Measuring Sustainability Performance with Multi Criteria Model: A Case Study

: The proposal of this research is the development of a hybrid multi-criteria decision analysis (MCDA) model of sustainability performance. The model is applied to a Brazilian oil and gas company and is constructed from the MCDA associated with statistical analysis. The MCDA technique is a preference ranking organization method for enrichment evaluation (PROMETHEE), with analysis of 20 indicators of the dimensions of sustainability. In the statistical analysis, the Principal Component Analysis (PCA) and Multiple Linear Regression (MLR) are used. The results of PROMETHEE showed that the company’s best sustainability performance was in 2011 and 2010. The worst sustainability performance was in 2015 and 2016. The application of the PCA technique aims to eliminate the existing multicollinearity and capture the direction of variability of the indicators. The ﬁrst PC with 53.2%, the second PC with 25.6%. An estimate based on the MLR equation was performed. The limitation of the paper is with data from the company’s sustainability reports as well as the choice and quantity of indicators. The analysis of the sustainability performance of the company through multi-criteria models is not new but their combination with mathematical models, comparing the sustainability reports per year, brings more complete results on the sustainability performance of the company.


Introduction
The most popular definition of sustainability was presented by the World Commission on Environment and Development in 1987 as, "sustainable development is development that meets the needs of the present without compromising the ability of future generations to meet their own needs." Sustainability seeks to ensure that the resources available today is not used to deprive the economic, environmental and social benefits of future generations [1].
Faced with the need for sustainability assessment, researchers and practitioners indicate evaluation systems that track the progress of sustainability over time [2]. The greatest difficulty for sustainability is the integration of multiple criteria into several dimensions, with many criteria conflicting with each other. Sustainability has been the focus of most organizational initiatives and innovations [3].
Although there are advances in practices and theories that are contributing to the sustainability of organizations, the issue is still far from maturing [4]. Many efforts were directed towards the development of indicators in the measurement, prevention and classification of sustainability. These indicators provide a standardized form of data for decision making. However, indicators alone reports, around 60 key indicators were identified, of which 20 were chosen for the assessment, 5 economic, 7 environmental and 8 social indicators. Reference [19] reported in their paper that social indicators are often used to assess the sustainability performance of production processes. Reference [20] suggested using quantifiable social indicators such as equity and safety at work in measuring sustainability.

Sustainability Performance
The evaluation of the sustainability performance of the Brazilian oil and gas company is carried out through the multi criteria modeling with the PROMETHEE technique. Preference flows, which are the results of the multi criteria analysis. In the third step, statistical analysis techniques with principal component analysis and multiple linear regression.
PROMETHEE consists of an array with a set of possible alternatives or actions (A). In the case of this paper, the alternatives are years. Sustainability performance of the company obtained from the PROMETHEE is compared on an annual time scale (2009 to 2017). For these alternatives there are the criteria that are evaluated from their function F (a). PROMETHEE I classifies alternatives partially through the Phi+ and Phi− flows, and PROMETHEE II classifies the alternatives globally through the Phi flow. Steps for PROMETHEE method are the determination of deviations based on parity comparison; application of the preference function; calculation of an overall or global preference index; calculation the PROMETHEE I partial ranking and the PROMETHEE II complete ranking. Steps are given below.
where φ denotes the global flow.

Sensitivity Test
A sensitivity test is performed from the input data change. Analysis is the act of studying the effect that variation of an input data can have on the results. Methods for sensitivity analysis are divided into mathematical, statistical and graphs. Statistical methods involve simulations with variations of inputs and analysis of the effect outputs [21].

Principal Component Analysis
The Principal Component Analysis (PCA) is a multivariate statistical technique that seeks to capture information about the linear correlation structure for correlated group variables [22]. This information is condensed into a smaller number of uncorrelated variables, called principal components (PCs), which represent the projections of the original variables on new orthogonal axes.
Let X nXk a matrix of set of data centered on k correlated variables, where each row contains a k-variant observation, represented by x j1xp . The correlation structure of the matrix X is obtained in the sample co-variance matrix (or correlations) S kXk As such matrix is symmetric and not singular, there exists an orthogonal matrix U kXk which diagonalizes S. Thus, we have U SU = S c , where S c is a diagonal matrix containing the k eigenvalues λ t positive values for S. The matrix U presents in its columns the k-eigenvectors u t that carry the charges of the linear combination for projects the original variables on the th th orthogonal axis given by the t th PC, for t = 1, . . . , k. The eigenvector λ t describes the variance of the th th . The vector z t(nX1) , brings the scores for the t th PC of the n initial observations, obtained through z t = Xu t , for t = 1, . . . , l. Considering that each variable follows a Normal distribution, the th th PC follows a Normal distribution with mean 0 and variance λ t .
The projection of a new k observation varied by the vector x(kx1), in orthogonal axes defined by the PCs, is obtained by z = U x, Where z = [z 1 , z 2 , . . . , z w ] is the vector containing the w scores for the new observations; the matrix U = [u 1 |u 2 | . . . |u w ] contains in its columns the associated eigenvectorsand U' represents its transpose [23].

Multiple Linear Regression
Multiple Linear Regression (MLR) is a generalization of simple linear regression when there is more than one independent variable. The basic model for multiple linear regression is: for each observation i = 1, . . . , n. The value n are the observations of a dependent variable and p the independent variables. Where γ i is the i-observation of the dependent variable, X ij is with the observation of the independent j-variable, j = 1, 2, . . . , p. The values βj are the parameters to be estimatedand i is the ith normal error independently distributed identically. In the multivariate linear regression, there is an equation for each of the dependent variables m > 1 that share the same set of independent variables and are therefore estimated simultaneously [24].

Results and Discussions: Case Study
The case study company is a large Brazilian oil. Main producer, distributor and seller of oil and gas the company has more than 150 thousand employees. The publicly traded reports its sustainability through annual in its media. From these reports were collected the essential information for the development of this research. Section presents the development with results of the PROMETHEE evaluation, PCA and the MLR.

Dimension, Themes, Indicators
The company's sustainability reports are based on The Global Reporting Initiative (GRI) which is an international organization that helps companies communicate their economic, environmental and social impacts. About 60 quantitative indicators were identified in the report. Were divided into three dimensions (social, environmental and economic). Five indicators of the economic dimension, seven of the environmental and eight of the social were selected. The selection of 20 indicators was made according to the criteria of data availability, comprehensiveness of the themes and dimensions. Table 1 illustrates the selected indicators. Selected 20 criteria in PROMETHEE through the bases of sustainability indicators, are determined the functions of each of them preference and the objective of each criterion in the maximization or minimization. It is observed that the preference functions used are the v-Shape and the linear function. Table 2 shows the inputs of PROMETHEE.

PROMETHEE Analysis
From these selected indicators were parametric and the functions of preference were defined. Evaluating according to the PROMETHEE method, individual flows (Phi− and Phi+) and global flows (Phi) were generated. According to the Phi results a ranking is performed as the final result of the evaluation. As shown in Table 3. The results showed that the company had its best performance in 2011 and its worst performance in the year 2015. From the ranking highlighted in Table 2 it can be inferred that the results can be related to two external indices, oil price.and exchange rate. For this understanding a multi criteria correlation analysis is performed using the PCA technique. Table 3. Flows, Global flows and rank. Adapted from Reference [18].  Table 4. In the second robustness test the weights relative to the indicators were changed. Initially, equal to all size independent were entered. Then, greater weights were added to economic indicators (50%) and environmental (35%) and the weights of social (15%) were decreased. Shown in Table 5.   Tables 6 and 7 . Red a negative and in blue a positive. The color intensity indicates whether the correlation is high, medium or low. These data are shown in Figure 2.

Year
The application of PCA technique aims to eliminate the existing multicollinearity and capture the direction of variability the indicators. Technique allows obtaining orthogonal main principal components PCs forming a linear combination distinct from the original indicators. PC eigenvectors represent the load and direction of variability in the indicators. PCs is listed in Table 8.
With a biplot chart, shown in Figure 3, you can see a split between two PCs. With the Pearson correlation coefficient of 0.829 it can be inferred that the multiple linear equation is an adequate technique to predict future values of sustainability from the parameters of the global flows generated in PROMETHEE. From these results can be realized a prediction with a multiple linear regression having as dependent variable the global flows and independent variables the exchange rate and Oil Price.    MLR data are shown in Table 9 and the multiple linear equation, shown in Figure 4, the future results of organizational sustainability can be estimated based on the values of the Oil Price and the exchange rate.

Conclusions
This paper presented a hybrid model using a multi-criteria decision analysis and statistical tools based on the principal component and a multiple linear regression model.
The hybrid model aimed to balance the dimensions of economic, social and environmental sustainability. The results of PROMETHEE showed that the company's best performance was in 2011 and 2010. The worst was in 2015 and 2016, the height of economic crisis in Brazil. The robustness of model was tested through the sensitivity test, changing the input data was verified small changes in the results. PROMETHEE as a multi-criteria model then proved to be an appropriate tool for sustainability performance analysis. The direction of variability of the indicators was highlighted by the principal component analysis. With the insertion of external indicators to the company, a multiple linear equation was proposed to be used as a forecasting tool.
The limitations of this research are through the collection and selection of indicators. Limited to publicly available corporate sustainability reports. The contribution and originality of this paper is the development of a hybrid model. PROMETHEE as a tool for evaluating corporate sustainability performance based on the comparison of years. PCA as a method for measuring indicator correlation and MLR as a forecasting mechanism for the future.
This hybrid model brings clear, objective decision-making results and can easily be replicated to other types and sizes of companies using publicly available sustainability reports. The technique employed offered a satisfactory result comparing the performance of organizational sustainability in the years 2009 to 2017. Assessment results provide information for business decision making. The company can identify which dimensions need improvement and allocate the necessary resources. Forecasting results can support more objective planning about the company's future.
Intelligent systems can be built for decision making based on the hybridization of models. Not only the combination of analytical and mathematical, but also with heuristic methods and simulation. A proposal for future work and for other researchers is the combination of multi-attribute and multi-objective models for assessing and optimizing corporate sustainability performance.
Funding: This research received no external funding.