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Assessing the performance of biogas plants with multi-criteria and data envelopment analysis

16 Sep 2009-European Journal of Operational Research (Elsevier)-Vol. 197, Iss: 3, pp 1084-1094

TL;DR: An assessment of 41 agricultural biogas plants located in Austria to determine their relative performance in terms of economic, environmental, and social criteria and corresponding indicators suggests that MCDA, and the use of IRIS in particular, constitutes a useful approach that can be applied in a complementary way to DEA.
Abstract: This paper performs an assessment of 41 agricultural biogas plants located in Austria to determine their relative performance in terms of economic, environmental, and social criteria and corresponding indicators. The comparison of these renewable energy conversion plants is based on two complementary analyses. Data envelopment analysis (DEA) was conducted to provide measures of radial efficiency relative to the observed frontier of production possibilities. Multi-criteria decision analysis (MCDA), using the IRIS/ELECTRE TRI methodology, was conducted to obtain a different perspective on the results, and as a tool that would enable to incorporate managerial preferences easily. To be able to use IRIS while keeping the spirit behind DEA, the evaluation criteria were defined as different output/input efficiency ratios, and no information about criteria weights was introduced at the outset. The results suggest that MCDA, and the use of IRIS in particular, constitutes a useful approach that can be applied in a complementary way to DEA.

Summary (4 min read)

1. Introduction

  • Over the last two decades, a growing environmental awareness has changed the focus of energy planning processes from an almost exclusive concern with cost minimization of supply-side options to the need of explicitly including multiple and potentially conflicting aspects, such as cost and environmental issues, in decision support models.
  • The Kyoto Protocol, the EU Renewables Directive 2001/77/EC, and the European Biomass Action Plan are examples of ambitious political goals fostering the development of energy conversion technologies based on RES.
  • With these intentions in mind, this paper also addresses the challenge of determining how MCDA methods can be used in the context of efficiency evaluation, trying to keep the spirit behind DEA, while being able to use MCDA’s capabilities of explicitly incorporating the preferences of a decision-maker, not necessarily in the form of trade-off restrictions.
  • Uncertainty is an intrinsic characteristic of real-world problems arising from multiple sources of distinct nature.
  • In Section 5 the findings from the analysis are discussed and some conclusions are drawn.

2.1. DEA

  • The attainment of high levels of performance is a key issue for the success of every organization.
  • DEA models use these inputs and outputs to compute an efficiency score for a given DMU when this particular DMU is compared with all the other DMUs considered.
  • The weights are chosen by the LP model such that a DMU is ‘‘shown in its best light”, i.e., that its efficiency score is maximized.
  • The CCR model was presented in the seminal work of Charnes et al. (1978).
  • In fact, the inputs and outputs are not generally equally relevant and some preference information must be included in the analysis.

2.2. MCDA

  • The above-mentioned considerations about DEA led us to envisage the use of MCDA models to perform efficiency evaluation.
  • In assessing the performance of DMUs in which technical, economic and environmental aspects are at stake, it is often important to use known standards (or theoretical maxima) and efficiency profiles.
  • The ELECTRE TRI method belongs to the ELECTRE family of multi-criteria methods developed by Bernard Roy and his co-workers (Roy, 1996).
  • Also, a set of indifference (qj), preference (pj) and veto (vj) thresholds for each criterion j and reference profiles can be defined.
  • Information about these parameter values can be provided through the introduction of intervals, linear constraints, or even sorting examples (which are translated into constraints on the parameters that guarantee that those example results are reproduced).

3. Case study

  • In Austria, an effective promotion of renewable energy technologies has been pursued in recent years, driven by the need to achieve ambitious energy and climate policy goals.
  • 1 Note that in 2006 a revised Green Electricity Act and Ordinance entered into force, with amended feed-in tariffs and budget restrictions (BGB1.
  • Please cite this article in press as: Madlener, R. et al., Assessing the perf Journal of Operational Research (2008), doi:10.1016/j.ejor.2007.12.051.
  • As a result, many different technologies, design concepts, and specific applications occurred on the market, some of which were either not very productive, energy-efficient, or reliable.
  • Due to the attractive feed-in tariffs granted, anaerobic digestion of energy crops currently mainly aims at the generation of electricity, and much less so at heat generation (or the feed-in of purified biogas into the natural gas grid, if available).

4.1. Description of the data and parameters used

  • The DMUs considered are a representative set of energy crop digestion plants in Austria, aimed at covering the whole spectrum of existing plant types and operating conditions.
  • Cooling, safe transport and appropriate storage were also scrutinized.
  • The sampled installations are geographically well distributed over the country.
  • The main groups of evaluation aspects at stake for assessing the efficiency of energy crop digestion plants are: (1) substrate provision, storage and pre-treatment; (2) biogas production (by means of anaerobic digestion); (3) net utilization of heat and electricity; (4) digestate handling and disposal; and (5) greenhouse gas (GHG) emissions.
  • For further details on data collection see Braun et al. (2005, 2007) and Laaber et al. (2005), and for further details about the various inputs and outputs and DEA model specifications scrutinized see Madlener (2006).

4.2. DEA

  • In the first DEA model considered in this paper, the authors have used substrate (i2) and labor (i1) as inputs and the amount of net electricity (o1) and external heat (o2) as outputs.
  • See Scheel, 2001; Seiford and Zhu, 2002), and although the choice influences the results, there does not seem to be an undisputed ideal method to handle undesirable outputs (Dyson et al., 2001).
  • A scale transla- Please cite this article in press as: Madlener, R. et al., Assessing the perf Journal of Operational Research (2008), doi:10.1016/j.ejor.2007.12.051 tion was used to account for the negative net values, another modeling option known to have an influence on the results (Lovell and Pastor, 1995).
  • On the other end of the spectrum, DMUs 5, 13, 14, 25, 26, 33, and 39 appear as some of the worst-performing plants, irrespective of whether GHG emissions are considered or not.
  • Keeping the same inputs and outputs presented here, the main implications of using the variable returns to scale version (BCC-O) would be to add DMU 15 to the set of efficient units, without GHG emissions, and adding DMUs 33 and 38 to the set of efficient units, with GHG emissions considered.

4.3. MCDA

  • In the MCDA approach the objective was to identify groups of DMUs that could be assigned to different efficiency labels, rather than computing a precise efficiency score or deriving a complete ranking.
  • Each plant has to be assigned to one of these ordered categories, according to the multiple evaluation criteria.
  • The indicators would then be labor/ODS (i1/i2), electricity/ODS (o1/i2), heat/ODS (o2/i2), and GHG/ODS (o3/i2).
  • Note that although this approach leads to a high number of indicators as the number of criteria increases, it mimics the spirit of DEA: to allow each DMU to be evaluated according to multiple indicators and to choose the most favorable indicators (within the constraints that the decision-maker may impose, as the authors will illustrate further below).
  • DMUs in the best categories, several options can be envisaged: (1) to make the category bound more demanding; (2) to require the support of more than one indicator (e.g., the support of half of the indicators, as depicted in Fig. 4); and/or (3) to add some information about the relative power of the indicators.

4.4. Comparing the results

  • The DMUs in Fig. 4 are ranked by order of their DEA efficiency score (for the case with GHG emissions), from the worst (DMU 26) to the best (the last six DMUs – 12, 15, 17, 18, 20, and 28 – have an efficiency score of 1).
  • The DMUs in Figs. 5 and 6 have similar profiles with few exceptions, and four of them are among the worst according to both approaches (DMUs 5, 13, ormance of biogas plants with multi-criteria and data ..., European 0.00 0.25 0.50 0.75 1.00 Lab. ODS GHG Elec.
  • Heat D EA fa ct or s (n or m al iz ed ) (best) 0.00 0.25 0.50 0.75 1.00 Elec./Lab. Elec./ODS.
  • Fig. 7 depicts the profiles of the DMUs with the best performance according to DEA, the efficient ones; Fig. 8 depicts the profiles of the best-performing DMUs according to MCDA which the authors have defined to be those that reach C4 on half of the indicators (at least) and are not placed in C1 by any indicator (i.e., ‘‘pessimistic” classification is C2 or better).
  • The difference between the approaches can be diminished as the number of categories increases, as the discrimination among DMUs would increase in the MCDA analysis.

4.5. Further analyses with IRIS

  • The choice of the best and worst DMUs in the MCDA study was performed without making any distinction between the indicators.
  • This implies that the importance of g2 (electricity/ODS) cannot be lower than the importance of g1 (electricity/labor).
  • Optionally, the ELECTRE TRI models also allow incorporating veto thresholds, such that, for instance, a DMU that is classified as C1 according to a given indicator will not be able to reach category C4 in a multi-criteria evaluation.
  • A form which is easily perceived by managers is to ask for intervals for some of the parameters (for instance, the weights), aimed at capturing information that is not precisely known but can be taken as bounded within some acceptable limits.
  • The MCDA analysis may complement the DEA analysis by providing another perspective from which the conclusions of DEA may be either strengthened or weakened.

5. Discussion and conclusions

  • DEA is a data-oriented approach that requires no a priori specification of the functional form of the production model converting inputs into outputs.
  • Moreover, managerial preference information is often required, since inputs and outputs do not generally have the same importance in assessing the efficiency of operational units.
  • This has been the main motivation for the use of MCDA techniques, in order to assess the extent by which these could overcome those characteristics of DEA, and what adaptations would be needed to improve the quality of the assessment.
  • An authority certifying sustainable development practices may use this type of MCDA to label energy production plants according to their efficiency, taking into account the inputs they consume, the energy and other desirable outputs they produce, as well as greenhouse gas emissions and other undesirable outputs.
  • DEA, on the other hand, can be particularly suited to identify DMUs with efficiency gaps relative to the state of the art, given the observed efficiency frontier.

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Assessing the performance of biogas plants with multi-criteria and data
envelopment analysis
Reinhard Madlener
a,
*
, Carlos Henggeler Antunes
b
, Luis C. Dias
c
a
Institute for Future Energy Consumer Needs and Behavior (FCN), Faculty of Economics/E.ON Energy Research Center, RWTH Aachen University,
Templergraben 55, 52056 Aachen, Germany
b
Department of Electrical Engineering and Computers, University of Coimbra and INESC Coimbra, Rua Antero de Quental, 199 Coimbra, Portugal
c
Faculty of Economics, University of Coimbra and INESC Coimbra, Rua Antero de Quental, 199 Coimbra, Portugal
article info
Article history:
Received 18 January 2007
Accepted 19 December 2007
Available online xxxx
Keywords:
Multi-criteria decision analysis
DEA
Renewable energy
Biogas
ELECTRE TRI
abstract
This paper performs an assessment of 41 agricultural biogas plants located in Austria to determine their
relative performance in terms of economic, environmental, and social criteria and corresponding indica-
tors. The comparison of these renewable energy conversion plants is based on two complementary anal-
yses. Data envelopment analysis (DEA) was conducted to provide measures of radial efficiency relative to
the observed frontier of production possibilities. Multi-criteria decision analysis (MCDA), using the IRIS/
ELECTRE TRI methodology, was conducted to obtain a different perspective on the results, and as a tool
that would enable to incorporate managerial preferences easily. To be able to use IRIS while keeping the
spirit behind DEA, the evaluation criteria were defined as different output/input efficiency ratios, and no
information about criteria weights was introduced at the outset. The results suggest that MCDA, and the
use of IRIS in particular, constitutes a useful approach that can be applied in a complementary way to
DEA.
Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction
Over the last two decades, a growing environmental awareness
has changed the focus of energy planning processes from an almost
exclusive concern with cost minimization of supply-side options to
the need of explicitly including multiple and potentially conflicting
aspects, such as cost and environmental issues, in decision support
models. It is now widely recognized that the largest source of
atmospheric pollution stems from fossil fuel combustion, upon
which current energy production and use patterns throughout
the world rely heavily. Therefore, severe environmental problems
arise from energy demand to sustain human needs and economic
growth. A more intensive use of renewable energy sources (RES)
by means of modern energy conversion technologies can be an
important remedy. Although the effective potential of RES is far
from being fully exploited, they are becoming increasingly impor-
tant as supply-side options to satisfy energy needs, taking into ac-
count their dispersed generation capabilities, low levels or absence
of pollutant emissions, and waste valuation potential. However,
some drawbacks can also be associated with RES, such as their
intermittent nature, as in the case of wind turbines, and various
types of negative environmental impacts (Abbasi and Abbasi,
2000; Dincer and Rosen, 1999).
The Kyoto Protocol, the EU Renewables Directive 2001/77/EC,
and the European Biomass Action Plan are examples of ambitious
political goals fostering the development of energy conversion
technologies based on RES. In this paper we address the case of
agricultural biogas plants in Austria, which use mainly energy
crops (silage) for anaerobic digestion, that have been effectively
promoted over the last couple of years through investment subsi-
dies (capital grants) and, probably more importantly, also by
means of guaranteed feed-in tariffs for electricity sold to the grid.
From an interdisciplinary point of view, the assessment of the
global performance of different entities (potential solutions,
courses of action, decision alternatives) can no longer be based
on a single-dimensional axis of evaluation, such as cost or benefit.
In most cases, multiple, incommensurate, and often conflicting
axes of evaluation of distinct nature are inherently at stake. There-
fore, economic, technical, societal, and environmental aspects must
be explicitly taken into account in models for decision support,
rather than aggregated in a single (and typically economic)
indicator.
This paper uses both data envelopment analysis (DEA) and mul-
ti-criteria decision analysis (MCDA) approaches for assessing the
efficiency of 41 agricultural biogas plants, with the purpose of
gaining some new insights about combining these complementary
evaluation techniques as well as the underlying methodologies. On
0377-2217/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.ejor.2007.12.051
* Corresponding author. Tel.: +49 241 80 97 162; fax: +49 241 80 92 206.
E-mail addresses: rmadlener@eonerc.rwth-aachen.de (R. Madlener), cantunes@
inescc.pt (C.H. Antunes), ldias@inescc.pt (L.C. Dias).
European Journal of Operational Research xxx (2008) xxx–xxx
Contents lists available at ScienceDirect
European Journal of Operational Research
journal homepage: www.elsevier.com/locate/ejor
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the one hand, DEA is the tool generally used to evaluate the effi-
ciency of decision making units (DMUs). These are comparable
organizational entities performing similar tasks in a homogeneous
operating environment. On the other hand, MCDA is the tool gen-
erally used to conciliate multiple evaluation criteria, taking into ac-
count the preferences of a decision-maker. The introduction of
managerial preference information is often relevant when assess-
ing the relative performance of the DMUs. In fact, a manager is nor-
mally not indifferent as to whether a unit turns out to be efficient
by using a less important combination of inputs and/or outputs,
and by underweighting inputs and/or outputs of high importance
to the business concerned.
With these intentions in mind, this paper also addresses the
challenge of determining how MCDA methods can be used in the
context of efficiency evaluation, trying to keep the spirit behind
DEA, while being able to use MCDA’s capabilities of explicitly
incorporating the preferences of a decision-maker, not necessarily
in the form of trade-off restrictions.
Uncertainty is an intrinsic characteristic of real-world problems
arising from multiple sources of distinct nature. Uncertainty
emerges from the ever-increasing complexity of interactions with-
in social, economic environmental and technical systems, charac-
terized by a fast pace of technological evolution, changes in
market structures, and new societal concerns. It is generally
impracticable to envisage decision aid models that would capture
all the relevant interrelated phenomena at stake, incorporate and
process all the necessary information, and also account for the
changes and/or hesitations associated with the explicit expression
of the stakeholders’ preferences. Besides structural uncertainty
associated with the global knowledge about the system being
modeled, input data may also suffer from imprecision, incomplete-
ness, or may be subject to changes. In this context, it is important
to provide managers and decision-makers with robust conclusions
(Roy, 1998; Vincke, 1999). The concept of a robust solution is gen-
erally linked to (1) a certain degree of ‘‘immunity” to data uncer-
tainty, (2) an adaptive capability (or flexibility) regarding an
uncertain future or ill-specified preferences, and (3) the guarantee-
ing of an acceptable performance even under changing conditions
(drifting from ‘‘nominal data”). This motivated the choice of the
IRIS/ELECTRE TRI methodology, which is fairly robust to changes
in data, is able to cope with imprecisely defined preferences, and
produces only a partitioning of the DMUs into classes, rather than
a complete ranking of the DMUs.
The paper is organized as follows: Section 2 introduces and
compares the two analytical frameworks studied. Section 3 de-
scribes the case study and how DEA and MCDA have been applied.
The main results obtained are reported in Section 4. In Section 5
the findings from the analysis are discussed and some conclusions
are drawn.
2. Comparison of analytical frameworks
2.1. DEA
The attainment of high levels of performance is a key issue for
the success of every organization. Therefore, an adequate manage-
ment framework is necessary for evaluating the current perfor-
mance, identifying benchmarks to use in seeking improvements,
and understanding why some units in a particular organization
are operating (in-)efficiently.
DEA is a non-parametric performance measurement technique,
based on linear programming (LP), for assessing the efficiency of
DMUs (e.g., Charnes et al., 1985; Cooper et al., 2000) relative to
an observed set of production possibilities. DMUs are homoge-
neous entities (such as sales outlets, electricity distribution compa-
nies, bank branches, schools, university departments, etc.) with
some decision autonomy, operating a production process that con-
verts a set of inputs into a set of outputs. DEA models use these in-
puts and outputs to compute an efficiency score for a given DMU
when this particular DMU is compared with all the other DMUs
considered. The relative efficiency of a DMU is usually defined as
the ratio between the sum of its weighted output levels to the
sum of its weighted input levels. The weights are chosen by the
LP model such that a DMU is ‘‘shown in its best light”, i.e., that
its efficiency score is maximized. In contrast to parametric econo-
metric approaches, such as stochastic frontier analysis, DEA does
not assume any specific functional form, thus avoiding problems
of model misspecification.
In DEA, a DMU is considered efficient if there is no other DMU,
or a linear combination of inputs and outputs of several DMUs, that
can improve one input or output, without worsening the value of
at least another one. The frontier is defined by the observed values
of the (relatively) efficient DMUs. If a DMU does not belong to this
envelopment surface and lies in its interior, then that DMU is oper-
ating inefficiently. DEA models usually return an efficient projec-
tion point of operation on the frontier for each inefficient DMU,
thus identifying the DMUs that can be used as performance bench-
marks (the ‘‘peers”) for the DMUs that are operating inefficiently.
Three basic DEA models are generally distinguished: CCR mod-
el, BCC model, and Additive model (see Cooper et al., 2000, 2004;
for a presentation and comparative analysis of these models).
The CCR model was presented in the seminal work of Charnes
et al. (1978). It is based on the radial minimization (maximization)
of all inputs (outputs) and assumes an environment of constant re-
turns to scale (CRS), i.e., if an efficient DMU increased its inputs by
a factor of a, then its outputs would be expected to increase by the
same factor.
Let us consider n DMUs to be evaluated; each of them consumes
m inputs to produce p outputs. The input data is denoted by the
matrix X
mn
and the output data is denoted by the matrix Y
pn
.
We denote by X
j
(the jth column of X ) the vector of inputs con-
sumed by DMUj, and by x
ij
(a positive quantity) the quantity of in-
put i consumed by DMUj. Analogous notation Y
j
and y
ij
is used for
outputs. We denote by 1 the summation vector (1,...,1).
The envelopment linear programming formulation to assess the
efficiency of a DMU (X
k
,Y
k
) and its dual, the multiplier formulation,
for the (input-oriented) CCR model can be written as
min h eð1s þ 1eÞ max lY
k
s:t: Yk s ¼ Y
k
; s:t: mX
k
¼ 1;
hX
k
Xk e ¼ 0; lY mX 6 0;
k P 0; m P e 1;
e P 0 ; s P 0: l P e1:
DMU (X
k
,Y
k
) is considered efficient only if the optimal solution of
the envelopment formulation yields h = 1 (the radial efficiency mea-
sure) and all ‘‘slacks” are null (i.e., s = 0 and e = 0). The multiplier
formulation emphasizes the relative weight vectors chosen by the
DMU for the inputs (m) and the outputs (l). A very small constant
e prevents null weights.
For the cases where the constant returns to scale assumption is
dropped, Banker et al. (1984) proposed a variable returns to scale
(VRS) version of the CCR model, referred to as the BCC model.
The difference between the two types of envelopment surfaces,
CRS and VRS, is that the latter is subject to a ‘‘convexity constraint”
so that the set of production possibilities is defined as the set of
convex combinations of the observed DMUs. In the envelopment
form of the linear programming formulation, this amounts to add-
ing the constraint 1k = 1. The third type of DEA model, the Additive
model (Charnes et al., 1985), also assumes VRS but is less fre-
quently applied.
2 R. Madlener et al. / European Journal of Operational Research xxx (2008) xxx–xxx
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DEA models have been extensively used to assess the perfor-
mance of DMUs in a broad range of real-world problems. However,
some important issues regarding the application of DEA with real-
world data remain. Firstly, the complete weight flexibility assumed
by DEA models often leads to efficiency results that are difficult to
justify. The freedom of each DMU to choose the weights of inputs
and outputs that show it under the best possible light can lead to
the assignment of very low weights to some inputs or outputs. In
practice, this means that certain inputs or outputs are effectively
ignored (a disturbing effect of the free specialization allowed in
DEA models, which is not generally acceptable in practice).
Moreover, the inputs and outputs can be weighted in a manner
that contradicts the views and/or preferences of the organizations
and their stakeholders, or even in a quite counterintuitive manner
by valuing secondary inputs or outputs more than priority ones
(Joro and Viitala, 2004). In fact, the inputs and outputs are not gen-
erally equally relevant and some preference information must be
included in the analysis. Also, whenever the number of inputs
and outputs grows, the trend is that more DMUs become efficient,
thus impoverishing the discriminating power of the DEA models.
One of the techniques generally used to circumvent these issues
is the introduction of additional restrictions on the variation al-
lowed for the weights. The most common type of weight restric-
tions (for a review see Thanassoulis et al., 2004) are assurance
regions of type I (intra inputs or intra outputs) or of type II (relating
inputs to outputs); other variants include transforming the data
matrices, or adding fictitious (unobserved) DMUs. However, as
pointed out by some authors (e.g., Podinovski, 2004), the resulting
efficiency score of weight-restricted models cannot be interpreted
as a realistic improvement factor (because the efficient radial tar-
get of an inefficient DMU is no longer technologically feasible). Fur-
thermore, these approaches are not natural to capture scale-
independent subjective value judgments elicited from the manag-
ers on the perceived importance of inputs and outputs: they are
more appropriate to reflect objective information such as prices.
However, in real-world problems in which inputs and outputs
are less tangible, market costs and prices may not be readily avail-
able, which introduces an additional degree of arbitrariness to the
results.
2.2. MCDA
The above-mentioned considerations about DEA led us to envis-
age the use of MCDA models to perform efficiency evaluation.
MCDA (see, e.g., Roy, 1996) includes a variety of sound theoretical
frameworks for eliciting and representing preferences. Some of
these frameworks, such as the one suggested in this paper, require
weights that do not necessarily represent prices or re-scaling
coefficients.
Instead of attempting to assign an efficiency measure to each
DMU we believe that, in most real-world situations, assigning
the DMUs to ordered efficiency categories is sufficient for analysis
and provides more confidence about the results, in the sense of
robustness to changes either in data or managers’ preferences, than
a single numerical figure. Moreover, a more detailed analysis with-
in each efficiency category is always possible whenever it is found
useful to improve the discrimination of the evaluation model.
In assessing the performance of DMUs in which technical, eco-
nomic and environmental aspects are at stake, it is often important
to use known standards (or theoretical maxima) and efficiency
profiles. There are also situations in which DMUs must be ap-
praised for efficiency on an ‘‘as they come” basis, i.e., they are
not included in a given set of DMUs (e.g., in growing markets,
where more and more DMUs are established over time). This re-
quired capability of evaluating each DMU in absolute terms, and
not just in comparison with other peers, as well as the need to in-
clude evaluation aspects expressed in different units, using any
sort of scales (including qualitative), can be achieved using the
ELECTRE TRI method (Yu, 1992).
The ELECTRE TRI method belongs to the ELECTRE family of mul-
ti-criteria methods developed by Bernard Roy and his co-workers
(Roy, 1996). ELECTRE methods are based on the construction and
exploitation of a so-called outranking relation (‘‘outranking” in this
context means ‘‘is at least as good as”). ELECTRE TRI is devoted to
the sorting problem (in contrast to choice or ranking problems),
which consists in partitioning a set of entities being evaluated into
a pre-defined set of ordered categories, according to several evalu-
ation criteria. Each entity object of evaluation (DMUs, in DEA lan-
guage, or ‘‘action”, in ELECTRE language) is described through a
vector of multi-criteria performances. The categories (C
1
,...,C
k
)
are also defined by specifying multi-criteria performance vectors
(b
0
,...,b
k
), or reference profiles. Each reference profile
b
h
(h =1,...,k 1) is simultaneously the upper bound of category
C
h
and the lower bound of category C
h+1
(see Fig. 1).
The assignment of each entity a to a category C
h
is done by com-
paring its value in each criterion to the reference profiles. The pro-
cedure assigns each entity to the highest category such that its
lower bound is outranked by a. The outranking relation is verified
by comparing a credibility index, computed by using the differ-
ences in performance and the criterion weights, with a cutting le-
vel k (k 2 [0.5,1]), which defines the ‘‘majority requirement” and
hence the exigency of the classification. For further details about
ELECTRE TRI see Yu (1992) and Mousseau et al. (2000), among
others.
Multi-criteria methods usually require a set of parameters that
embody the preferences of the decision-makers. The ELECTRE TRI
method requires the specification of the reference profiles associ-
ated with the categories (b
0
,...,b
k
), the criterion weights, and the
cutting level (k). Also, a set of indifference (q
j
), preference (p
j
)
and veto (v
j
) thresholds for each criterion j and reference profiles
can be defined. Indifference and preference thresholds characterize
the acceptance of imprecision in the judgment by considering two
entities as indifferent when their individual performances in each
criterion j differ less than a specified amount q
j
. Moreover, the
transition from indifference to preference is made gradual, chang-
ing linearly from q
j
to p
j
. The veto thresholds are aimed at captur-
ing situations in which very bad scores in any criterion should
prevent an entity of being classified in the best category, or if these
bad scores should force it to be classified in the worst category
independently of having very good scores in all other criteria. This
...
1st Criterion
b
0
b
1
b
2
b
3
b
k-1
b
k
C
1
C
2
C
3
C
k
2nd Criterion
3rd Criterion
Last Criterion
Fig. 1. Definition of categories C
1
,...,C
k
through reference profiles b
0
,...,b
k
.
R. Madlener et al. / European Journal of Operational Research xxx (2008) xxx–xxx
3
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enables, as it is often required in practice, to introduce a certain le-
vel of non-compensation into the evaluation model.
In the present application of dealing with an efficiency evalua-
tion problem by means of a multi-criteria sorting model the soft-
ware IRIS has been used (Dias and Mousseau, 2003). IRIS
implements a methodology developed by Dias et al. (2002) that
is based on the ELECTRE TRI method, but which does not require
precise values for some input parameters (criteria weights and
the cutting level). Information about these parameter values can
be provided through the introduction of intervals, linear con-
straints, or even sorting examples (which are translated into con-
straints on the parameters that guarantee that those example
results are reproduced). Given these constraints on the parameter
values, IRIS infers a ‘‘central” vector through the maximization of
the minimum slack associated with the constraints, when the con-
straints are consistent. For each entity being evaluated, IRIS shows
the category corresponding to this central combination, and the
other possible classifications that respect the constraints imposed.
In case the set of constraints is inconsistent, IRIS suggests the con-
straint subsets that may be removed to restore consistency.
A relevant issue in this context is the meaning of the weights in
ELECTRE methods. In this type of methods, weights are perceived
as true coefficients of importance assigned to the criteria, and
not just as technical devices for translating the performances in
the criteria considered into a common value measure. Therefore,
they are scale-independent (that is, they are not linked to the
scales in which each criterion is measured), thus making them eas-
ier to be specified by managers. These parameters bear the prefer-
ence information and insights into the sorting process. In principle,
they must be elicited from managers and stakeholders (preferably
via an analyst with expertise on the methodological component). It
should be noted that this method imposes a non-negligible burden
associated with the specification of all the parameters required.
However, some of these parameter data can be preset according
to the experience of the analyst, in general associated with previ-
ous case studies. For instance, indifference and preference thresh-
olds can be fixed as percentages (say 1% and 10%, respectively) of
the value ranges in each category.
The IRIS software allows for the consideration of uncertainty in
the weights (as well as in the cutting level). This feature contrib-
utes to reducing the data requirements and increasing the confi-
dence in the results.
3. Case study
In Austria, an effective promotion of renewable energy technol-
ogies has been pursued in recent years, driven by the need to
achieve ambitious energy and climate policy goals. These include
the goals contained in the Kyoto Protocol (13% greenhouse gas
emissions by 2008/12, relative to 1990 levels) and the EU Renew-
ables Directive 2001/77/EC (to raise the renewable electricity share
of Austria to 78.1% by 2008, compared to 70% in 1997). In particu-
lar, the last few years witnessed a remarkable boom in the con-
struction of agricultural biogas plants, mainly due to the
introduction of substantial feed-in tariffs of between 10.3 and
16.5 Cents/kWh
el
(depending on the plant size and the type of
substrate used) for ‘‘biogas electricity” fed into the grid, which
are guaranteed for a period of 13 years (Green Electricity Act,
2002).
1
As a consequence, the number of plants rose from 119 at
the end of 2003 to 231 by the end of year 2005 (Braun et al.,
2007). These plants use mainly energy crops (silage) for digestion.
However, up to now the promotion of energy crop digestion
was hardly linked to any specific cost effectiveness or energy effi-
ciency or other performance criteria. As a result, many different
technologies, design concepts, and specific applications occurred
on the market, some of which were either not very productive, en-
ergy-efficient, or reliable.
Due to the attractive feed-in tariffs granted, anaerobic digestion
of energy crops currently mainly aims at the generation of electric-
ity, and much less so at heat generation (or the feed-in of purified
biogas into the natural gas grid, if available). As a consequence, the
heat energy produced in cogeneration units remains largely
wasted. Furthermore, many plants use electricity for cooling pur-
poses, in order to prevent adverse effects that arise from the self-
heating of crop digesters. Therefore, in many cases up to two thirds
of the available technical energy potential remains unused (Braun
et al., 2005, 2007; Walla, 2005).
A comprehensive monitoring and benchmarking project was
initiated in March 2004, which includes a detailed investigation
of a set of 41 Austrian energy crop digestion plants spread all over
the country.
2
The project, completed in February 2007, also aimed at
creating and establishing an evaluation system for the transparent
assessment and benchmarking of the productivity of biogas plants
by means of energetic, business economic, ecological and socio-eco-
nomic criteria, characterizing the overall production cycle of biogas.
Since anaerobic digestion has the potential of reducing greenhouse
gas emissions (Braschkat et al., 2003), an important objective of
the project was to evaluate the environmental impacts through the
overall ‘‘crops to energy” process. Finally, positive and negative so-
cio-economic impacts were accounted for to a limited extent by
means of a questionnaire survey among plant operators (subjective
valuation by the farmers interviewed, supplemented by measurable
data); see Braun et al. (2007) for further details.
4. Results
4.1. Description of the data and parameters used
The DMUs considered are a representative set of energy crop
digestion plants in Austria, aimed at covering the whole spectrum
of existing plant types and operating conditions. Samples were ta-
ken from the substrate, digester, fermentation residues and biogas
plant types. Cooling, safe transport and appropriate storage were
also scrutinized. The sampled installations are geographically well
distributed over the country. They range from small-scale installa-
tions using mainly manure and energy crops (down to 18 kW
el
)to
larger-scale plants that use considerable amounts of co-substrates
(up to 1.7 MW
el
). Both single substrate (energy crops or manure)
installations as well as co-digestion plants (agricultural by-products
and industrial bio-wastes) have been considered in the analysis.
The main groups of evaluation aspects at stake for assessing the
efficiency of energy crop digestion plants are: (1) substrate provi-
sion, storage and pre-treatment; (2) biogas production (by means
of anaerobic digestion); (3) net utilization of heat and electricity;
(4) digestate handling and disposal; and (5) greenhouse gas
(GHG) emissions.
3
1
Note that in 2006 a revised Green Electricity Act and Ordinance entered into
force, with amended feed-in tariffs and budget restrictions (BGB1. I Nr. 105/2006,
BGBl. II Nr. 401/2006; for details see Energie-Control, 2006).
2
For a description of the project ‘‘Development of an Assessment System for Biogas
Plants ‘Quality Certificate Biogas” (funded by the Austrian Federal Ministry of
Transport, Innovation and Technology) see http://www.energiesystemederzukunft.at/
results.html/id34 69?active= (in German) , or research database entry #8289 in
www.rdb.ethz.ch (in English).
3
Based on life cycle analysis, a biogas plant may or may not reduce greenhouse gas
emissions, compared to a situation where the plant does not exist. The net amount of
GHG emissions attributable to a particular biogas plant depends, in essence, on the
type of fertilizer used, the fossil fuel use for substrate production and transporting,
and the methane emissions released from the digested substrate storage facility, the
spreading of digested substrate in the fields, and the cogeneration unit.
4 R. Madlener et al. / European Journal of Operational Research xxx (2008) xxx–xxx
ARTICLE IN PRESS
Please cite this article in press as: Madlener, R. et al., Assessing the performance of biogas plants with multi-criteria and data ..., European
Journal of Operational Research (2008), doi:10.1016/j.ejor.2007.12.051

In a first series of model specifications, the following criteria
have been considered for evaluating the efficiency of the energy
crop digestion plants (for the sake of comparison between the
DEA and the MCDA approaches): (1) labor (i.e., time) spent for
plant operation; (2) amount of substrate used (organic dry sub-
stance, ODS); (3) amount of biogas or net electricity produced
(i.e., electricity delivered by the biogas plant for external consump-
tion, net of what the plant consumes itself); (4) net heat produced
(for external consumption); and (5) net GHG emissions released to
the atmosphere (including credits that accrue from a comparison
with the base case of not having the biogas plant, measured in
CO
2
equivalent). For further details on data collection see Braun
et al. (2005, 2007) and Laaber et al. (2005), and for further details
about the various inputs and outputs and DEA model specifications
scrutinized see Madlener (2006). Some descriptive statistics are
displayed in Table 1.
4.2. DEA
In the first DEA model considered in this paper, we have used
substrate (i
2
) and labor (i
1
) as inputs and the amount of net elec-
tricity (o
1
) and external heat (o
2
) as (desirable) outputs. GHG emis-
sions (o
3
) have been considered as well in a second model, as an
undesirable output. We chose to consider these emissions as an in-
put in the DEA model, which is a common option to model unde-
sirable outputs. Although other options exist (e.g., see Scheel,
2001; Seiford and Zhu, 2002), and although the choice influences
the results, there does not seem to be an undisputed ideal method
to handle undesirable outputs (Dyson et al., 2001). A scale transla-
tion was used to account for the negative net values, another mod-
eling option known to have an influence on the results (Lovell and
Pastor, 1995). Fig. 2 depicts the outcome of the (output-oriented)
CCR DEA model specification (CCR-O). DMUs 12, 17, 18, 20 and
28 form the efficiency frontier.
A similar analysis was performed considering GHG emissions.
These results are depicted in Fig. 3. The main consequence of incor-
porating this new factor into the analysis is that DMU 15, which
has relatively low net emissions, joins the set of efficient solutions.
On the other end of the spectrum, DMUs 5, 13, 14, 25, 26, 33, and
39 appear as some of the worst-performing plants, irrespective of
whether GHG emissions are considered or not.
The DEA results just reported are part of a wider study (Braun
et al., 2007; Madlener and Honegger, 2006) where other models
were considered as well (e.g., considering the output Biogas in-
stead of Electricity and Heat), including versions using the BCC
model to benefit DMUs not operating at an optimal scale. In this
paper, however, we will consider only the results presented in Figs.
2 and 3, with the underlying assumption of constant returns to
scale, since the MCDA approach described below will also not take
into account the scale of operation. Keeping the same inputs and
outputs presented here, the main implications of using the variable
returns to scale version (BCC-O) would be to add DMU 15 to the set
of efficient units, without GHG emissions, and adding DMUs 33 and
38 to the set of efficient units, with GHG emissions considered.
4.3. MCDA
In the MCDA approach the objective was to identify groups of
DMUs that could be assigned to different efficiency labels, rather
than computing a precise efficiency score or deriving a complete
ranking. Four efficiency categories were defined to classify the
DMUs according to their efficiency: C
1
= ‘‘Poor”, C
2
= ‘‘Fair”,
C
3
= ‘‘Good”, and C
4
= ‘‘Very good”. Each plant has to be assigned
to one of these ordered categories, according to the multiple eval-
uation criteria.
To define the different categories in IRIS, it is necessary to set
the category bounds b
0
,...,b
4
according to n
crit
criteria/indicators
which we denote as the evaluation functions g
j
()(j =1,...,n
crit
).
The decision-maker must set these bounds, taking into account
that according to an indicator g
i
() a DMU
k
with
g
i
(DMU
k
) 2 [g
i
(b
j1
), g
i
(b
j
)[ should be placed into category C
j
. When
Table 1
Descriptive statistics (N = 41)
Mean SD Min Max
Inputs
i
1
labor 1581.29 1958.51 50.42 10950.00
i
2
ODS 1508.00 1 333.75 119.94 5514.04
Outputs
o
1
electricity 1940 136.06 1960 911.08 123600.83 7760 000.00
o
2
heat 735319.76 1112935.01 0.00 6000000.00
o
3
GHG (undesirable
output)
248532.63 282431.82 203248.11 1 123981.23
CCR-O / Labor and ODS - Electricity and Heat
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
28
20
18
17
12
21
41
22
34
2
36
19
6
11
15
37
10
4
29
8
3
1
9
23
16
38
7
40
35
32
27
31
30
24
14
5
25
13
39
33
26
DMU
Efficiency
Fig. 2. DEA results without GHG emissions (inputs: labor, substrate; outputs: electricity, heat).
R. Madlener et al. / European Journal of Operational Research xxx (2008) xxx–xxx
5
ARTICLE IN PRESS
Please cite this article in press as: Madlener, R. et al., Assessing the performance of biogas plants with multi-criteria and data ..., European
Journal of Operational Research (2008), doi:10.1016/j.ejor.2007.12.051

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References
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Journal ArticleDOI
TL;DR: A nonlinear (nonconvex) programming model provides a new definition of efficiency for use in evaluating activities of not-for-profit entities participating in public programs and methods for objectively determining weights by reference to the observational data for the multiple outputs and multiple inputs that characterize such programs.
Abstract: A nonlinear (nonconvex) programming model provides a new definition of efficiency for use in evaluating activities of not-for-profit entities participating in public programs. A scalar measure of the efficiency of each participating unit is thereby provided, along with methods for objectively determining weights by reference to the observational data for the multiple outputs and multiple inputs that characterize such programs. Equivalences are established to ordinary linear programming models for effecting computations. The duals to these linear programming models provide a new way for estimating extremal relations from observational data. Connections between engineering and economic approaches to efficiency are delineated along with new interpretations and ways of using them in evaluating and controlling managerial behavior in public programs.

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01 Sep 1984-Management Science
Abstract: In management contexts, mathematical programming is usually used to evaluate a collection of possible alternative courses of action en route to selecting one which is best. In this capacity, mathematical programming serves as a planning aid to management. Data Envelopment Analysis reverses this role and employs mathematical programming to obtain ex post facto evaluations of the relative efficiency of management accomplishments, however they may have been planned or executed. Mathematical programming is thereby extended for use as a tool for control and evaluation of past accomplishments as well as a tool to aid in planning future activities. The CCR ratio form introduced by Charnes, Cooper and Rhodes, as part of their Data Envelopment Analysis approach, comprehends both technical and scale inefficiencies via the optimal value of the ratio form, as obtained directly from the data without requiring a priori specification of weights and/or explicit delineation of assumed functional forms of relations between inputs and outputs. A separation into technical and scale efficiencies is accomplished by the methods developed in this paper without altering the latter conditions for use of DEA directly on observational data. Technical inefficiencies are identified with failures to achieve best possible output levels and/or usage of excessive amounts of inputs. Methods for identifying and correcting the magnitudes of these inefficiencies, as supplied in prior work, are illustrated. In the present paper, a new separate variable is introduced which makes it possible to determine whether operations were conducted in regions of increasing, constant or decreasing returns to scale in multiple input and multiple output situations. The results are discussed and related not only to classical single output economics but also to more modern versions of economics which are identified with "contestable market theories."

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Abstract: This book deals with exergy and its applications to various energy systems and applications as a potential tool for design, analysis and optimization, and its role in minimizing and/or eliminating environmental impacts and providing sustainable development. In this regard, several key topics ranging from the basics of the thermodynamic concepts to advanced exergy analysis techniques in a wide range of applications are covered as outlined in the contents. It provides comprehensive coverage of exergy and its applications. It connects exergy with three essential areas in terms of energy, environment and sustainable development. It presents the most up-to-date information in the area with recent developments. It provides a number of illustrative examples, practical applications, and case studies. It features an easy to follow style, starting from the basics to the advanced systems.

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31 Aug 1996-
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