Making Sustainability Rankings Using Compromise Programming . An Application to European Paper Industry

This paper characterizes the sustainability of the European paper industry. To undertake this task the sustainability of each country is defined by using fourteen indicators of a diverse nature (economic, environmental and social). These indicators are aggregated into a composite or synthetic index with the help of a compromise programming model. In order to associate different weights with each indicator, a survey among international experts has been carried out. In this way, a ranking of seventeen European countries analysed in terms of the sustainability of the European paper industry has been established, where Finland is the most sustainable paper industry in Europe except when the most balanced solution is chosen. Also, the results are robust when different preferential weights are attached. Finally, this methodology can be applied at a more disaggregated level and other indicators can be introduced.


Introduction
Since the consolidation of the Summit of Río, held in 1992, the idea of sustainability has been spreading not only to fields associated with the management of natural resources, but also to applications in industry (Singh et al. 2007), in energy (Zhou et al. 2007), in tourism (Blancas et al. 2010) or in agriculture (Gómez-Limón and Sánchez-Fernández 2010).
Sustainability has been dealt with from several angles, although there is a certain consensus in that it can be approached by defining an initial set of indicators.Namely, this abstract concept is specified by adequately defining a pluridisciplinary list of acceptable criteria and indicators (Raison et al. 2001), which cover aspects that are assumed to be integrated into the idea of sustainability.On the other hand, the term "sustainability" is easy to understand intuitively, although it is not at all easy to conceptualise, to measure or to formalize rigorously.Besides, from an entrepreneurial perspective, the concept of sustainability is more questionable.In fact, from a business perspective, sustainability on many occasions is linked to components related to competitiveness, innovation and the marketing of companies.Thus, with this combination of ideas a certain company is able to differ from its competitors in order to improve its economic performance.
The main purpose of this study is to analyse the sustainability of the paper industry at a European level using a set of indicators.In fact, sustainability here is analysed in relative terms.With the methodology proposed, a benchmarking tool for comparing the sustainability of paper industry in Europe was obtained.Thus, we have defined a set of indicators that permit the characterization of the managerial reality of the paper industry in each country analysed under sustainability terms.The proposed approach has been applied to the paper industries of a significant number of European countries.To undertake this task, the methodology used has been based on a compromise programming model with binary variables.NACE1 21 industries have been adopted in this study.This product classification has been used in other wood-based industry studies (e.g., Stendahl 2009).NACE 21 includes the manufacture of pulp, paper and converted paper products.The manufacture of these products is grouped together since they constitute a series of vertically connected processes.
There are few papers explicitly dealing with this topic in the wood-based industry.One exception to this trend is the work of Hart et al. (2000), in which different cases corresponding to multinational firms were analysed.They mainly focused on qualitative aspects, related to how some of these firms managed their forests.A similar approach can be found in Johnson and Walck (2004), who described five criteria necessary for integrating sustainability into forest industries.The number of papers analysing comparatively rankings of countries in terms of the level of sustainability of their respective wood-based industries is somewhat scarce (Ojala et al. 2006).In most cases, this type of work is orientated towards the compilation of statistical data or to the formulation of models with the purpose of explaining several aspects associated with the production and consumption of forest products (Buongiorno et al. 2003).Besides, we would like to point out that our paper does not research the relationships in terms of sustainability of the forest management with forest-based industries (see Östlund andRoome 1998, Korhonen et al. 2001, among other works).Finally, it should be noted that the analysis of various aspects regarding wood-based industries using multi criteria techniques is a wellestablished topic in the literature (Diaz-Balteiro and Romero 2008).In Nyrud and Baardsen (2003) or Lähtinen et al. (2008), there are examples of the application of these methodologies to problems in these industries.
In relation to the methodology employed, many studies focus exclusively on the analysis phase, i.e. describing and measuring a set of previously defined indicators, without going on to the phase of explicitly aggregating the indicators cited.With this in mind, and concentrating on the forestry context, numerous studies on sustainability have been published but all of them fall short in some aspects; it is assumed that the indicators cannot be aggregated, or, if they are, the aggregation rule is introduced in a rather mechanistic way.
In other cases, it is also supposed that the same weight is conferred to each indicator (Carabelli et al. 2007).However, the assumption of equal weights is rather unrealistic, since the importance attached by a decision-maker to each indicator can be different.For that reason, in this work an extensive survey has been made among international experts with the aim of justifying the conferring of different weights to each of the indicators selected.
In the next Section, it is demonstrated how the use of multicriteria tools to tackle sustainability problems is widely documented in the literature.After that, it will present the compromise programming methodology.Section 4 introduces the case study, embracing 17 European countries.Section 5 shows the results of the paper and, finally, the main conclusions derived from the research, as well as possible further extensions, are presented in the last section.

Sustainability Indicators and MCDM Methods
In view of multidimensionality being intrinsic to the sustainability concept, many works have attempted to characterize this term by falling back on multicriteria techniques (from now on the acronym MCDM (Multiple Criteria Decision Making) will be associated with the word "multicriteria").In the forestry sphere this fact can be verified by referring to the review work published by Diaz-Balteiro and Romero (2008).Continuing in the forestry context, works like those of Mendoza and Prahbu (2000a,b), Mendoza and Dalton (2005) or Babaie-Kafaky et al. ( 2009) recommend the use of discrete MCDM methods, like the Analytical Hierarchy Process (AHP), in order to evaluate sustainability.Vacik et al. (2007), to characterize the sustainability of possible forest management alternatives, employ the Analytical Network Process (ANP), the enlarged version of the AHP.This comparison between AHP and ANP for approaching sustainability in forest management by means of a set of indicators can also be seen in the works of Wolfslehner et al. (2005) and Wolfslehner andVacik (2008, 2011).Other authors (Mendoza et al. 2002, Men-doza andPrabhu 2003)  Similarly, Ducey and Larson (1999) apply a methodology which hybridizes the multicriteria techniques with approaches based on the fuzzy theory in order to evaluate the sustainability of some decisions relative to forest management.On another methodological line, Kangas et al. (1998) have recommended the use of multiattribute techniques to carry out this indicator aggregation process.Other authors combine these tools by integrating a spatial component into the analysis, as can be observed in the work of Store (2009).In relation to the continuous MDCM methods, in Diaz-Balteiro and Romero (2004a,b) a methodology based on goal programming is proposed to aggregate the sustainability indicators in an acceptable way.Maness and Farrell (2004) apply a multi-objective optimization with fuzzy sets in order to aggregate different criteria and indicators.Finally, Voces et al. (2010) address a problem of sustainability in the European paper industry by resorting to a "satisficing" logic that leads to goal programming formulation, whereas in this paper we resort to an "optimization" approach through a composite compromise programming.

Methodology
Let us introduce the following general scenario.We have i = 1,2,...n countries, each one is evaluated according to j = 1,2,...m sustainability indicators.The key question is to obtain a cardinal "ranking" of the n countries in terms of aggregate sustainability.We shall undertake this task by adapting a procedure proposed by Diaz-Balteiro and Romero (2004 a, b) from a "satisficing" context to an "optimizing" scenario.The first step of the procedure will consist of defining nxm outcomes R ij , that measure the value reached by the ith country when it is evaluated according to the jth sustainability indicator.Given that, normally, sustainability indicators are measured in different units and their absolute values might differ considerably, their straightforward aggregation (e.g., a weighted sum of indicators) has no meaning.In order to avoid this type of problem, the following normalization system is proposed: where R ij is the normalised value reached by the ith country when it is evaluated according to the jth indicator.It should be noted that R j * is the optimal or ideal value for the jth sustainability indicator.This ideal value represents the maximum value if the indicator is of the type "more is better" or the minimum value if the indicator is of the type "less is better".In the same way, R * j is the worst value or anti-ideal value for the jth sustainability indicator; that is, the minimum value if the indicator is of the type "more is better" and the maximum value if the indicator is of the type "less is better".With this normalization system, the indicators do not have any dimension and they are all them bounded between 0 and 1; that is, from the worst to the best of the criteria values according to a local scale.Moreover, for this normalization system the ideal vector for the normalized values is R * = (1,1,…1) and the antiideal vector R * = (0,0,…0).
Let us introduce parameters such as a j that are weights measuring the relative importance attached by an expert or by a panel of experts to the jth indicator of sustainability with respect to the other indicators.Finally, binary variables X i are introduced into the analysis.We will see below how if X i = 1 the ith country is chosen, otherwise X i = 0.With this ingredient, we can formulate the following general binary compromise programming model (Yu 1973, Zeleny 1974): where p is the metric defining the L p family of distance functions.In short, model ( 2) minimizes the topological distance between the achievement of the generic ith country in the m indicators considered with respect to the unit vector (1,1,…1) that represents the ideal values for the m indicators.Thus, by solving (2) the "most sustainable" country will be obtained.By solving model ( 2) in an iterative way we can also obtain the ranking of the n countries in terms of aggregate sustainability.Thus, we only need to attach value 0 to the X i decision variable corresponding to the "most sustainable country".Accordingly, after solving model ( 2) n -1 times with the incorporation into each computer run of an additional constraint such as X i = 0 (when the ith country is the most sustainable one), then the optimal values of the objective functions will provide the aggregate index of sustainability attached to each one of the n countries considered.
From the numerable infinite models underlying (2), two interesting models with a clear preferential interpretation for the problem analysed will be derived.First, the model corresponding to metric p = 1.For this, metric model (2) turns into the following binary linear programming model: ) implies a minimum average disagreement; that is, for this particular model, by applying the iterative procedure mentioned above, we will obtain the ranking of countries in terms of the maximization of the weighted sum of normalised sustainability indicators.This solution is an appealing one since it provided the best aggregate performance.However, for this solution extremely poor results for one of the indicators can be obtained, which might be unacceptable in terms of sustainability.
For metric p = ∞, model (2) turns into the new following binary linear programming model (Romero 1991): where D represents the maximum deviation or disagreement.In this way, the deviation or disagreement with respect to the ideal of the most displaced indicator is minimised.Thus, the "most balanced" sustainable country is obtained.Again, by solving iteratively model (4) as explained above, we will obtain the ranking of countries in terms of maximum equilibrium or balance.Again, this solution is appealing due to its balanced character, but this type of solution can produce a poor "average" result, which might be unacceptable.
To deal with this conflict between "average" versus "balance", we can trade-off the L 1 with the L ∞ compromise programming models, through the formulation of the following binary composite programming model (André and Romero 2008): where l plays the role of a control parameter.Thus, when l = 1 model ( 5) turns into model (3), and when l = 0 model (5) turns into model ( 4).For values of control parameter l belonging to the open interval (0,1), intermediate solutions between the L 1 and the L ∞ can be obtained if they exist.Therefore, control parameter l trades-off "average" versus "balance" solutions, allowing us to determine best-compromises among these desirable but usually opposite criteria.

Case Study: European Paper Industry
In order to define the sustainability of an industry or of a group of industries, it is necessary to measure different types of indicators: economic, social, environmental, etc. Nowadays, it is essential to link sustainability at the entrepreneurship level not only to the existence of the firm as a simple supplier of goods with a market value, but also to another group of attributes (social, environmental) that can provide it with a higher value added as a function of the consumers' perceptions.In the last few years, these intangible attributes have been integrated into expressions like "corporate social responsibility".
Although we have incorporated all these attributes into this study, the industrial nature of the activities considered imposes the prevalence of economic indicators.Also, the scant level of the disaggregation of environment information, which still awaits an adequate treatment, should be underlined.In fact, no other potential environmental indicators in the paper industry have been included due to their data not being disaggregated at the paper industry level.In short, fourteen indicators encompassed in the above perspectives have been selected and are shown in Table 1.In this way, we aimed to include the different aspects of the value chain of the European paper industry which determine a greater or lesser sustainability.The selection of these indicators was conditioned, firstly, by the information available at a European level.The statistical sources used, such as Eurostat databases, are mainly of an international nature.Similarly, United Nations statistical data of wood products and international trade have been used because the paper industries are integrated into these databases.Nevertheless, when necessary, different National Statistical Offices have been consulted.
Next, we have analysed the meaning of the fourteen indicators selected, which can be classified into two classes or categories: "less is better", or "more is better", since a reduction or an increment in the indicators' values supports the sustainability of the industry.The first indicator selected was the gross value added as a percentage with respect to the paper industry in the manufacturing sector.It constitutes an indicator that shows the relative weight of this industrial sector in the total manufacturing activity of each country.It has been considered that a reduced contribution of the value added implies a reduced allocation of resources compared to other more productive and dynamic industrial sectors.Regarding energetic efficiency, this indicator represents a marginal cost, because it covers the amount of energy that it is necessary to buy in order to obtain an additional metric ton of product.Logically, a greater sustainability is reached when the value of this indicator is a low one.The third indicator, dependence on industrial roundwood, gives valuable information about the different national market strategies for this input, and it is defined by the quotient between imports and apparent consumption.It should be remembered that the latter is equal to the sum of national production plus the imports less the exports.
On the other hand, the following indicators present, direct or indirectly, labour use as a production factor.Thus, the unitary average wage indicator shows workers' earnings for this industrial sector in each country.Without analysing the differences associated with the national income per capita, a higher value of this indicator is considered as being more sustainable from a social point of view.Conversely, the gross value added per employee shows an approach to the traditional "labour productivity" concept.Finally, the intensity in the labour force (percentage of labour costs in total production) gives information on the intensity in the use of labour as a production factor for the paper industry in each country.The more traditional sectors, of a lesser complexity and vitality, also use this factor more intensively.For that reason, in this study it was preferable for this indicator to reach its lowest possible value.
The investment rate provides information on the intensity in the use of the capital factor for this industry in each country, measured as the quotient between investment and value added at factor cost.Next, we show four indicators related to innovation.First, it has been considered to be appropriate to incorporate the acquisition of built-in technology into this group of indicators, because this is the principal way to incorporate innovation, mainly in small and medium-sized firms.The second indicator in this group, the percentage of innovative firms with respect to the total number of firms, shows the penetration rate of innovative activities in the paper industry.Also, the percentage of the total turnover of the paper industry in each country due to innovative firms is another indicator of the importance of innovation in paper industries (effects of the innovation).Finally, the number of patents applications to the European Patent Office in the reference year ( 2004) is a widely used indicator of the output due to the innovative activities developed in each country, and it has been used in this research.These indicators have been considered as belonging explicitly to the category "more is better", since the higher the figures, the more the paper industry will be sustainable.This is because it is usually recognized that a good way to achieve a greater sustainability of firms could be by increasing the results associated with the research and development (Paech 2005).
A complementary indicator selected could be the external competitiveness (Balassa index).This has been defined as the relationship between the importance of the exports of a certain industrial sector with respect to the total industrial exports in a particular country, and, over a wider area that might be the whole world, Europe, or, in this case, the cluster of European countries analysed.It represents an external competitiveness indicator, and if this index has a larger value than the unit, a competitive advantage does exist, or, in a contrary sense, it does not.
Finally, in this investigation we included two indicators related to some environmental characteristics of these firms.First, the waste generated by them gives information on the pollutants produced by their industrial activity.To allow a comparison between the different countries, this figure is divided up between the added value corresponding to each specific paper industry.It has been assumed that "less is better", because, in this way, the sustainability of these firms increases.The last indicator in Table 1 shows the quotient between the total current expenses for environmental protection and the number of employees.Here, only the expenditure on environment protection that exclusively affects the period in which it was incurred, without any future economic projection, will be included.For the purpose of comparing the different figures corresponding to the European countries included in this analysis, this value is distributed between the number of employees.
It was aimed to apply these indicators to the forest industry of all the EU countries.However, in certain countries, there was no information available for one or several indicators.In those cases it was opted to remove those countries from the analysis.In end, data corresponding to 17 countries were obtained.This figure is considered to be highly representative of the paper industry in Europe since, according to EUROSTAT, the turnover of these countries exceeds 88% of the total turnover of European countries (EU27).Once the indicators were obtained, the following step consisted of their normalization (see expression (1)).Table 2 shows the values of each indicator, now normalized, for each country selected.It should be noted that the ideal values for each indicator are in bold-face and the anti-ideal values in italics.
The following step is related to the obtaining of the weights which will be incorporated into the compromise programming models introduced above.The preferential weights have been obtained by means of a survey sent to 104 experts from 22 different countries.The experts have been selected for their publications, and their links to firms or organizations related to wood-based industries.In short, the experts had to compare, following a "pairwise" comparison format, the different indicators used in this model, employing the scale defined by Saaty in his AHP model (Saaty 1980).Twenty consistent responses were obtained, but some experts' judgements have not been computed for exceeding the consistency threshold required by the AHP procedure.In short, some experts have considerably departed from the transitive property when they respond to the survey making paired comparisons.Although the number of surveys received could appear to be meagre, this is a habitual figure in this type of study (Caballero et al. 2008).On the other hand, in works tackling similar problems the opinion of experts is replaced by some weights conferred arbitrarily by the authors themselves, accompanied by a sensitivity analysis (Ruiz et al. 2011).
From these answers the individual priorities of each expert were elicited.To obtain the aggregation of these preferences, it was opted, in accordance with previous studies (Forman and Peniwati 1998), to calculate their geometric mean for each indicator, so that their total sum was equal to one.
The preferential weights obtained in this way are shown in Table 3.

Results
Table 4 shows the final ranking of the 17 countries, according to the different values of control parameter l, when model shown in Eq. ( 5) has been applied.It can be seen how Finland is the country with the most sustainable paper industry, unless we lean towards the most balanced solution (l = 0), in which case Sweden would be that country.In other words, except for that last solution, for the rest of the values associated with the control parameter l the solutions are very alike, with the following four countries with the most sustainable paper industry: Finland, Sweden, Austria and Germany and the two countries with the least sustainable industry: Lithuania and Romania remaining invariable.
As was observed when explaining the methodology employed, the solution shown in Table 4 integrates the preferential weights of a set of experts shown in Table 3.The first question that we could ask ourselves is if the solutions are robust ones in the presence of changes in the preferential weights.The answer is incorporated into Table 5, where the problem has been solved by attaching the some preferential weight to each indicator.
It can be verified how, the same as in Table 4, the solutions are very similar to each other for the values of the control parameter l higher than 0.1.In fact, in all these solutions shown in Table 5, the most sustainable country is Finland, followed by Germany, Austria and Sweden.Conversely, the least sustainable countries are the Czech Republic and Romania.On the other hand, and related to the most balanced solution (l = 0), the same type of "ranking" is obtained when different preferential weights were integrated.However this solution (l = 0) differs considerably to the solution obtained when different preferential weights are considered.In fact, it can be observed how, in this case, the country with the most sustainable paper industry was Austria, followed by Germany, Spain and France.

Discussion and Conclusions
This work has presented a methodology by which the sustainability of the paper industry in Europe has been evaluated, using compromise programming for this purpose.The models employed permit the aggregation of a set of indicators of different types, as well as assigning different preferential weights to each of them.Also, different solutions have been obtained, according to the compromise between the most efficient solutions (l = 1) and the most balanced ones (l = 0).And what perhaps is the most important issue, all the solutions provided here have a clear preferential interpretation.
The results show how, with the exception of the case in which the solution is most balanced, Finland is the country with the most sustainable paper industry, followed by Sweden, Austria and Germany.At this point, one could compare this ranking with the structure of the European paper industry.In Table 6, data (production and number of employees) belonging to the 17 countries analysed in this paper are attached.Thus, some of the countries where production is higher (both in tons and in euros) are occupied by former top ranking.However, it appears that not always are countries with a high production or employing more workers are the most sustainable ones, as evidenced by the cases of Italy and the UK demonstrate.In addition, some studies could explain the results obtained in this paper.Thus, Kärnä et al. (2003) through a comparison of wood-based industries between different European countries, suggest that the Finnish firms are "greener" than those of other countries.Also, in Mikkilä et al. (2005) a survey was made of stakeholders in 4 countries, including Finland, in relation to aspects associated with the corporate social performance in the paper industry, showing how there is a greater environment awareness in Finland than in other countries.Finally, although this work does not aim to describe all the possible reasons for this ranking, people interested could developed statistical or econometric analyses in order to find some variables which explain the ranking of the countries analysed.Thus, the dependent variables could be the numerical values obtained by applying the above CP models, and a new set of independent variables (different to the indicators chosen in this paper) could be selected as explanatory variables.
A possible weakness in this paper might be the selection of the indicators, conditioned by the data existing at the level tackled in this study.For example, other additional indicators of an environmental nature could be included, and issues regarding the interdependence of the different wood product markets (Kallio 2001) have not been addressed with this battery of indicators.Thus, a possible extension of this research would consist of adapting the analysis at a more disaggregated level, for instance at a managerial one, or analysing in more detail certain industrial sub-groups.Besides, if the proposed indicators have been defined at an entrepreneurial level, environmental aspects like the "triple bottom", eco-efficiency, or the installation of certain environmental management systems could be addressed with a different battery of indicators.However, in that case, the methodology used to aggregate the indicators would be the same.

Table 1 .
Indicators used in this study.
Sources: European statistics (Eurostat) by theme: Industry, trade and services, Economy and finance, 4th Community Innovation Survey, Patent Statistics, Waste Statistics Regulation, Environmental Accounts.UNECE: Timber Committee Forest Products Statistics.UN Comtrade Database.Statistics Sweden.Czech Statistical Office.Statistik Austria

Table 2 .
Normalized indicator values for each country and each indicator.In bold, the ideal values, and in italics, the anti-ideal values.

Table 3 .
Preferential Weights obtained for each indicator.

Table 4 .
Results obtained for the different values of the parameter l and preferential weights given by experts.

Table 5 .
Results obtained for different values of the parameter l, when the same weights are considered for the indicators selected.

Table 6 .
Main figures of the European paper industry regarding the countries analysed in this research (year 2004).