑j=1

f jkx j (11)

Subject to:

P∑i=1

τi ≥ D (12)

P∑i=1

κiτi ≤ B (13)

P∑i=1

cijτi = y j, j = 1, . . . , N (14)

x = (I − A)−1 y (15)

τi ≥ 0, i = 1, . . . , P (16)

where:

f jk: Discharge rate of pollutant k per $ of productionin industry sector j. Discharge rates are measuredin Metric Tons per $.

wk: Conversion factor to obtain GWP associatedwith discharges of pollutant k. The coefficientsare measured in Metric Tons of CO2 Equiva-lent/Metric Tons of pollutant discharges.

κi: Cost borne by an advertiser to place an ad inmedium i, adjusted to a per-unit basis.

cij: Production requirements per advertisement unitin media type i implied on economic sector j.These requirements correspond to the inputsfrom sector j needed to produce a unit of i, aremeasured in $/unit, and correspond to the para-meters that appear in a product structure tree orBill of Materials.

A: the matrix of requirements of other sectors re-quired to produce each dollar of output to eachsector

y: Implied demand across all industry sectors as-sociated with an advertising strategy. These de-mands are measured in $.

x: Production requirements across the N economicsectors to satisfy the implied demand.

The objective function, Eq. (11), measures the GWPin EMTs of CO2 of an advertising campaign (repre-sented by the set τi, i = 1, . . . , P). Equation (12) isa constraint that requires that the total advertisingexposures be at least equal to the target population,D. Constraint (13) limits the advertiser’s expendituresto the predetermined budget, $B. Equation set (14)is used to estimate the implied demand on the N

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Advertising Exposure Advertising Exposure

Newspaper Ad Online Ad

Newsprint

Ink

DeliveryCell Phone

Manuf.Electricity

Inputs from All Economic Sectors(IO Table)

Inputs from All Economic Sectors(IO Table)

0.5 1

N1

N2

N3 O1 O2

Level 0

Level 1

Level 2

Level 3+

Fig. 3 Dual product structure tree for the advertising case study

economic sectors associated with the advertising cam-paign, i.e., this set of constraints is used to determinethe demand y. Equation set (15) is used to calculatethe gross requirements across the economy associatedwith satisfying the demand y. Finally, the nonnegativ-ity constraints, given in equation set (16), constitutelogical restrictions on the decision variables in themodel.

As case study parameters, we consider an adver-tiser with a budget of $120,000 targeting a populationof ten million customers in the Chicago MetropolitanArea. For simplicity, and to allow for a graphical rep-resentation of the model, we restrict the advertiser’schoices to two media types: a widely distributed printednewspaper, or a high-traffic newspaper website. In ourexample, we replace the PDA from the 2004 case studywith a modern cellular phone, e.g., the iPhone, designedfor extended internet use. A product structure treedepicting the alternatives in this problem is presented inFig. 3 with the corresponding Bill of Materials in matrixform below.

Bnp =⎡⎣

0 0 00.5 0 00 0 0

⎤⎦ ; Bol =

⎡⎣

0 0 01 0 00 0 0

⎤⎦ (17)

where the rows and columns of Bnp and Bol correspondto the Level 0 and Level 1 products in Fig. 3.

B̂np =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣

Bnp O3×N

0 N1 00 N2 00 N3 0 A

0 0 00 0 0O(N−5)×3

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦

;

B̂ol =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣

Bol O3×N

0 0 00 0 00 0 0 A

0 0 O1

0 0 O2

O(N−5)×3

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦

(18)

The level 1 products correspond to the decision vari-ables of the linear program, τnp and τol. Level 2 inputsare specified, while Level 3 and beyond are modeledusing the IO tables of the US economy. Further detailsabout the construction of the Bill of Materials andvarious level inputs can be found in Appendix A.

Among the parameters we note that:

– For the Level 1 inputs, one unit of NewspaperAdvertising gives us twice the exposure as one unitof online advertising. Therefore, we can satisfy de-mand with 1/2 the number of newspaper ad units asonline ad units.

– The relative costs of placing ads is calculated as (2 ×κnp)/κol = 1.71; that is, each newspaper ad (whichsatisfies two units of demand) is slightly less thantwice the cost of an online ad; and

– The ratio between the environmental impact of thetwo media Enp/Eol = 1.91 where Ei is the measureof environmental impact (GWP) associated withmedium i.

4.1 Results and discussion

We begin to analyze the problem of designing an en-vironmentally friendly advertising campaign by com-paring the optimal advertising campaign to two bench-marks utilizing an exclusive media outlet. We thenanalyze the structure of the linear program, and inparticular the tradeoffs between conflicting objectivesand constraints. We also highlight the capability of thisframework to conduct sensitivity analysis. We illustratethis feature by considering how the optimal strategyand ensuing emissions change in response to pertur-bations in the budget, B, the demand, D, the cost ofplacing ads, κi, and in the bill of materials, cij.

In Table 1, we compare the optimal advertising cam-paign obtained by solving the above linear program,to two benchmark strategies where a single medium isused. The first column of Table 1 corresponds to thebaseline strategy where the demand is satisfied usingnewspaper advertising.4 The second baseline is for the

4τnp = 0.5 units of Newspaper Advertising, hence only D/2 unitsof advertising are required to satisfy D units of demand

Int J Life Cycle Assess

Table 1 Advertiserexpenditure and envi-ronmental impact ofadvertising strategies

Advertising strategies

Newspaper only Online only Optimal

τnp 10,000,000 0 τnp∗ = 4.3Mτol 0 10,000,000 τol∗ = 5.7MNewspaper ad expenditure $109,500 $0 $47,351Online ad expenditure $0 $128,000 $72,649Total $109,500 $128,000 $120,000GWP (E) 29,842 EMT 15,588 EMT 21,752 EMTCampaign cost per consumer $0.011 $0.013 $0.012E per consumer 2.98 kg 1.56 kg 2.17 kg

strategy utilizing exclusively online advertising.5 Thetwo campaigns illustrate the tradeoffs between envi-ronmental impact and monetary costs, i.e., the secondcampaign results in reduced emissions and increasedadvertising expenses. Indeed, the advertising expendi-tures exceed the predetermined budget of $120,000 by6.7%. Finally, the third strategy, as found by solving thelinear program, corresponds to the optimal advertisingcampaign. We note that the optimal solution, denotedτ ∗

np, τ∗ol is for the advertiser to reach 43% of customers

with newspaper ads, and the remaining 57% with onlineads. The associated, minimum GWP is 21,752 EMTs ofCO2. We also observe that the optimal strategy has acampaign cost per individual ($0.012) that is 8% lessthan the online-only strategy,6 and 8% higher thannewspaper only strategy. Importantly, we note that theoptimal strategy yields a 37% reduction in the environ-mental impact (E) per individual (from 2.98 to 2.17 kg),and that the online only strategy provides an additionalreduction of 28% (from 2.17 to 1.56 kg).

Greenhouse gas emissions and energy use To illustratethe versatility of the IO approach, we proceed to ana-lyze the environmental impact of the three strategiesconsidered above. In particular, we first break downthe environmental impact into component greenhousegases. We then analyze the energy consumption asso-ciated with each of the strategies and disaggregate theresults by energy sources. We note that the results pre-sented herein are consistent with other similar studiesof print and online media (Toffel and Horvath 2004;Moberg et al. 2007).

Figures 4 and 5 present the environmental effects—greenhouse gas emissions and energy use, associatedwith the three strategies described earlier. In bothcases, the first two bars correspond to the baselinescenarios. The third bar corresponds to the optimal

5τnp = 1 unit of Online Advertising6Percentages are calculated with respect to the optimal strategylevels.

scenarios found using the LP model. In particular, Fig. 4breaks down the GWP reported in Table 1 into compo-nent greenhouse gases, CO2, CH4, N2O, CFCs, releasedunder each strategy. The total amount of greenhousegases from energy generation is also present. We ob-serve that the strategy to advertise online exclusivelyminimizes emissions of each of the component green-house gases. When broken down into component gases,the newspaper only strategy results in emissions thatare between 29% (N2O) and 44% (CFCs) above thoseassociated with the optimal strategy. Conversely, emis-sions under the online-only strategy are 22–34% belowthose of the optimal strategy. A very high proportionof the greenhouse gases are due to the generation ofelectricity, a breakdown of which is presented in Fig. 5.

Figure 5 shows that the largest energy source re-quired for the campaigns is coal, which varies 15–20%between strategies. This variation is smaller than thoseof other fuels, due to the high usage of coal in utilitiesand other mining/power generation sectors, which aremain contributors of the energy use in both newspa-per and electronics production. Other fuels vary about35–55% between strategies. Distillate Fuel has one ofthe highest variations (43–56%), largely due the heavyfuel requirements of transporting and delivering news-papers. Electricity use, measured in million kilowatthours, equivalent to Giga-watt hours also varies about40% between strategies.

Structural analysis In the remainder of this section, weanalyze the structure of the linear program and how themodel trades off conflicting objectives or constraints.We also emphasize one of the most attractive featuresof the approach from a managerial perspective: theability to conduct sensitivity analysis.

Figure 6 displays the relationships between the ob-jective function and constraints in the above linear pro-gram. In particular, we map the two decision variablesτnp and τol on to the space of the percentages of thetarget population reached through the two availablemedia types. The horizontal axis is used to measurethe percentage reached through online ads, whereas the

Int J Life Cycle Assess

Fig. 4 Greenhouse gasemissions of benchmark andoptimal strategies

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vertical axis measures the percentage reached throughnewspaper ads. The problem’s feasible region, i.e., theadvertising campaigns that satisfy the (demand satisfac-tion and budget) constraints, is given by the intersectionof the constraints/inequalities (12–16), and correspondsto the shaded region that is bounded by the verticalaxis, the demand constraint (12), and the budget con-straint (13). The slope of the budget constraint reflectsthe ratio between the costs to reach the target popula-tion with online vs. newspaper ads.

Figure 6 also includes four lines labeled “GWP Iso-quants” obtained by setting the objective function (11)to various levels, i.e., they are level curves that yieldthe same GWP. The slope of these lines is the rate atwhich the media types can be substituted for each otherto produce the same GWP. From Table 1, newspaperads are associated with 2.98 kg per person, while on-line ads are associated with 1.56 kg per person. Thesubstitution rate, τnp/τol is therefore 1.91. The arrowlabeled “Direction of Improvement” is in the direction

Fig. 5 Energy requirementsof benchmark and optimalstrategies

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of the negative gradient and defines the direction ofsteepest descent of the objective function. We observethat the “Optimal Mixture” corresponds to the corner-point of the feasible region given by the intersectionof the demand and budget constraints. The optimaladvertising campaign, τ ∗

np and τ ∗ol, specifies that 43%

of the target population be reached via newspaper ads,and the remainder via online ads. When evaluated atτ ∗

np and τ ∗ol, constraints (12) and (13) are satisfied with

equalities, and referred to as binding. The other con-straints that define the feasible region, i.e., the nonneg-ativity constraints (16), are non-binding. We note thatthe point labeled “Optimal Mixture” corresponds tothe feasible advertising campaign that falls on the mostdesirable isoquant, i.e., no feasible ad campaigns can bereached from the “Optimal Mixture” in the direction ofimprovement.7

Managerial insights/implications In the next few para-graphs, we discuss the managerial insights and implica-tions of the advertising case study. First, we interpretthe shadow prices or dual variables in terms of describ-ing the sensitivity of the optimal level of emissions tochanges in the resources or requirements imposed by

7In technical terms, we note that, at τ ∗np and τ ∗

ol, the negativegradient of the objective function is in the span of the gradientsof the binding constraints.

the constraints (see Hillier and Lieberman 2010, page217). We then consider the sensitivity of the results tochanges in the relative costs to place ads in the twomedia types. Finally, we consider the effect of changesto the underlying bills of materials for the two mediatypes.

Shadow prices reveal the sensitivity of the optimalobjective function value to changes in the parametersrepresenting the available resources or the require-ments imposed by the binding constraints. In the ex-ample, the binding constraints, (12) and (13), requirethat the target population, D, be reached without ex-ceeding the predetermined budget, B. The shadowprices associated with these constraints are 0.0114 and−0.7705, respectively. The shadow price of constraint(12) implies that the marginal environmental impact ofchanging the size of the target population of ten millionis 0.0114 EMTs of CO2per customer. Similarly, theshadow price of constraint (13), 0.7705 EMTs of CO2,is the rate at which the GWP of the optimal campaignis reduced for every dollar added to the budget of$120,000.

In both cases, the shadow prices apply in rangeswhere both of the aforementioned constraints remainbinding. In the example, these ranges correspond tocases where the budget is sufficiently large to reachthe target population with newspaper ads, but not largeenough to reach the target population exclusively withonline ads. The allowable increase is $8,000, and theallowable decrease is $10,500. To illustrate, considera 5% increase in the advertiser’s budget to $126,000.The budgetary increase leads to a change of −0.7705 ×6, 000 = −4, 623 EMTs of CO2, a 21.25% reductionfrom the emissions in the original optimal strategy. Theoptimal ad campaign with the increased budget is suchthat 89% of the target population is reached via onlineads, whereas 11% is reached via newspaper ads. Thischange is represented in Fig. 7 by shifting the budgetline to the Northeast.

Next, we consider the effect of changes in the (rela-tive) prices to place ads in each of the media outlets. Tomake the discussion tangible, consider a 5% reductionκol, the cost of online ads. This increase the ratio κnp/κol,and decreases the slope of the budget line, as shown inFig. 8. This change, in turn, allows a higher fraction ofthe demand to be served by the online ads, and thusdecreases GWP by 4,279 EMTs (19.7%).

We now examine the effect of changing the under-lying bill of materials of the media. Initially, the ratioof environmental impact, Enp/Eol = 1.91, implying thatnewspaper ads contribute to the optimal GWP at abouttwice the rate online ads. Now, consider a technologicaladvancement that decreases the production cost and

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energy consumption of a cell phone by 5%. Noticingthat online ads result in 41% of the environmentalimpact, we expect on the order of 2.1% change in theoptimal level of emissions. Indeed, the environmentalimpacts decrease by 1.9–2.2%, as shown in Table 2,and the environmental impact ratio, Enp/Eol increases,indicating a higher marginal cost (in terms of GWP)between the two ad media.

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Table 2 Effect of technological advancement on greenhouse gasemissions

Environmental distress Percentage change in E

Global warming potential −2.0%CO2 −2.0%CH4 −2.1%N20 −2.2%CFC −1.9%Total GH gas from energy generation −2.1%

The change in relative environmental impact is indi-cated by a change in the slope of the GWP isoquantsto the southeast, as shown in Fig. 9. The optimal adver-tising strategy does not change as long as the directionof steepest descent is in the span of the gradients of theactive constraints. Thus a change in Enp/Eol will notresult in a strategy change, even though the total E maychange.

Finally, we consider an example where the opti-mal solution changes. In a situation where newspa-pers decrease the raw materials used in productionand delivery significantly, so that they become moreenvironmentally friendly than online ads (Enp/Eol < 1)the slope of the objective changes to favor newspaperads as the environmentally friendly component. Asshown in Fig. 10, the direction of improvement changesto the northwest, and the optimal strategy shifts to anewspaper only mixture.

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5 Conclusions

We present a practical, prescriptive framework to sup-port problems associated with the design and produc-tion of sustainable products, processes and services.The proposed framework relies on the use of IO analy-sis as a tool to quantify the life cycle and supplychain environmental impact associated with meeting agiven, exogenous demand. The framework also buildson literature in production economics, where numerousIO models with substitution have appeared to supportproduct/process design, as well as production planningand scheduling problems. In the latter, models areoften analyzed and solved as linear programs, whichprovides an appealing computational approach to solvethe ensuing problems, as well as an established theoryto conduct subsequent sensitivity analysis. One of theimportant contributions of our work is to bridge thesetwo streams of literature.

In addition to describing the proposed frameworkin detail, we present an example inspired by Toffeland Horvath (2004). In particular, we consider a hy-pothetical, “environmentally conscious” advertiser, inthe Chicago Metropolitan Area, wishing to allocate abudget to place ads in either the print or the online ver-sions of a local newspaper. We formulate the problemof finding an advertising strategy that minimizes globalwarming potential, subject to reaching a target popula-tion, as a linear program. We then solve the problem

and compare the optimal strategy to two benchmarks,in terms of discharges of component greenhouse gases,and in terms of requirements imposed on various en-ergy sources. The results illustrate how the model cap-tures and balances economic and environmental mea-sures/concerns. In particular, the optimal policy tradesoff the reduced environmental repercussions of onlineadvertising with the increased effectiveness per dollarof print advertisements to reach the target population.To showcase the versatility of IO analysis, we alsopresent the energy requirements by source that areimposed by the advertising strategies that we consider.

We analyze the sensitivity of the optimal advertisingstrategy (and associated global warming potential) toperturbations in the budget, the size of the target popu-lation, the relative costs to place ads, and in the relativeenvironmental impact associated with each medium.Among the interesting observations, we interpret theshadow prices or dual variables in the linear program-ming formulation as the marginal environmental im-pact associated with changing the size of the targetpopulation or the budget. Thus, shadow prices providea measure of the value of flexibility associated withchanging the resources or requirements. In particular,the shadow price associated with the budget constraintprovides a conversion factor between environmentalimpact and direct costs to the advertiser, and thuswould be useful, for example, in the context of tradingpollution credits (in financial markets).

With the current popular focus on sustainability andthe potential for stricter environmental regulation inthe future, we confidently predict that LCA will bea focus for research for many years. Future researchdirections of interest include the integration of uncer-tainty analysis and multi-objective modeling into lifecycle models. Furthermore, the integration of environ-mental impacts and indicators with monetary marketsand policy will require advancement and refinement ofcurrent modeling techniques.

Acknowledgements This work was partially supported by aDwight David Eisenhower Transportation Fellowship from theUnited States Department of Transportation awarded to the firstauthor.

Appendix A: Parameters for the case study

In this section, we discuss the assumptions and ap-proach used to generate the parameters in the linearprogram presented in Section 4. Much of the costand other technical information was obtained from theChicago Tribune Media Group (2008).

Int J Life Cycle Assess

A.1 Advertising costs, κnp and κol

In terms of advertising products, we consider a newspa-per ad consisting of a 1/8-page ad placed on the frontpage vs. an online ad consisting of a static, highlighted,homepage based “Cube Ad” appearing on the firstdisplayed page to the right of the text.

A 1/8-page ad measures 5 × 2.875 inches, whichtranslates to 14.375 column inches. At a posted rate of$1,135 per column inch (plus $7,100 for a front pagespace) on Sunday and a rate of $455 per column inch(plus $4,700 for a front page space) on a weekday orSaturday, this sums to a weekly running cost $90,859.38.The Chicago Tribune reports a distribution 4,148,681papers on a weekly basis, which translates into a per-paper cost of 2 × κnp = $0.0219. A conservative reader-ship assumption for a major newspaper is two readersper paper, and so we assume that the total readership isdouble the circulation.

A static, highlighted, “Cube Ad” appearing on theTribune’s homepage costs $50,000 per week. The Tri-bune reports 16,943,601 monthly visitors to their web-site, which translates into 3,899,349 visitors per week,and a cost per visitor of κol = $0.0128.

A.2 Bill of materials, cij

In the example, newspapers are modeled as havingdirect inputs from three economic sectors: newsprint,ink and printing, and transportation delivery. Onlineads, on the other hand, are assumed to consist of in-puts from two sectors: electronics manufacturing, andenergy production. The assumptions used to estimatethe inputs that appear in Fig. 3 are presented below:

– Newsprint

– Newsprint is a commodity that varies in costeach year because of price variations. Toffel andHorvath (2004) estimated the cost for newsprintat $540 per metric ton. Newsprint varied from$580 to US $660 per metric ton between 2006–2008 (Newfoundland Labrador Department ofFinance, Economic Research and Analysis Di-vision 2008). Newsprint costs are expected toincrease 15% in 2009, as commodity prices con-tinue to rise. We used a price of $580 per tonto align the costs for newsprint with those es-timated in previous research, and to minimizethe bias that inflated prices would have on theanalysis.

– The weight of the Chicago Tribune was mea-sured to be 4.05 g per numbered page. From asmall sample, we estimate the weekly averagenumber of pages at 108 (not including separate

circular advertisement sections). Thus, the esti-mated weight per paper is 4.05 · 108=437.4 g perpaper. Thus, the estimated weight per paper is437 g per paper, and a single newspaper requires$0.2537 in inputs from the newsprint sector.

– Ink and printing

– Data are not available on ink usage in printingthe Chicago Tribune. From Toffel and Horvath(2004), we estimate inputs of $0.1249 per kilo-gram (converted to 2007 dollars) for ink andprinting costs. The corresponding cost for theChicago Tribune is calculated to be $0.1249 ·437.4=$.0546 per paper.

– Delivery

– Delivery costs were calculated using the costin diesel fuel to deliver the newspapers, plusa yearly maintenance allowance for each ve-hicle. The average diesel fuel price for 2007was reported from the US Department of En-ergy as $2.94 per gallon. An estimate of 5 mpgwith a carrying capacity of 1,000 newspaperswas used. The Chicago Tribune is printed at777 West Chicago Avenue, Chicago IL. Theaverage population-weighted distance for CookCounty and the six surrounding counties, thearea comprising the majority of the ChicagoTribune subscribers, is 15.99 statute miles. Fora round trip, the cost per truck in diesel fuel iscalculated to be $9.40, and the cost per paperis $0.0188. A maintenance allowance is givenas $1,000 per year per truck, i.e., $0.01923 perpaper. This totals $0.038 per paper in deliverycosts.

The components of Online Ads used in this paperare from two sectors: electronic and cell phone manu-facturing, and energy generation.

– Electronic and cell phone manufacturing

– We considered a popular, small size, multi-function, internet ready cellular phone. The2007 production cost of this phone is estimatedby iSuppli Corporation to be $245. Assuminga cell phone life of 3 years, the cost per weekis $1.57. Users were estimated to spend 5% oftheir time on news sites, resulting in a per usercost of $0.0785.8

8For reference, see: http://www.energy.gs/2008/08/how-much-energy-does-apple-iphone-use.html, http://www.eia.doe.gov/cneaf/electricity/epm/table5_3.html, and http://www.eia.doe.gov/emeu/steo/pub/gifs/Fig21.gif

Int J Life Cycle Assess

– Energy generation

– The energy use was estimated to be the energyrequired to regularly charge the cellular phone.The phone in question was estimated to con-sume 4–6 W while recharging daily, plus 0.5 Wof use when left in the charger. At an averagecost of 10.4 cents per kWh this translates to$0.47 in electricity usage per week, and a costof $0.024 (5% of total cost) allocated to theOnline ad.

A.3 Economic input-output tables and environmentalimpact coefficients

The economic IO Tables were obtained from US De-partment of Commerce Bureau of Economic Analy-sis Benchmark Input-Output Tables for 2002. Theemissions and energy use coefficients are derivedfrom the US 1997 Industry Benchmark EconomicInput-Output Life Cycle Assessment (EIO-LCA) mod-els, http://www.eiolca.net (Carnegie Mellon UniversityGreen Design Institute 2008).

Global Warming Potential (GWP) is defined as “theratio of the time-integrated radiative forcing from theinstantaneous release of 1 kg of a trace substance rel-ative to that of 1 kg of a reference gas” (Houghtonet al. 2001). In practice, GWP values represent theamount to which gases add to the greenhouse effect inthe atmosphere with reference to the impact of CO2.Thus, GWP can be used as a measure of the totalimpact of greenhouse gases associated with a product orprocess.

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