Integration of Life Cycle Assessment and Data Envelopment

Analysis using a Free Disposable Hull Approach to Evaluate

Farms’ Eco-efficiency

Leonardo Vásquez-Ibarra

, Alfredo Iriarte

, Ricardo Rebolledo-Leiva

Marcela Gonzalez-Araya

and Lidia Angulo-Meza

Doctoral Program in Engineering Systems, University of Talca, Camino a Los Niches km.1, Curicó, Chile

Department of Industrial Engineering, University of Talca, Camino a Los Niches km.1, Curicó, Chile

Master Program in Operations Management, University of Talca, Camino a Los Niches km.1, Curicó, Chile

Production Engineering Department, Universidade Federal Fluminense, Rua Passo da Patria 156, São Domingos,

Niterói 24210-240, Brazil

lidiaangulomeza@id.uff.br

Keywords: Eco-efficiency, Free Disposable Hull, Life Cycle Assessment, Data Envelopment Analysis, Raspberries

Production.

Abstract: The joint use of Life Cycle Assessment and Data Envelopment Analysis, also known as LCA+DEA, appears

as a suitable methodology to evaluate eco-efficiency of multiple units. This methodology has been developed

mainly during the last decade, and different methodological aspects has been proposed. However, there are

other such as the use of advanced DEA models that have been poorly explored. In this sense, this study seeks

to integrate the Free Disposable Hull (FDH) approach into LCA+DEA methodology, applied an agricultural

case study. The five-step method is employed to a sample of 37 raspberry producers considering carbon

footprint as environmental category. The results indicated that 11 farmers are identified as inefficient for

which operational and environmental targets are proposed. The use of FDH model is suitable for the use into

the LCA+DEA methodology since it allows to determine one benchmark for inefficient farmers, unlike others

models widely used in this methodology, such as BCC, SBM or CCR.

1 INTRODUCTION

Sustainable development has received great attention

during the last decade. Since its proposal eco-

efficiency has been coined as a quantitative

management approach for studying both,

environmental and economic aspects (Rybaczewska-

Błażejowska & Gierulski, 2018). The World Business

Council for Sustainable Development (WBCSD)

defined eco-efficiency concept as “the delivery of

competitively priced goods and services that satisfy

human needs and bring quality of life, while

progressively reducing ecological impacts and re-

https://orcid.org/0000-0001-8514-8685

https://orcid.org/0000-0002-8281-829X

https://orcid.org/0000-0003-1082-169X

https://orcid.org/0000-0002-4969-2939

https://orcid.org/0000-0003-4557-0210

source intensity throughout the life-cycle, to a level at

least in line with the earth's estimated carrying

capacity” (Schmidheiny & Stigson, 2000).

Eco-efficiency has been evaluated using different

methodologies, which can be classified into linear

programming methods, statistical and econometric

tests, and, accounting and indicator techniques

(Nikolaou & Matrakoukas, 2016). Among these

methodologies, the joint use of life cycle assessment

and Data Envelopment Analysis appears as one of the

most recent approaches, allowing to assess the

operational and environmental performance of

multiple units (Rebolledo-Leiva, Angulo-Meza,

Iriarte, & González-Araya, 2017a).

Vásquez-Ibarra, L., Iriarte, A., Rebolledo-Leiva, R., Gonzalez-Araya, M. and Angulo-Meza, L.

Integration of Life Cycle Assessment and Data Envelopment Analysis using a Free Disposable Hull Approach to Evaluate Farms’ Eco-efﬁciency.

DOI: 10.5220/0010240201850191

In Proceedings of the 10th International Conference on Operations Research and Enterprise Systems (ICORES 2021), pages 185-191

ISBN: 978-989-758-485-5

185

LCA is a widely used methodology to evaluate the

potential environmental impacts through the whole

life cycle of products or services (ISO, 2006). This

methodology allows to identify opportunities to

improve their environmental performance.

DEA is a non-parametric tool that uses linear

programming to estimate the relative efficiency of

several homogeneous units, known as Decision

Making Units (DMU) (Cooper, Seiford, & Tone,

2007). These DMUs use multiple inputs (resources)

to produce multiple outputs (outcomes of the

processes). The relative efficiency is measured

employing inputs and outputs into different

mathematical DEA models. In general terms, these

models, could be oriented to inputs or to outputs. The

former (input-oriented models) seek to minimize the

inputs while maintaining the outputs constant. On the

contrary, the second (output-oriented models) aim to

maximize all outputs while maintaining the inputs

constant (Ten Raa & Greene, 2019). DEA models

classified the DMUs into efficient if its score is 1 (or

100%) and inefficient otherwise. For the inefficient

ones, DEA also provides targets and benchmarks in

order to become efficient.

The joint use of LCA and DEA, also namely

LCA+DEA methodology, has been developed into

three different LCA+DEA methods, five-step method

Vázquez-Rowe et al. (2010), three-step method

Lozano et al. (2010) and four-step method Rebolledo-

Leiva et al. (2017). The main differences among these

methods are the number of steps and the kind of

variables used into the DEA model (Vásquez-Ibarra,

Rebolledo-Leiva, Angulo-Meza, González-Araya, &

Iriarte, 2020). Beyond the LCA+DEA methodology,

others Life Cycle approaches have been coupled with

DEA, outstanding the development of the LC+DEA

concept. Due to the current relevance of GHG

emissions mitigation, based on the Carbon Footprint

(CF), a methodological framework is based on the

combined use of CF and DEA, known as CF+DEA

(Rebolledo-Leiva et al., 2017a; I Vázquez-Rowe &

Iribarren, 2015).

The use of LCA+DEA has increased during the

last decade. Vásquez-Ibarra, Rebolledo-Leiva,

Angulo-Meza, González-Araya, & Iriarte (2020)

conducted a critical review, proposed a taxonomy and

proposed future research related to the development

of this methodology. One item developed by these

authors were the widely used of three DEA models:

CCR (Charnes, Cooper, & Rhodes, 1978), BCC

(Banker, Charnes, & Cooper, 1984), SBM (Tone,

2001). In these models, inefficient DMUs can achieve

an efficient point on the frontier reducing their inputs

(in input-oriented models), adding output (in output-

oriented models), or both (in non-oriented models).

This efficient point is a combination of available

efficient units and they not necessarily represent real

units, as pointed out by Safari, Jafarzadeh, & Fathi

(2020). Furthermore, these models provide many

reference units (benchmarks) for inefficient DMUs,

making difficult their implementation in real world,

for example in agricultural sector. Particularly, small

farmers could be one of the most challenge group in

agricultural context, since its limit access to

information and communication technologies (Otter

& Theuvsen, 2014), making difficult to follow

operational practices of many benchmarks.

One way to deal with these issues is the use of

Free Disposable Hull (FDH) approach. FDH relaxes

the convexity assumption of DEA models providing

just one benchmark for each inefficient DMU as a

reference unit. This implies that FDH’ reference set is

more consistent and corresponds with real world

(Deprins, Simar, & Tulkens, 1984; Safari et al.,

2020). Therefore, the use of FDH model can provide

benefit from a practical point of view, since small

inefficient farmers have just one benchmark.

In this context, this study seeks to evaluate the use

of the FDH DEA model into the joint use of LCA and

DEA methodology to evaluate eco-efficiency. To do

this, we employ a case study of 37 Chilean raspberries

producers using the five-step method.

2 METHODS

In this Section, methodological aspects of five-step

CF+DEA method are presented. Briefly, the five-step

method consists of five stages: life cycle inventory,

actual environmental characterization using CF;

operational efficiency performed for each DMU

through DEA; environmental characterization using

the target DMUs from the previous step; and,

comparison of the current and target environmental

impacts.

2.1 Data Collection of Multiple Units

The first step of the five-step CF method is to develop

a Life Cycle Inventory (LCI), i.e. input and output

data for the assessed system are collected.

2.2 Carbon Footprint Assessment

In this step, carbon footprint (CF) assessment for

every DMU is performed. This step represents the

actual environmental characterization of all DMUs

under study. CF is an environmental indicator that

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems

186

estimated the overall greenhouse gas (GHG)

emissions associated to a product or activity during

its whole life cycle. The most common GHG

emissions are carbon dioxide (CO

), nitrous oxide

O) and methane (CH

), among several others

(ISO, 2018).

2.3 Data Envelopment Analysis

In this step, the DEA model is performed. As mention

in the Introduction section, the FDH DEA model is

employed in order to determine operational efficiency

of 37 farmers. The selection of this model lies on that

it provides one benchmark for inefficient DMUs,

unlike CCR, BCC or SBM which provides many

efficient units as references which could result

difficult to implement from a practical point of view

for small farmers. Furthermore, benchmarks and

calculation of the target for each inefficient DMU is

conducted.

The five-step CF method employs an input-

oriented DEA model (I Vázquez-Rowe & Iribarren,

2015). In this sense, the FDH model is used

considering operational inputs and outputs, while the

CF is evaluated before and after DEA model.

The mathematical formulation of DEA model is

as follow. Suppose there are n observed DMUs and

assume that each one uses m inputs to produce s

outputs. The FDH model that minimize the inputs of

DMU

assuming Variable Returns to Scale (VRS) is

presented from Eqs. (1) to (6).

Min

(1)

Sub

ect to

















∀

(2)

















∀ r

(3)





1







(4)



∈ 0,1 ∀ j

(5)

is unconstrained

(6)

Where,

j is the subindex of the set of observed DMUs,

i is the subindex of the inputs,

r is the subindex of the outputs,

θ corresponds to the proportion by which all

inputs can be reduced (efficiency level),

is the intensity of the participation of the DMUj

in the construction of the “compound” DMU or

benchmark,

is the amount of input i consumed by DMUj,

is the amount of output r produced by DMUj,

is the amount of input i of DMU

is the amount of output r of DMU

In the FDH model, Eq. (1) seeks to minimize the

proportion of inputs used by DMU

and it represents

the efficiency of this DMU. Eq. (2) guarantees the

proportional reduction of inputs limited by the

efficient frontiers. Similarly, Eq. (3) prevents that the

outputs of DMU

are limited by the efficient frontier.

Eq. (4) (4) stablishes that each DMUs evaluated is

compared with DMUs in similar size and scale. Eq.

(5) and (6) represent the nature of the decision

variables.

2.4 Carbon Footprint using Target

Values

After the target values were obtained for inefficient

DMUs through the FDH model, the CF is calculated

using the new LCI. This step is carried out with the

aim to calculate the potential environmental targets of

inefficient DMUs if they operate under efficient level.

This procedure entails the environmental

benchmarking of the sample.

2.5 Interpretation and Eco-efficiency

Assessment

In this step, the environmental impacts calculated in

step 2 are compared with those obtained in step 4

associated to the targets. In this sense, as stated I

Vázquez-Rowe & Iribarren (2015), “…the

environmental consequences of operational

inefficiencies are revealed…” and the eco-efficiency

can be verified. Furthermore, benchmark (best

practice) provided by FDH model can be used as a

guideline for inefficient farmers.

3 RESULTS AND DISCUSSION

This section presents the results obtained using the

five-step CF+DEA method following the FDH.

3.1 Data Collection of Multiple Units

The data of raspberries producers were obtained from

works of our research group (Fernández

Integration of Life Cycle Assessment and Data Envelopment Analysis using a Free Disposable Hull Approach to Evaluate Farms’

Eco-efﬁciency

187

Figure 1: System boundaries and DEA factors employed.

Cáceres, 2018; Rebolledo-Leiva, Angulo-Meza,

Iriarte, González-Araya, & Vásquez-Ibarra, 2019)

and based on Consultora Campo Nova Ltda (2011)

who obtained them through face-to-face interviews.

The study considers 37 farmers of the Maule

Region in Chile, between the 35th and 36th parallel

south. This is one of the main regions where raspberry

is cultivated, totalizing 1216 hectares of this fruit

(Larrañaga et al., 2016).

The agricultural operations are made manually

and consequently, energy is not considered.

Furthermore, agricultural inputs are classified

considering it main function, i.e. fertilizer input

represents all chemical and organics compounds that

contribute to nutrition of the plants. The LCI is

extracted from Rebolledo-Leiva et al. (2019) and

consider as inputs the amount of fertilizers,

pesticides, waste pruning and packaging residues,

while the output is the raspberry production.

3.2 Carbon Footprint Assessment

In the second step, the system boundaries for CF

assessment were setted from cradle-to-gate. This

imply that the agricultural factors evaluated

correspond to fertilizers, pesticides, waste pruning

and packaging residues. Figure 1 presents LCA

factors used in this study. While the functional unit

(FU) is 1 kg of harvested raspberries.

The CF was obtained using the software CCalC2

v1.43 of the University of Manchester (2016)

following the CML 2001 method (Guinée et al.,

2002). Background processes, e.g. extraction of raw

material, fertilizer production, etc., were obtained

mainly from the Ecoinvent v.2.2 database (Wernet et

al., 2016). While the field emissions were calculated

following World Food Guide LCA Database

(Nemecek et al., 2015).

The total amount of CF produced by raspberry

production is on average 4409 kgCO

2-eq

(0.82 kgCO

/ kg of raspberry). Farmer 29 has the highest value

per FU (5.5 kgCO

2-eq

/ kg of raspberry) while farmer

9 has the lowest one (0.1 kgCO

2-eq

/ kg of raspberry).

The agricultural factors with the highest contribution

to the total CF are widely fertilizers (93.4%) followed

by pruning waste (4.2%), and pesticides (2.4%).

Packaging residues contributes only 0.01%.

3.3 Data Envelopment Analysis

Considering the low contribution of packaging

residues to the total CF, the inputs used in the FDH

model are fertilizers, pesticides and pruning waste,

while the output is raspberry production (see Figure

1). The DEA model was performed using software

IBM ILOG CPLEX Optimization Studio v.12.7.1.0.

According to the input oriented FDH model, a

total of 26 DMUs were classified as efficient and 11

DMUs as inefficient. Figure 2 presents efficiency

score for the inefficient DMUs. These DMUs

obtained an average score of 0.6, with the lowest

value of 0.2 (DMU 37) and highest value of 0.9

(DMUs 22, 27 and 30).

Inefficient DMUs produce 65% less raspberries

than the efficient ones, despite they use 17% less

fertilizers, 34% less pesticides and 34% less pruning

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems

188

Figure 2: Efficiency score using FDH DEA model.

Figure 3: Current and targets CF level.

waste. This implyes that, even though farmers use

less inputs, their actual operation points is much

fewer than the efficient operating point. Therefore,

they should reduce actual amount of inputs

consumed.

For each inefficient DMU, FDH model provides

one benchmark, making suitable from a practical

point of view, since inefficient farmers should focuss

only on one efficient farm. For instance, farmer 9

(efficient) is benchmark of farmer 36 (inefficient).

Both produce the same amount of raspberries (2500

kg), however, farmer 9 uses 96% less fertilizers, 41%

less pesticides and 73% less pruning waste than

farmer 36. Consequently, if farmer 36 want to

improve their actual performance, it is advisable to

review operational practices of farmer 9.

3.4 Carbon Footprint using Target

Values

This step presents the new CF performed using the

targets provided by DEA model in step 3 for

inefficient DMUs. Figure 3 presents current and

target CF for the 11 inefficient DMUs. As can be

seen, on average inefficient farmers could reduce

their actual level of CF from 3530 kg CO

2-eq

until to

1021 kg CO

2-eq

which represents 71%. The most

dramatic reduction is observed in farmer 7 and 36

(95% and 94%, respectively).

3.5 Interpretation and Eco-efficiency

Assessment

In this last step, eco-efficiency level of the raspberry

farmers is analyzed. Eco-efficiency comprises

operational and environmental aspects. From an

operational point of view, the most critical reduction

observed for inefficient DMUs is related to fertilizers

(71%), followed by pesticides (55%) and prunning

waste (50%). It is importan to observe that fertilizers

are also the main contributor to the current CF level

(see Sub-section 3.2) This operational reduction

implies also an improving of CF performance.

Integration of Life Cycle Assessment and Data Envelopment Analysis using a Free Disposable Hull Approach to Evaluate Farms’

Eco-efﬁciency

189

On the other hand, the use of FDH model allows

the implementation of best practices easier than the

actual existing DEA models in the LCA+DEA

literature. Since, for the inefficient farmers it is

possible to provide operational factors through

bechmarking of one efficient farmer. Therefore, it is

recommendable that inefficient farms have to follow

the agricultural practices of the efficient farms, which

coul ensure not only achieving the CF targets but also

the final production targets.

4 CONCLUSIONS

This study integrates the FDH aproach into the joint

use of LCA+DEA methodology. The main

contribution is to suitability of FDH model into

LCA+DEA methodology from a practical point of

view in order to provide operational and

environmental targets for inefficient DMUs based on

one benchmarks.

The case study considered 37 chilean raspberries

farmers. The five-step CF+DEA method was

employed. The environmental assesssment (CF) was

evaluated in a cradle-to-gate system boundary

considering fertilizers, pest control (use of

pesticides), prunning waste and plastic waste. While

the DEA assessment considered the FDH model

through input orientation.

A total of 11 farmers were classified as eco-

inefficient, for whose operational and environmental

targets were proposed. On average, the highest

reduction is observed for fertilizers and pesticides.

This reduction implies a decrease of CF level of 71%

for the inefficient farmers.

The use of the FDH model appears as a suitable

DEA model for it use in the LCA+DEA methodology

since it allows to identify one benchmark (best-

practice) for inneficient DMUs. This enable that

inefficient farmers could follow agricultural practices

of the efficient ones in order to reduce operational

levels and CF, while maintaning actual raspberry

production.

Despite its novelty for LCA+DEA methodology,

future works could extend the use of the FDH model

comparing it with others DEA models widely used in

LCA+DEA literature, such as BCC, SBM or CCR.

Moreover, future works can propose further

methodology in order to rank the efficient DMUs and

increase the discrimination of the model.

ACKNOWLEDGEMENTS

Leonardo Vásquez-Ibarra is funded by CONICYT

PFCHA/DOCTORADO BECAS CHILE/2018–

21180701. Ricardo Rebolledo-Leiva gives thanks to

CONICYT–PFCHA/MagísterNacional/2019–

22190179 for financial support. Lidia Angulo-Meza

thanks the CNPq project 409590/2018-5 for financial

support.

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