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A multi-objective interactive approach to assess economic-energy-
environment trade-offs in Brazil
Ariovaldo Lopes de Carvalho b*
Carlos Henggeler Antunes a, c
Fausto Freire b
Carla Oliveira Henriques a, d
a INESC Coimbra, R. Antero Quental 199, 3000–033 Coimbra, Portugal b ADAI-LAETA, Department of Mechanical Engineering, University of Coimbra, Pólo II Campus, Rua
Luis Reis Santos, 3030-788 Coimbra, Portugal c Department of Electrical Engineering and Computers, Faculty of Sciences and Technology, Polo II,
University of Coimbra, 3030–290 Coimbra, Portugal d ISCAC, Polytechnic Institute of Coimbra, Quinta Agrícola, Bencanta, 3040–316 Coimbra, Portugal
*corresponding author and presenter: Tel.: +351 239 708580; Fax: +351 239 708589.
ABSTRACT
An interactive method devoted to multi-objective linear programming (MOLP)
models is used to assess the trade-offs between economic, energy and environmental
objectives in the Brazilian economic system. The MOLP model is based on a hybrid
Input-Output (IO) framework, with monetary (R$) and physical (tons of oil equivalent)
units, developed from the Brazilian IO table and the National Energy Balance. This
framework is extended to assess different Greenhouse Gas (GHG) emissions, which are
then aggregated into a single indicator (CO2eq). The model includes 435 variables, 582
constraints and 3 objective functions: maximization of Gross Domestic Product (GDP),
minimization of energy consumption and minimization of GHG emissions. The
interactive decision support tool enables a progressive and selective search of non-
dominated solutions making the most of graphical displays, namely the parametric
diagram associated with the objective function “weights”, to provide insightful
information to the Decision Maker. A representative sample of non-dominated solutions
has been computed in the interactive process, allowing to identify three main regions
corresponding to solutions with different characteristics, i.e. different patterns of trade-
offs between the conflicting objective functions. Illustrative results indicate that the
maximization of GDP leads to an increase of both energy consumption and GHG
emissions, while the minimization of either GHG emissions or energy consumption
cause negative impacts on GDP.
Keywords: Greenhouse Gas (GHG), Input-Output (IO) analysis, Multi-objective linear
programming (MOLP), Multi-sectoral economy-energy-environment models,
interactive methods.
JEL: C61; C67; Q40.
Conference topic: Energy Modelling; Environmental and Social Impact Assessment;
Economic Growth and Sustainability.
1
1. INTRODUCTION
Energy and environmental concerns have gained a significant role in public
policy agenda. Economic growth usually leads to an increase of energy consumption,
which in turn has adverse effects on the environment since current energy supply is
heavily reliant on fossil fuels, which are an important source of Greenhouse Gas (GHG)
emissions. On the other hand, restrictive energy and environmental policies may lead to
negative impacts on economic growth and social welfare. Hence, it is relevant to assess
the interactions and trade-offs between economic, energy and environmental indicators
in order to provide consistent tools for planners and decision makers (DM) (Oliveira
and Antunes, 2004).
The current economic growth in Brazil has influenced positively the welfare and
energy consumption. Although renewable energy supply has been increasing, fossil fuel
production has also been raising namely due to the exploitation of new oil extraction
areas. As a result, more fossil fuel consumption has led to higher impacts in terms of
GHG emissions, which is a drawback for current and prospective economic growth.
Input-Output Analysis (IOA) has been traditionally used to study the inter/intra-
relationships among different sectors in the economic system, describing the
relationship between the inputs used and the outputs produced (Leontief, 1985; Miller
and Blair, 1985). The IO models have been modified to account for environmental
impacts: generalized IO models including additional rows and columns within the IO
system to incorporate the environmental impacts (Leontief, 1970), economic ecological-
models utilizing intra/inter-sector sub-matrices linking the economic and environmental
sectors (Daly, 1968), and commodity by industry models considering the ecological
commodities as products (Victor, 1972). An external expansion of the IO framework
can also be made to incorporate the environmental impacts, assuming a proportional
relation between the output of the sectors and the corresponding impact levels (Suh and
Huppes, 2005).
IO hybrid models have been developed to assess the Brazilian economic system,
investigating the interactions between employment and sector’s output levels and
carbon and energy intensity (Hilgemberg and Guilhoto, 2006), as well as the energy
intensity and CO2 emissions related to a specific region (Figueiredo et al., 2009).
Some studies have developed linear programming (LP) models coupled with the
IO framework for different purposes (Moulik et al., 1992; Hristu-Varsakelis et al.,
2010). However, MOLP models coupled with IO framework can provide a more
complete assessment of different axes of evaluation of potential policies, enabling to
exploit the trade-offs between competing objectives. IO MOLP models have been
applied to study the impacts of regional policies on the employment, water pollution
and energy consumption (Cho, 1999), evaluate the impact of energy conservation
policies on the cost of reducing CO2 emissions (Hsu and Chou, 2000), investigate the
impact of mitigating CO2 emissions considering the maximization of the GDP and the
minimization of CO2 emissions (Chen, 2001), analyze alternative development options
for a national economy considering the maximization of GDP and foreign trade balance
and the minimization of the energy requirements (Kravtsov and Pashkevich, 2004).
Zhou et al. (2006) proposed a modified multiple objective dynamic IO optimization
(MODIO) model considering a set of objective functions and a set of dynamic IO
constraints. Borges and Antunes (2003) implemented an interactive approach to deal
with fuzzy MOLP problems applied to an IO energy-economy planning model. San
Cristobal (2012) applied an Environmental IO MOLP model combined with goal
programming to assess economic, energy, social and environmental goals. Oliveira and
2
Antunes (2004, 2011, 2012) constructed IO MOLP models to assess the trade-offs
between the maximization of GDP and employment level, and the minimization of
energy imports and environmental impacts. Antunes et al. (2002) developed an IO
MOLP model using the TRIMAP interactive environment to analyze the interactions of
the energy system with the economy for Portugal. TRIMAP is an interactive method
devoted to three-objective linear programming models that enables a progressive and
selective search for non-dominated solutions to grasp the trade-offs between the
conflicting objective functions.
A hybrid IO MOLP model is herein presented and applied to the Brazilian
economic system aimed at assessing the trade-offs associated with the maximization of
GDP and the minimization of the total energy consumption and GHG emissions,
considering the timeframe of 2017. The TRIMAP interactive method, which is
described in section 2, has been used to make a progressive and selective search for
non-dominated solutions. The extended hybrid IO model formulated in this study is
analyzed in section 3. Some illustrative results are presented in section 4. Some
conclusions and future developments are drawn in section 5.
2. AN INTERACTIVE DECISION SUPPORT TOOL FOR MOLP
The TRIMAP method plays a key role in an interactive decision support tool
enabling a progressive and selective search for non-dominated solutions, thus
facilitating to focus the computational effort on the non-dominated regions where
solutions more interesting for the Decision Maker (DM) are located. TRIMAP is
designed for problems with three objective functions in which graphical tools, in
particular the parametric diagram, provide the DM insightful information about the
trade-offs at stake in those regions. TRIMAP combines three main procedures:
parametric diagram (objective function “weight space”), introduction of constraints
directly in the weights, and introduction of constraints in the objective function space
that are then translated into the parametric diagram (Clímaco and Antunes, 1987; 1989).
The parametric diagram display is used for collecting and presenting to the DM the
information obtained during the search process. The parametric diagram is filled with
the indifference regions corresponding to the (basic) non-dominated solutions already
computed, i.e. the regions defined by the objective function weights for which the
optimization of a (scalar) weighted-sum function aggregating the multiple objective
functions leads to the same (non-dominated) solution. Another graph shows the non-
dominated solutions already computed, also enabling to identify non-dominated edges
and faces of the feasible polyhedron in the objective function space.
This interactive system offers the DM the possibility of progressively exploiting
and learning the characteristics of the non-dominated region, and then narrowing down
the search toward a solution (or set of solutions) according to his/her preferences. The
TRIMAP search process generally starts with a broad strategic search to gather
information about distinct solutions, in particular those that individually optimize each
of the conflicting functions, and then gradually focus onto regions in which more
interesting solutions are found taken into account the trade-offs unveiled throughout the
interactive procedure. In this way irrelevant solutions, from the DM’s point of view, are
avoided and a learning process of the characteristics of solutions and the trade-offs at
stake between the competing objectives is privileged. Also a clarification of the own
DM’s preferences and judgments is facilitated. The interactive process continues until
the DM has gathered "sufficient knowledge" about the set of non-dominated solutions
rather than pre-specifying a given number of iterations or any other stopping condition.
3
3. EXTENDED HYBRID INPUT-OUTPUT MODEL
The first step to build this Extended Hybrid IO model is rearranging the IO table
to make the energy use coefficients directly available in hybrid units (physical units per
monetary units). In this step, the energy flows in the Brazilian National Energy Balance
(MME, 2009) are incorporated into the 2009 Brazilian IO table (Guilhoto and Sesso
Filho, 2010) by considering artificial sectors (see also Oliveira and Antunes, 2004,
2011, 2012). For this purpose some adjustments and inclusion of new rows and columns
in the IO table are necessary in order to incorporate the different energy sectors (or
commodities). This procedure generates a new transaction matrix, thus leading to a new
technical coefficient matrix and new vectors for final demand and the total output with
hybrid units, in which energy flows are considered in physical quantities of energy (tons
of oil equivalent, toe) and all non-energy sector flows are measured in monetary units.
The adjustments performed in the IO framework provide: a square matrix with 109
activity sectors split into 51 economic sectors, 6 energy producing sectors, 5 artificial
sectors used for distributing the energy consumed by each means of transportation and
47 artificial energy product sectors; 6 column vectors with the components of final
demand (exports, public consumption, resident consumption, gross fixed capital
formation - GFCF - and stock changes); 1 column vector for competitive imports
(considered for energy products only); and 6 row vectors for the primary inputs (wages,
gross mixed income, gross operating surplus, other production taxes and other
production subsides).
An external expansion of the IO model is made to estimate GHG emissions from
energy combustion, industrial processes, agriculture activities, waste management,
wastewater treatment and discharge, and fugitive emissions. In this step, based on the
IPCC (2006) methodology, emission factors for GHG emissions from carbon dioxide
(CO2), methane (CH4) and nitrous oxide (N2O) are used in combination with the level of
activity of specific sectors and final demand components. These estimates give a vector
with the environmental impacts per unit of output of the sectors and the final demand,
considering the corresponding Global Warming Potential (100-year horizon: 25 for
CH4, 298 for NO2) relative to CO2 (IPCC, 2007).
Finally, the MOLP model based on IO analysis proposed by Oliveira and
Antunes (2004, 2011, 2012) for Portugal is adapted to the Brazilian economic system,
which has a very different structure leading to important changes in the mathematical
model. The model includes (internal) coherence constraints derived from the IO
analysis and other sets of constraints associated with the structure of the economic
system, employment and energy consumption, which are briefly described below.
Further details about the multi-objective model can be found in Carvalho et al. (2013).
3.1 Model constraints
Coherence constraints are used to determine that the intermediate consumption
and final demand of each activity sector shall not exceed the corresponding total amount
available from national production and competitive imports.
The GDP (expense approach) is computed considering the final demand minus
imports at FOB (free on board) prices (including tourism). The GDP (production
approach) is computed by the sum of gross value added and the total of taxes less
subsides on products that are not included in the production.
The gross value added is given by the sum of wages, gross mixed income, gross
operating surplus, other production taxes minus other production subsides.
4
Taxes less subsidies on goods or services are calculated for the intermediate
consumption and final demand items.
The model also establishes some assumptions for several consumption relations:
the households’ consumption on the territory includes the consumption on the territory
by resident and non-resident households; the residents’ consumption includes the
consumption of households and Non-profit Institutions Serving Households (NPISH);
the resident households’ consumption on the territory is linearly dependent on the
available income; and the tourism imports is given as a proportion of the residents’
household consumption.
The GDP at current prices is estimated considering the components of GDP
(expense approach) at constant prices and the corresponding deflators. Additionally, the
consumption of goods and services by the public administration at current prices and the
GFCF at current prices are exogenously defined.
The residents’ disposable income at current prices is computed by subtracting
the public administration and (non-financial and financial) corporations’ disposable
incomes from the National Disposable Income.
Public debt is given by the summation of the previous period debt with the
symmetrical value of the public administration global balance, plus an adjustment
variable.
Public administration’s global balance is computed by subtracting the public
administration’s expenditures from the public administration’s revenues.
The employment level is obtained by using labor gross productivity coefficients
for each sector.
The total energy consumption is obtained from the sum of national and imported
energy excluding the energy consumed for non-energy purpose. Specific technical
coefficients are applied to the intermediary consumption and final demand.
3.2 Objective Functions
The model considers three competing objective functions:
- F1: Maximization of GDP as an indicator of global economic performance
(thousand R$).
- F2: Minimization of total energy consumption to assess the impacts associated
with economic growth and GHG emissions, taking into account that energy supply in
Brazil is mostly domestic (thousand toes).
- F3: Minimization of GHG emissions considering the links with economic
activity (and energy use) as well as the international agreements on the reduction of
GHG emissions (Gg of CO2 equivalent).
The detailed presentation of the multi-objective mathematical model can be
found in Carvalho et al. (2013).
4. RESULTS AND DISCUSSION
The MOLP model has been supplied with realistic data gathered from several
Brazilian sources (MME, 2009; Guilhoto and Sesso Filho, 2010; MCT, 2010) and
estimates for the year 2017 (Carvalho et al., 2013). The MOLP model has 435 decision
variables, 582 constraints and 3 objective functions. Some illustrative results obtained
with the interactive decision support tool briefly described in section 2 are herein
described.
5
Firstly, each objective function was optimized individually, resulting in 3
distinct non-dominated solutions. These solutions provide a first overview of the range
of variation of the objective values within the non-dominated region. The
characterization of these solutions (objective function values, decision variable values,
indifference region in the parametric diagram) is presented to the DM. Therefore the
DM should indicate a set of weights not yet belonging to an indifference region in the
parametric diagram to compute a new non-dominated solution. The weight specification
should be understood not as a precise “importance coefficient” but rather as an
indication of the objective functions to be (temporarily) privileged in the subsequent
search. Note that the area of the indifference region in the parametric space also gives
an indication of the solution “robustness” regarding weight changes. Information about
some solutions may lead the DM to conclude that it is not worthwhile to proceed with
the search using weights in-between the corresponding indifference regions because the
solutions then obtained would not be so different and therefore would not be relevant
for decision support purposes. This enables a progressive and selective search of the
non-dominated solution set using the parametric diagram as a valuable visual feedback
enabling to identify sub-sets of solutions sharing similar characteristics, namely trade-
offs between the competing objectives, until a satisfactory compromise solution is
identified. In this example, the parametric diagram has been filled with indifference
regions corresponding to 20 non-dominated (basic) solutions that have been considered
providing sufficient information about different policies - see figure 1, in which
( denote the weights assigned to each objective function (F1, F2, F3) to build
a scalar weighted-sum function to be optimized leading to the identification of the
corresponding indifference region using the multi-objective simplex tableau.
Analyzing the objective function values, for example, of solutions 11 and 12 it is
possible to conclude that the DM has information to conclude that it is not worthwhile
searching for new solutions in the parametric diagram region located between the
indifference regions corresponding to those solutions. The visual information displayed
in the parametric diagram thus contributes to minimize the computational effort and the
number of irrelevant solutions generated during the exploitation of the problem (and
thus the information processing effort required from the DM).
A useful tool offered by the TRIMAP interactive method is the possibility to
impose additional bounds on the objective function values in order to narrow the scope
of the search to regions of interest of the non-dominated solution set. This information
stated in the objective function space (which is the most familiar space for the DM) is
translated via an auxiliary problem into the parametric space, in which the regions of
weights leading to solutions satisfying those bounds can be computed. In this example,
the DM established two bounds in the values of F1 ≥ R$ 3,903,355 x 103 and F2 ≤
237,249.5 toe x 103 (see figure 2). These bounds represent the expression of reservation
levels, i.e. the DM stating that he/she is not interested in solutions providing inferior
values than those stated for those functions. This restricts the search process to regions
that include the solution 12 and a still not yet searched region nearby this solution (in
which new non-dominated solutions can be found if the DM wants to). This feature of
TRIMAP is particularly valuable to reduce the scope of the search aligned to the DM’s
preferences (see Clímaco and Antunes, 1987 and 1989, for technical details).
6
Figure 1 - Decomposition of the parametric diagram into indifference regions (corresponding to
basic non-dominated solution).
Figure 2 - Additional bounds on the objective functions and regions in the parametric diagram
satisfying them.
The objective function values of the 20 non-dominated solutions computed using
the TRIMAP interactive method are presented in table 1. The values in bold are the
7
components of the ideal solution with the optimal values for F1, F2 and F3 (GDP,
energy consumption and GHG emissions, respectively).
Table 1 – Objective function values for some non-dominated solutions Solution F1 (10
3 R$) F2 (10
3 toes) F3 (Gg CO2 equiv)
1 4,465,863 271,392 2,708,369
2 3,902,394 237,248 2,537,554
3 3,900,231 237,267 2,537,377
4 4,465,863 271,449 2,708,333
5 4,465,863 271,544 2,708,327
6 4,465,863 271,244 2,708,918
7 4,465,863 271,392 2,708,369
8 4,465,863 271,392 2,708,369
9 3,924,972 237,499 2,542,324
10 4,022,372 240,443 2,565,221
11 3,901,036 237,249 2,537,409
12 3,903,358 237,248 2,537,659
13 3,938,117 238,387 2,543,422
14 3,962,958 238,748 2,548,863
15 4,002,566 240,061 2,558,992
16 4,044,838 241,818 2,570,861
17 4,037,694 241,175 2,569,085
18 3,955,369 238,299 2,547,625
19 3,932,868 238,036 2,542,672
20 4,015,388 240,242 2,562,830
A more detailed analysis of the characteristics of the solutions can be made
using the results of the model decision variables besides the objective function values.
However, the illustrative results herein described will be focused on their most relevant
aspects and characteristics of the main variables.
It is possible to verify a conflicting relation between GDP and energy
consumption (or GHG emissions). In solution 1, which maximizes GDP (R$ 4,465,863
x 103), both energy consumption and GHG emissions values are very close to their
worst value known in the non-dominated region (271,392 toe x 103 and 2,708,369 Gg
of CO2 equivalent, respectively). On the other hand, for solution 2, which minimizes
energy consumption, GDP achieves a value (R$ 3,902,394 x 103) not far from its worst
one (see table 1) and GHG emissions are very close to the optimum (2,537,554 Gg of
CO2 equivalent). In addition, for solution 3, which minimizes GHG emissions
(2,537,377 Gg of CO2 equivalent), GDP achieves the worst level (R$ 3,900,231 x 103)
while energy consumption is only 0.01 % higher than the optimal level.
Three main regions can be distinguished in the parametric diagram
corresponding to solutions with different characteristics. It is possible to note that
solutions 4, 5, 6, 7 and 8 are alternative optima of solution 1 with respect to F1. It is also
possible to recognize through the visual inspection of the parametric diagram that a well
defined “cut” exist marked by the “western” boundaries of the indifference regions
associated with those solutions (1, 4, 5, 6, 7 and 8). Until that boundary the values for
GDP is the same (the optimal one) with small variations in F2 and F3 values. The GDP
value decreases smoothly for solutions beyond that boundary as the weight assigned to
F1 approaches zero (that is, 1=0 and 2+3=1). Different combinations of 2 and 3
with 1=0 enable to obtain solutions 2, 11 and 3. An important characteristic of those
regions is the high values obtained for the Gross Fixed Capital Formation (GFCF) and
employment, which achieves its highest value in solution 5 (56,818,158 employees).
8
The sectors that have the highest output improvement are linked to the energy,
construction and manufacturing industries.
A second region involves solutions 2, 3, 11 and 12, where the values for all
objectives are very similar varying less than 0.1% for GDP and 0.01% for energy
consumption and GHG emissions. This region is characterized by lower values for GDP
and values close to the optimum for energy consumption and GHG emissions. An
important drawback of these solutions is the negative impact on the employment level,
which achieves its lowest values, especially in solution 3 (50,749,014 employees). The
industrial sectors with negative impacts on their outputs in solutions 2 and 3 are the
energy intensive sectors, such as the extractive industry, petroleum refining and coke,
chemicals and cement.
Finally, the region containing solutions 10, 15, 16, 17 and 20 is characterized by
intermediary values for all objective functions, with a variation of 1.0% for GDP, 0.7%
for energy consumption and 0.5% for GHG emissions. Solution 20 is representative of
the main characteristics of the solutions within this region, with well-balanced values
also for employment (52,146,818 employees).
5. CONCLUSION
Since, in general, energy, economic and environmental aspects of distinct
policies have conflicting interactions, a broad scrutiny of these evaluation axes and a
thorough appraisal of the trade-offs at stake are important for the policy making
process. In this context MOLP models enable to exploit the trade-offs between those
competing objectives and provide an important tool in the assessment of distinct
policies associated with different non-dominated solutions.
In this paper a hybrid IO framework is used to develop an MOLP model applied
to the Brazilian economic system, which is investigated by using the TRIMAP
interactive method. The aim is to assess the trade-offs between economic, energy and
environmental objectives through a progressive and selective search of non-dominated
solutions in order to provide decision support to DMs. The TRIMAP interactive
environment has been used to perform a progressive and selective search based on the
parametric diagram. The non-dominated solutions computed allowed to unveil some
patterns and the main characteristics of three main regions in the parametric diagram
corresponding to sub-sets of solutions sharing the same features. The illustrative results
obtained with this model provide valuable insights about the trade-offs involved and
allow identifying the performance and trends of the main variables. The IO framework
coupled with the MOLP model provided an important tool to assess the interactions and
trade-offs between the objective functions. The TRIMAP interactive method has
provided great flexibility to the analysis, allowing a progressive and selective
exploration of the compromise solutions in a user-friendly graphical environment.
Future developments of this work will involve the use of other multi-objective
interactive methods within an integrated framework to facilitate the DM’s tasks and
provide a user-friendly interactive environment to assess the merits of distinct policies.
Acknowledgements
This work has been framed under the Initiative Energy for Sustainability of the
University of Coimbra and supported by the Energy and Mobility for Sustainable
Regions Project CENTRO-07-0224-FEDER-002004, and the Portuguese Foundation
9
for Science and Technology (FCT) under grant SFRH/BD/42960/2008 and projects
MIT/SET/0014/2009, PEst-C/EEI/UI0308/2011 and PTDC/SEN-TRA/117251/2010.
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