Hélène Le Cadre
email: helene.le_cadre@mines-paristech.fr

Cédric Auliac
email: cedric.auliac@cea.fr

Energy Demand Prediction in a Charge Station: A Comparison of Statistical Learning Approaches

Keywords: Supervised Learning, Regret algorithms, Electric Vehicle Demand

In this article, we compare the performances of 5 learning techniques: artificial neural networks, support vector machines, ARIMA processes, regret based methods and a naive approach based on the periodic repeatitions of the predictions. They have been tested over a real database which can be associated with the energy demand generated by electric vehicles wishing to reload, in a specific charge station. Using this generic database, our simulations highlight the fact that regret based methods clearly outperform the other learning approaches. This class of methods is all the more interesting as it enables the introduction of game theory to model the interdependencies between the agents composing the ecosystem and provides economic guidelines.

Introduction

The management of Electric Vehicle (EV) charging infrastructure requires both to optimize the location of the various charge stations composing the underlying network and to provide relevant predictions to the EV drivers and to the utilities managing the charge stations. We proposed and tested an algorithm based on the crossentropy method in [START_REF] Cadre | Infrastructure Topology Optimization using the Cross-Entropy Method[END_REF], to optimize the charging infrastructure, under competition between the utilities. The solving of the non-cooperative geographic location game between the utilities required to make simplifying assumptions about the EV drivers' energy demand. To improve the accuracy of the modelling assumptions regarding the EV drivers' energy demand, it is necessary to develop efficient learning approaches. One major problem is that it is impossible to measure explicitly the real energy demand of the drivers. Indeed, it is the consumption that the utilities like Better Place, monitor in their charge stations. Of course, there exists a non-trivial relation between demand and consumption but it appears as impossible to infer analytically. In the context of the european FP7 project Elvire, we modeled the problem as a partial information game and provided predictions about the energy demand us-ing regret based methods [START_REF] Cesa-Bianchi | Prediction, Learning, And Games[END_REF], [START_REF] Le Cadre | Energy Demand Prediction: A Partial Information Game Approach[END_REF]. Following this direction, the goal of this article is to compare the performances of 5 energy demand prediction methods on a real data set.

The prediction system is based on data measurements available online on the machine learning repository PEMS-SF [START_REF] Frank | UCI Machine Learning Repository[END_REF]. More precisely, we have downloaded 15 months worth of daily data from the California Department of Transportation website. The data describes the occupancy rate, between 0 and 1, of different car lanes of San Francisco bay area freeways. The measurements cover the period from january 1, 2008 to march 30, 2009 and are sampled every 10 minutes. We consider each day in the database as a single time series of dimension 963 i.e., the number of sensors which functioned consistently throughout the studied period, and length 144. We remove public holidays from the dataset, as well as two days with anomalies (march 8, 2009 and march 9, 2009) where all the sensors were muted between 2 and 3 a.m. This results in a database of 440 time series. Associating a sensor with a charge station, we have kept only the first sensor historical data.

To be more generic, we will consider any data measurements to improve our predictions. The data probes can measure for example:

• The time series of the number of EVs in the charge stations of the utility managing the charging infrastructure

• The time series of the road occupancy, under the assumption that the road occupancy is measured by a coefficient between 0 (no vehicle) and 1 (maximal congestion)

• The time series of the energy demand in a specific region

• The revenues of an energy producer, etc.

As mentioned above, the data measurements are stored in a database server. They are all synchronized and associated with a time instant. Then, there exists at least two approaches to forecast the energy refuelling demand:

Approach A: Either, estimate the real demand from the aggregation of the different measures given by all the sensors at past time periods, and through a time series forecasting method, forecast the future values.

Approach B: Or, use directly a forecasting method starting from the data measurements. It is also called a partial feedback forecasting method.

Under Approach A, we will use artificial neural networks, support vector machines and ARIMA models. Under Approach B, we will use the regret based monitoring technique.

In Section 2, we will describe artificial neural networks, support vector machines and ARIMA models, while in Section 3 we will detail the principles of the regret based methods. Finally, in Section 4, we will provide an interpretations of the results that we obtained using the PEMS-SF database.

Approach A: Description of the time series forecasting algorithms

There are three major learning processes, each corresponding to a particular abstract learning task. These are supervised learning, unsupervised learning and reinforcement learning.

In supervised learning, we are given a set of example pairs (x, y) ∈ X × Y ⊂ R 2 and the aim is to find a function f : X → Y in the allowed class of functions that matches the examples. In other words, we wish to infer the mapping implied by the data. The cost function is related to the mismatch between our mapping and the data and it implicitly contains prior knowledge about the problem domain. A commonly used cost is the mean-squared error. With this performance measure, the forecaster will try to minimize the average squared error between the network's output f (x), and the target value y, over all the example pairs. Tasks that fall within the paradigm of supervised learning are pattern recognition, also known as classification, and regression, also known as function approximation.

In unsupervised learning, some data x is given and the cost function to be minimized can be any function of the data x and the network's output. Tasks that fall within the paradigm of unsupervised learning are in general, estimation problems. The applications include clustering, the estimation of statistical distributions, compression and filtering.

In reinforcement learning, data x are usually not given, but generated by an agent's interactions with the environment. The aim is to discover a policy for selecting actions that minimizes some measure of a long-term cost i.e., the expected cumulative cost. The environment's dynamics and the long-term cost for each policy are usually unknown, but can be estimated. Tasks that fall within the paradigm of reinforcement learning are control problems, games and other sequential decision making tasks.

In this section, we will concentrate on the supervised learning paradigm, assuming that we have some real historical data on the electric refuelling demand to predict the future, even if in practice, we will most probably not get data on the exact value of the demand but on some indirect measures of it, like cars stopping at the station or the quantity of battery exchanged in a day.

Artificial Neural Networks (ANNs)

Artifical Neural Networks (ANNs) are non linear statistical data modeling tools. They are usually used to model complex relationships between inputs and outputs, or, to find patterns in data. It is inspired by the structure and/or functional aspects of biological networks.

The network pictured in Figure 1, has three layers. The first layer has input neurons, which send data via synapses to the second layer of neurons, and then via more synapses to the third layer of the output neuron. More compex systems will have more layers of neurons with some having increased layers of input neurons and output neurons. The synapses store parameters called weights that manipulate the data in the computations. An ANN is typically defined by three types of parameters:

• The interconnection pattern between the different layers of neurons

• The learning process for updating the weights of the interconnections

• The activation function that converts a neuron's weighted input to its output activation In our application for the energy demand forecast, we have decided to stick to three layers of neurons. The input layer encodes the time of the measure. The output layer is a single neuron representing the demand. However, the number of hidden neurons is not fixed. We consider that all input neurons send their information to all hidden neurons and that all hidden neurons send their information to the output neuron. This structure is sometimes called a feed-forward neural network.

We also add to each neuron a specific input which is a white noise. It enables some probabilistic behavior.

The activation function is linear. It equals the weighted sum sent by the input neurons of a given neuron. The output has values in [0; 1].

To make less computation errors, we will need to scale the inputs of the neural network to have values in [0; 1]. This scaling is needed in most neural network applications but may result in quite large absolute errors if the considered domain for the demand is large.

Referring to the supervised learning framework described at the beginning of the section, we will learn the following function: demand = f (month, day, hour, minute) represented as a graph of neurons from n historical data points and then predict the future demand by applying this function on some future dates.

We fit a neural network with 5 hidden neurons on the data of occupancy of a California road for 60 days with 144 measures per day. It gives us the neural network pictured in Figure 2 where each value on a synapse is the weight of the synapse and the activation function is linear.

We can check the good fit of the ANN by showing the output which was produced by the input data of the second week of the learning data in Figure 3

Support Vector Regression (SVR)

A support vector machine (SVM) is a supervised learning method that analyzes data and recognizes patterns, used for classification and regression analysis. In that sense, it is very close to a neural network and can even be interpreted as an extension of a specific neural network named the perceptron. However, there is no a priori on the dependency structure between inputs and output and on the activation functions forms in the case of SVM contrary to neural networks. In addition, during the learning phase, a SVM model tries to separate output categories by a clear gap that is as wide as possible and not just big enough to classify the learning data correctly. As a result, it is less sensitive to learning data isolated errors (outliers) than a neural network.

The standard SVM is a non-probabilistic binary linear classifier. It takes a set of input data and predicts, for each given input, which of two possible classes forms the input by defining two parallel hyperplanes as far as possible from each other, separating the learning data. In Figure 4, we separate green points on one side of a first hyperplane from white points on the other side of a second hyperplane. These two hyperplanes are the most distant possible hyperplanes of the considered space separating the two types of points.

In 1992, Boser et al. suggested a way to create nonlinear classifiers by applying the kernel trick [START_REF] Aizerman | Theoretical foundations of the potential function method in pattern recognition learning[END_REF] to maximum-margin hyperplanes. This allows the algorithm to fit the maximummargin hyperplane in a transformed feature space. The transformation may be nonlinear and the transformed space high dimensional. Thus, though the classifier is a hyperplane in the highdimensional feature space, it may be nonlinear in the original input space. Some common kernels include: polynomial, hyperbolic tangent and Gaussian radial basis kernels. The separation line between the two classes which is a hyperplane in the feature space may be a very complex curve in the original space as depicted in Figure 5. In our application, we will use the radial basis kernel which means that the formula exp(-γ|u-v| 2 ) is used instead of the scalar product of u and v. We will choose γ as the inverse of the number of observations.

A version of SVM for regression was proposed in 1996 by Vapnik et al. [START_REF] Drucker | Support Vector Regression Machines[END_REF]. This method is called support vector regression (SVR). It performs linear regression in the high-dimension feature space using ε insensitive loss and, at the same time, tries to reduce model complexity by minimizing the linear regression factor ω. This can be described by introducing (non-negative) slack variables ξ i , ξ * i , to measure the deviation of training samples outside ε insensitive zone. Thus, SVM regression is formulated as minimization of the following functional:

min 1 2 ω 2 + c n i=1 (ξ i + ξ * i ) y i -f (x i , ω) ≤ ε + ξ * i f (x i , ω) -y i ≤ ε + ξ i ξ i , ξ * i ≥ 0, ∀i = 1, ..., n
In our application, we will choose ε = 0.1 and c = 1 for our computations and f (.) is the radial basis kernel.

We run the support vector machine algorithm on the PEMS-SF database. The algorithm gives us more than 4000 support vectors which means that the space of days of the week and hours of the day is very fragmented in terms of road occupancy.

We can check the good fit of the SVR model by showing the output produced by the input data of the second week of the learning data in Figure 6

ARIMA processes

An autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. They are applied in some cases where data show evidence of non-stationarity, where an initial differencing step (corresponding to the integrated part of the model) can be applied to remove the nonstationarity.

The model is generally referred to as an ARIMA(p, d, q) model where p, d, and q are non-negative integers that refer to the order of the autoregressive, integrated, and moving average parts of the model respectively. ARIMA models are used for observable non-stationary processes x t that have some clearly identifiable trends:

• A constant trend i.e., zero average, is modeled by d = 0

• A linear trand i.e., linear growth behavior, is modeled by d = 1

• A quadratic trend i.e., quadratic growth behavior, is modeled by d = 2

Sometimes a seasonal effect is suspected in the model. For example, if we consider a model of daily road traffic volumes. Weekends clearly exhibit different behavior from weekdays. In such cases, it is often considered better to use a SARIMA (seasonal ARIMA) model than to increase the order of the AR or MA parts of the model.

The ARMA model consists of two parts, an autoregressive (AR) part and a moving average (MA) part. The autoregressive part of the model of order p is written:

x t = c + p i=1 φi x t-i + ε t
where the φi , i = 1, ..., p are the parameters of the model, c is a constant and ε t is a white noise.

The moving average part of the model of order q is written:

x t = µ + ε t + q i=1 θ i ε t-i
where the θ i , i = 1, ..., q are the parameters of the model, µ is the expecation of x t . It is often assumed to equal 0 and the ε t , ε t-1 , ..., ε t-q are white noise error terms.

We can see from these definitions that a (S)ARIMA model assumes that the time series we are studying are mainly stationary or have a constant trend in their evolution. If there is a shift in car drivers behaviors, due for example to tax increase or promotion or other external events, it will not be taken into account. In addition, to catch all the trends in the evolution, we need quite a long period of observed data to detect the autocorrelation. For example, if there is a seasonal effect such as a big increase in transportation during summer holidays we should need more than one year of data to detect it. This is too long to ensure an optimal mining of the data.

The estimation of the ARIMA model corresponding to some learning data is done through the Box and Jenkins method [START_REF] Newbold | The Principles of the Box-Approach[END_REF]. The original model uses an iterative three-stage modeling approach:

• Model identification and model selection: making sure that the variables are stationary, identifying seasonality in the dependent series (seasonally differencing it if necessary), and using plots of the autocorrelation and partial autocorrelation functions of the dependent time series to decide which (if any) autoregressive or moving average component should be used in the model.

• Parameter estimation using computation algorithms to arrive at coefficients which best fit the selected ARIMA model. The most common methods use maximum likelihood estimation or non-linear least-squares estimation.

• Model checking by testing whether the estimated model conforms to the specifications of a stationary univariate process. In particular, the residuals should be independent of each other and constant in mean and variance over time. (Plotting the mean and variance of residuals over time and performing a Ljung-Box test or plotting autocorrelation and partial autocorrelation of the residuals are helpful to identify misspecification.) If the estimation is inadequate, we have to return to step one and attempt to build a better model.

We follow the Box and Jenkins method [START_REF] Newbold | The Principles of the Box-Approach[END_REF] to decompose the PEMS-SF database. First, we run an autocorrelation diagram. Its output is represented in Figure 7 historical data out of the seasonal part is an auto regressive model of order 2. We estimate the corresponding coefficients and we obtain a full model of the road occupancy.

We can check the good fit of the ARIMA process by showing the output produced by the input data of the second week of the learning data in Figure 8 3 Approach B: Description of the regret based forecasting algorithms

Time series forecasting

We can imagine from the previous section that there is a lot of possible techniques to model and predict the energy refuelling demand of electric car vehicles; for example, we can think about all the possible kernel functions when considering support vector machines. But how can we select the best candidate model among all the possible? In many cases, it is a long process of iterative selection which last a few years until the industry reaches a consensus on the best model.

It is even more difficult in our case as the refuelling technologies are not stabilized, the available measures to make the prediction are not so clear, and the car drivers' behavior is in definition. One possible solution is to use the regret based techniques to select dynamically the best forecasting technique. Indeed, the starting idea of regret based techniques is to select the best forecasting expert among a finite set by estimating the regret of not having followed that expert at each time period.

The advantages of regret-based techniques are:

• It does not require any a priori on the data that we are forecasting

• It is an online learning algorithm in the sense that it can accept any fresh data measures at each time period to improve its accuracy without needing to rerun the algorithm on all the learning phase contrary to ANNs, SVMs or ARIMA estimation methods

• The error that we make in our predictions are bounded with a computable theoretical expression and under certain circumstances this bound is the best that we can obtain for any forecaster

• They extend the SVM and ANN based techniques

For the regret based forecasting, we take away the seasonal part of the PEMS-SF dataset like in the ARIMA process case. Having removed the data seasonality, we use the Vovk-Azoury-Warmuth forecaster to model the resulting data [START_REF] Cesa-Bianchi | Prediction, Learning, And Games[END_REF]. Formally, let x t be a vector containing the time index and the day index corresponding to each time period t and y t be the value of the road occupancy rate for each time period t, the Vovk-Azoury-Warmuth forecaster p t is defined by:

p t = < w t , x t > A t = I + t s=1 x s x T s w t = A -1 t t-1 s=1 y s x s
A specificity of the regret based algorithm is that it can benefit from new data points after the learning step to improve its forecasts. Contrary to ANN, SVR or ARIMA process for which the learning process has to be repeated to take into account recent data, the regret based techniques is an online forecasting tool. To be more precise, it is made of two phases:

• Exploration: the algorithm gathers data so as to extract the most reliable information. The forecaster explores all the possible prediction values and keeps in memory its regret performance.

• Exploitation: the algorithm exploits the information that it has already acquired and optimizes its estimates by selecting the best forecaster.

This two stage process explains why the regret algorithm might need some time to learn over the training set and why its learning capacity might be observed only after a sufficiently large number of iterations. can notice that the algorithm takes benefit from data points after the learning phase to improve its forecasts contrary to neural networks, support vector machines and ARIMA processes as it is an online forecasting tool. We compare the performance of the regret-based technique to the support vector machine method by plotting the cumulative regret obtained by these two techniques in Figure 10. The cumulative regret is the sum of the prediction errors made from time period 1 to the considered time period t and the good property of regret-based technique is that they minimize this value in the long run.

One possible extension of our work could be to use the regret based technique to select dynamically the best forecasting period between support vector machines, ARIMA and ANNs.

Comparison of the prediction method performances

To compare the performances of the various forecasting methods over the datasets, we use as criterion, the expectation of the mean of the absolute errors: road occupancy rates over two consecutive weeks belonging to one learning set and then, to the other. We observe that it is worth using elaborate predictions tools over the considered dataset. Indeed over the training set, the regret based approach, ARIMA process and SVR perform better than the naive approach and over the test set, solely, the ANN performs worse that the naive approach. Over the test set i.e., to perform the prediction task, the regret based algorithm generates the smallest value for the absolute loss followed closely by the SVR.

In the last row of Table 1, we have tested a naive learning approach based on the repetition of the road occupancy rates over two consecutive weeks belonging to one learning set and then, to the other. We observe that it is worth using elaborate predictions tools over the considered dataset. Indeed over the training set, the regret based approach, ARIMA process and SVR perform better than the naive approach and over the test set, solely, the ANN performs worse than the naive approach. Over the test set i.e., to perform the prediction task, the regret based algorithm generates the smallest value for the absolute loss followed closely by the SVR.

Conclusion

In this article, we compared the performances of 5 learning methods: artificial neural networks, support vector machine methods, ARIMA process and regret based algorithm, over the PEMS-SF database which is a freely available machine learning repository [START_REF] Frank | UCI Machine Learning Repository[END_REF]. Over the test set i.e., to perform the prediction task, the regret based algorithm generates the better performances in terms of absolute loss minimization, followed closely by the support vector machine method. As a result, energy demand forecasters should favor one of these techniques.

One possible extension could be to use the regret based technique to select dynamically the best forecasting period between support vector machines, ARIMA and artificial neural networks.

It is worth mentioning that regret methods are all the more interesting since they enable the introduction of game theory to model interdependences between the agents composing the ecosystem and might provide economic guidelines.

Figure 1 :

 1 Figure 1: Example of a three layer neural network.

  (a) and of the data points corresponding to the week between day 67 and 74 in Figure 3 (b), and by comparing it with the true values. The black line represents the true measurements while the red points are the estimated ones, generated by the ANN.

Figure 2 :Figure 3 :

 23 Figure 2: The experimentally optimized three layer ANN used in our study.

Figure 4 :

 4 Figure 4: SVM as a binary classifier.

Figure 5 :

 5 Figure 5: Illustration of the kernel trick (source: Wikipedia).

  (a) and of the data points corresponding to the week between day 67 and 74 in Figure 6 (b), and by comparing it with the true values. The black line represents the true measurements while the red points are the estimated ones, given by the SVR method.

Figure 6 :

 6 Figure 6: Learning based on SVR over a week.

  (a). We see that there is a strong seasonality of 144 time periods (which corresponds to one day). We extract the seasonal part of the historical data and we draw again an autocorrelation diagram and a partial autocorrelation diagram which outputs are drawn in Figure 7 (b). We see that the remaining part of the (a) (b)

Figure 7 :

 7 Figure 7: Autocorrelation diagrams for the PEMS-SF data.

  Figure 8: Learning with an ARIMA process over a week.

Figure 9 :

 9 Figure 9: Learning with a regret based algorithm over a week.

Figure 10 :

 10 Figure 10: Comparison of the cumulative regret of regret based (black) and SVM (red) methods.

Table 1 :

 1 The methods are ranked from 1 to 5 over both sets. Smaller is the rank, smaller is the mean absolute error i.e., better is the method.In the last row of Table1, we have tested a naive learning approach based on the repetition of the Learning method v.s. Dataset Training set Test set Ranking of the learning algorithms based on the mean absolute errors.

			|y t -y|p t (y)
	L =	t∈S y∈Y	|S|
	where the set S can represent either the train-
	ing or the test set, 0 < |S| < +∞ denotes
	its cardinal and Y is the set containing all the
	possible road occupancy values over the dataset.
	At time period t, predictor p t is a density func-tion over space Y for the regret based learning
	method whereas it is a real belonging to Y in
	case where ANN, ARIMA process or SVR are
	used. As a result, in this latter case, the per-
	formance criterion can be sligthly modified to
	|y t -p t |
	give: L = t∈S

|S|

.

Acknowledgements

This work was supported by the European FP7 project Elvire and the Atomic Energy and Alternative Energies Commission (CEA).


Myriam Merad
email: myriam.merad@ineris.fr

Nicolas Dechy

Lisa Serir

Michel Grabisch

Frédéric Marcel

Using a multi

Keywords: Sustainable Development indicators, Sustainable Development action plan, Multi-Criteria Decision Aid, ELECTRE and Choquet Integral. Ac .12-15 Ac.12-16 Ac.12-13 Ac.12-14 Ac.12-20 Ac.12-19 Ac.12-7 Ac.12-18 Ac.12-8

come

Introduction

Sustainable Development (SD) within an Organization can be achieved by Corporate Social Responsibility (CSR). In France, CSR is denoted by Responsabilité Sociétale des Organisations (RSO) -Organization Societal Responsibility (OSR) and aims to find an equilibrium between economic, social and environmental considerations. With all these considerations, the management of the Organization is becoming more and more complex due to the increasing number of: (i) regulations to fulfill, (ii) other actors that are impacted by the decisions of the Organization who must be consulted and (iii) indicators (parameters or criteria) to follow.

As it has been commonly stated in classical economic and management theories, firms need to make profits in order to survive. However, management needs to adopt a viable posture in the face of a variable environment. This new vision promoted by the SD principle has changed the way profit, costs and risks are considered. Indeed, profit is not only financial quantification (e.g. euro), but also represents social and environmental gains (e.g. more diversity within the organization and less pollution). The SD principle needs a strong political engagement because of the constant need to seek equilibrium between economic, environmental and social concerns (see Figure 1) that cannot be obtained without the implementation of a participative governance model. To move from an ethical perspective of operation to an action, the SD principle requires methods and tools to be implemented. Multi-criteria decision aid methodology can help practitioners to deal with the expectations and perceptions of different actors with varied objectives to fulfill (economic, social and environmental). Our paper will focus on the contribution of multi-criteria decision aid methodology in outlining SD problems within the Organization and structuring recommendations for different actors inside and/or outside the Organization. We will also discuss various tools (aggregation procedures) that can be achieved in various contexts. We will cover these topics by discussing the use of multi-criteria decision aid methodology for the implementation of SD principles in a Public Organization whose mission is to prevent industrial and environmental hazards.

Multi-criteria decision aid methodology for the implementation of the SD principle within the Organization

To reach a sustainable development following the SD principle, the Organization should constantly seek for equilibrium (to reduce risks and increase benefits) with respect to interactions within its external environment (Figure 2 (a)).

SD and the different level of decision with the Organization

Different actions can be taken at different levels of decision-making within the Organization. These levels (Figure 2 (b)) are differentiated according to: (i) the practical objectives that are sought, (ii) the nature and the level of information/knowledge that is available and (iii) the potential impacts: The strategical level. At this level, the objective of decision-making is action planning. The decision is a long term decision (more than 8 years) and is dominated by both political and regulatory dimensions. At this level, the information is abundant but imprecise and difficult to sort and select.

The tactical level. The decisions/actions are less influenced by political and regulatory dimensions than at the strategical level. The decision is a middle term one (4 years). At this level, the decisions are under the constraints and objectives within the Organization (social, technical and economic). This level is represented by the intermediate staff of management.

The operational level. Decision-making pertains to short-term goals achieved in less than 1 year. The decisions made are more concrete involving technical information which is often specialized, precise, and more specific than the higher levels.

For each level of decision, the SD principle makes the decision maker reach for an equilibrium between economic, social and environmental concerns (risks/costs, benefits). The difficulty here is to both (i) clarify what measures (actions) must be taken at each level of decision-making and (ii) consolidate all the measures at each level in order to become a Societal Responsible Organization (SRO). In order to go beyond these limits, we have chosen to use a multi-criteria decision aid methodology. The methodology is based on a two-step approach. The first step consists in "outlining and structuring the problem". To do so, it is necessary to identify and explicit the stakes, the constraints, the actors and stakeholders concerned or affected by the SD problematic and then to choose the adequate method according to the level and to the nature of information and knowledge.

The second step is the "implementation of a method". This step consists in restructuring the available information according to the method to be used and analyzing the results of the method in order to provide the adequate recommendation to the decision-maker. The figure 3 describes these two steps. The problematic of "Description and structuring" (Figure 3, point 2) in decision sciences is a challenging problem. We have chosen to use an Organizational Analysis (OA) technique crossed with a "contextual diagnostic" to describe the SD problem [START_REF] Merad | Aide à la décision et expertise en gestion des risques[END_REF]. These two techniques are imported from social sciences and help to make explicit what is at stake and what are the rationale between actors inside and/or or outside the Organization.

Once the context is described, the Analyst should move to a prescriptive model (Figure 3, point 3).

MCDA is an interesting methodology that can help the Decision Maker (DM) in respecting the accountability principle that is a challenging aspect when dealing with sustainable development.

Multi-criteria decision aid methods: general principles

The great majority of decision aid methods tend to structure the decisional aid process into three principal phases: formulation of decision-aid problematic, exploitation, and recommendations (Figure 4). Formulating a decision-making problem consists in finding an adequate model for the decision-making process. In a context where reality is represented by a multi-criteria form, this first phase consists of:

Describing the decision making context and process. This requires the identification of the actors, their value systems and the different significant points that affect the decision making process which can vary in time.

Defining the actions that are elements of decision-making.

Identifying decision making situations which consists of looking at how the recommendation or the results should be presented (e.g., is the aim behind SD methodological or procedural with an intention to be repeated?); and identifying the spirit in which the decision aid process was designed.

Defining a set of criteria and a set of indicators and modeling the consequences of actions and drawing up criteria in order to compare the different actions with each other. This first phase is undoubtedly the most delicate one because the conclusions reached and the recommendations provided depend on the way in which the SD principle is considered. The second phase is more mathematical. The so-called operational phase consists of defining or choosing an "aggregation procedure" for the available information for each action with the aim of reaching an overall conclusion (recommendation) that will serve to lend support to the decision.

From a Partial Evaluation to an Global Evaluation: Aggregation

Aggregating the evaluations of an action x taking into account the evaluations of the different criterion j g and opinions on the importance that each player gives the F criteria is also a way of asking the question of compensation levels that one wishes to obtain between the criteria [START_REF] Vincke | Analysis of multicriteria decision aid in Europe[END_REF]. For every multi-criteria decision aid method there is a choice made of the kind of logic applied:

Compensatory. The most well known example is the case of a weighted sum. Consequently the aggregation methods found in this category range derive from the postulate that it is possible to compare, in an absolute manner, the various evaluations of an action x .

Consequently a high evaluation of one criterion 1 j g (g is the criteria function) will compensate for a lower evaluation of another criterion 2 j g .

Partially-compensatory. A certain level of compensation is acceptable.

Non-compensatory. Applying these kinds of methods, the evaluations of an action x based on criteria j g are not mutually compensatory.

Furthermore, there are several aggregation procedures that can be gathered into three categories, each relating to an operational approach to performance aggregation (Roy and Bouyssou, 1992):

Using a single summary criterion. This comprises summarizing the criteria family into a single criterion. In this approach incomparability is ruled out (see [START_REF] Bouyssou D | Aide multicritère à la décision[END_REF].

By upgrading the summary. This comprises moving from a comparison relationship drawn up for each criterion to a global comparison relationship. This approach accepts incomparability.

By reaching an interactive local judgment with trial and error iterations. If in the other two approaches the rules are set out to provide an exhaustive summary response, this is not the case here. This is because aggregating is the result of a sequence of local judgments.

Which aggregation procedures should be chosen for the implementation of the SD principle?

When facing the decisional problem that consists in the implementation of the SD principle, actors are brought to discriminate and/or choose between various options/actions/projects whose consequences are often badly controlled insofar as they are confronted with complex problems with multiple dimensions and whose stakes are often of big importance.

Looking at the literature about the use of Multi-Criteria Aggregating Procedure (MCAP) in the implementation of SD principles, we came to the following remarks:

• There is not a lot of research and work that has been done on the implementation of the use of MCAP to the implementation of the SD principle [START_REF] Faucheux | Multicriteria Decision Aid and the Sustainability Tree[END_REF]).

• MCAP is mainly applied as regards environmental management problems (Janssen, 1992 ; [START_REF] Munda | Multicriteria Evaluation in a Fuzzy Environment[END_REF][START_REF] Paruccini | Applying Multiple Criteria Aid for Decision to Environmental Management[END_REF] mainly in Canada [START_REF] Chevallier | Démarche Participative Multicritère pour la gestion environnementale[END_REF] and in Switzerland [START_REF] Maystre | Méthodes multicritères ELECTRE : Description, conseils pratiques et cas d'application à la gestion environnementale[END_REF][START_REF] Maystre | Aide à la négociation multicritère[END_REF].

• Methods such as ELECTRE (Hokkanen and Salminen, 1997 [START_REF] Kowalski | Sustainable energy futures: Methodological challenges in combining scenarios and participatory multi-criteria analysis[END_REF] provides an interesting synthesis of the methods applied to the energy management problems.

• We found only one document giving applications at the level of an Organization (company) [START_REF] Omann | Multi-criteria decision aid as an approach for sustainable development analysis and implementation[END_REF]. The case study presented is about how to obtain a sustainable Product Service Systems and the method used is based on MACBETH.

• Let us notice that the majority of studies published are generally at a national scale. The According to these observations, we have considered as central to try to elaborate some recommendations on the use of MCAP for the implementation of SD principle within an Organization. We have previously stressed the necessity to consider the fact that different levels of concern (levels of decision) coexist in the same Organization. We argue that for each level of concern, there is a set of characteristics that do constrain the decision aid process. These constraints can help us to make a choice between the different multi-criteria aggregating procedures (MCAP) used, also considering that each MCAP must respect specific assumptions and postulates. In a more generic way, Guitouni and Martel (1998) have proposed seven key questions to choose an MCAP.

These general questions are useful for global decision-making contexts. In a more specific context, De Monti and al. (2003,2004) and Omann ( 2004) have proposed respectively a set of quality criteria and a set of questions to respectively evaluate or choose MCDA methods when implementing the SD principle.

In our case, we wanted to propose a method to choose a MCAP when implementing the SD principle within an Organization. Based on the different papers listed above and the work done by [START_REF] Merad | Use of multi-criteria decision-aids for risk zoning and management of large area subjected to mining-induced hazards[END_REF][START_REF] Merad | Aide à la décision et expertise en gestion des risques[END_REF], we have proposed that the implementation of the SD principle within an Organization can lead to two major categories of problems:

Category A "A need to debate and initiate a dialogue between actors about the way to make SD principle move from philosophical concept to pragmatic and operational tool". The objective is to build a common representation of the boundary of the application of the SD principle and to rationalize the involvement and the investment in SD actions that will be done and will have an impact on both the tactical and the operational level within the Organization. In this category of problem the information is more qualitative and the actors involved are those that belong to the strategic and the tactical levels of decision (Figure 2).

As example: the implementation of the ISO 26 000 norm about Corporal Social Responsibility.

Category B "A need to rationalize the implementation of SD actions". In this category, the information is more quantitative and the actors involved are those of the operational level of decision (Figure 2). As example: the implementation of a Displacement Action Plan to reduce CO 2 emission.

This prophylaxis based on two categories leads us to suggest some conditions on the use of MCAP for the implementation of the SD principle within an Organization:

Category A. We suggest using MCAPs based on:

-MCAPs that are non-or only partially-compensatory such as summary upgrades.

-Preference structures (see Roy and Bouyssou, 1992) of types (S, R) seem of interest to us because the incomparability relation R invites the actors to question themselves on their representation of the problem, on the relevance of the set of criteria used, etc.

-Using information that is both quantitative and qualitative.

-The ability to let the different opinions of the actors and actors involved be explicitly expressed.

Category B. We suggest using MCAPs based on:

-Single summary criterion type PMCAs.

-Preference structures (see Roy and Bouyssou, 1992) of types (I, P) or even (I, P, Q) seem of interest to us. Given the strong tendency of operational actors to ask for precise data and concise conclusions, the incomparability relationship R is not seen as an invitation to debate, but a problem blamed on the method.

Hereafter, we will give an illustration on the use of the multi-criteria decision aid methodology focusing on the prescriptive phase (Figure 3) of the decision aid process. The illustration is the implementation of a Sustainable Development Plan (SDP) in a public institute of expertise. The results of the implementation of the descriptive phase are presented on the papers by [START_REF] Merad | Aide à la décision et expertise en gestion des risques[END_REF].

Two MCAPs were chosen based of these two categories:

ELECTRE III (see Roy and Bouyssou, 1992) to rank a set of SD actions. This MCAP offers the possibility of dealing with both qualitative and quantitative information and deals with the preference of a large variety of stakeholders with different backgrounds and constraints.

The Problem of ranking a set of SD actions is a decision problem done at a strategical level of the Organization. With ELECTRE III, we have the opportunity to use the preference structures of types (S, R). The S, R relations will help us in creating a deliberation context between stakeholders and discuss about the impact of the SD action plan (see category A).

Choquet integral (Labreuche and Grabisch, 2006) to rank actions to control energy consumption of the Institute's buildings. The problem is an operational and practical problem. The stakeholders involved are specialists in this field that are able to give precise information and that expect an (I, P) preference structure (see category B). Even if the SD principle has been known and defined since 1987 in the Brundtland report, it is quite innovative in the French public Organization to make explicit and rationalize a set of actions that will be followed each year, and contribute to SD, considering economic, social and environmental aspects. How can all the possible actions at INERIS be identified? How can we rank the actions from the most beneficial actions to the less beneficial ones?

Example of the implementation of the SD principle in a Public

In what follows, we have chosen to discuss the use of two methods to rationalize the SD principle.

Use of ELECTRE III MCAP for the ranking of SD actions for all the Institute

Actions to implement SD principles within the INERIS Organization are those which contribute to achieve an accepted equilibrium between environmental, social and economic constraints. An organizational analysis was carried out within the Institute. This analysis, mainly based on investigations aiming at explicating the nature of the relations between actors and the inherent stakes that influence the sustainability of the Institute, has helped us to identify more than 48 actions proposed by the staff [START_REF] Merad | Aide à la décision et expertise en gestion des risques[END_REF]. These actions were reduced to 22 actions that respect the constraints made by the ministry of Environment. These actions are presented in the table 1 below: These actions are under the responsibility of the top management staff within the Institute. Each of them has a different role and perspective but share common tasks that consist of seeking a financial equilibrium of their Division and defining a strategical vision (see Category A, chapter 2).

Set of criteria and weighting

These actions are coordinated by the General Director and his Advisory board (Staff of directors).

Criteria were needed to be able to organize a discussion between the Board of Directors and compare one action to the other according to the different available points of view. Two sets of criteria were asked to be necessary: expected benefits due to the implementations of the SD actions and necessary expenses due to the implementations of the SD actions. The 22 SD actions are assessed according to the three criteria of benefits and three criteria of cost (expenses).

a) Set of benefit criteria (see figure 5): The 22 actions have all positive impacts in terms of environmental, social and economic responsibility that can be estimated qualitatively. After a debate with the Board of Directors, we have considered that it was possible to identify 4 levels for each criterion. Each action takes a value going from 1 (the impact is difficult to estimate or does not have impact) to 4 (high level of impact): investments (e.g., equipment). Each action takes a value going from 0 (not possible to assess), 1 (low level) to 4 (high level) for the two criteria "Internal expenses" and "Investments" and a value of 0 (not possible to assess), 1 (low level) to 3 (high level) for the criterion "External expenses". To each level of the "External expenses" and the "Investments" criteria corresponds an interval in K€ (see figure 6). To each level of the "Internal expenses" criterion corresponds an interval estimated in man/year (see figure 6). The choice of criteria-specific weightings has required the formalization of the opinion given by the staff of Directors. We have chosen to use the 'cards method' [START_REF] Merad | Post mining management in the Lorraine region: method of grading of mining subsidence risk under building and infrastructure[END_REF]Figuera and[START_REF] Figueira | Determining the weights of criteria in the ELECTRE type methods with a revised Simos' procedure[END_REF] because this method is well-adapted to ELECTRE III and can help to frame a common representation of the SD strategic problem between the staff of directors. Each criterion is associated to a card and presented to the Directors that are asked to sort the cards from the least important to the most important criterion and to insert blank cards to indicate the relative importance among criteria from one rank to the next. This revised Simos method (Roy and Figuera, 1998) has many advantages, namely preventing criteria from being eliminated by a zero-weight assignment and incorporating the various weightings ascribed by Directors as a function of their expectations and preferences [START_REF] Merad | Post mining management in the Lorraine region: method of grading of mining subsidence risk under building and infrastructure[END_REF]. This method was applied separately to obtain one weighting set to the benefit criteria and another weighting to the cost criteria (see Table 2). Each of the three benefit criteria has an equivalent weight in the choice of the priority between SD actions. The weight of the internal expenses (D Int ) was considered to be equivalent to the weight of the investment (Inv). The weight of both the Inv and D Int are strictly higher than the external expenses (D Ext ).

From a partial to a global assessment of the SD actions

At this level of decision (strategical and tactical) see Figure 2 (b), most of the available information is qualitative. This is mostly due to the fact that there is a need to frame a common representation of strategical objective of the Institute once the actions are identified and the criteria specified. This problem belongs to the "category A" defined in chapter 2. The "category A" proposes a set of MCAP based on preference structures of types (S, R). The ELECTRE MCAPs (see Roy and Bouyssou, 1992) correspond to this category. The Institute is very familiar with ELECTRE methods and so we have decided to use ELECTRE III (see [START_REF] Merad | Use of multi-criteria decision-aids for risk zoning and management of large area subjected to mining-induced hazards[END_REF].

By conducting a set of interviews within the staff of Directors, it was possible to fill out the SD actions dashboard. Each action is coordinated by a Director. Each Director gives an estimation of the SD action according to the two sets of criteria. These assessments are carried out once per year and synthesized in "Impacts SD dashboard" and consolidated in a collegiate way.

Table 2. Impacts SD Dashboard

Each action is compared to the others according to the set of criteria defined in the table below.

After discussion with the staff of Directors we have been able to fix equivalence and preference thresholds for each qualitative criterion. The ELECTRE III method was run two times using the software ELECTRE III/V Version 3.1b for each set of criteria. Two credibility indices σ(a i ,a j ) and σ(a j ,a i ) are calculated each time for each pair of actions a i and a j of the 22 actions presented in Table 2. This calculation allows us to define an outranking relation between all the actions. It then became possible to draw up both a partial pre-order, that gives the possibility of having a situation of an incomparison between two actions, and a final pre-order presented in Table 3. 21 were considered before explaining their preferences as the most important actions to be done to become an OSR. The great majority of these actions are eco-responsible actions which means that they are considered as having a principal impact on the environmental sphere. In fact, the interview done with internal and external actors has shown that the minimum set of actions that have to be done to apply the SD principle are the actions listed below. This is why the achievement of the objective fixed in the action 5 "To control the use of paper" was considered as an emblematic ecoresponsible action for an Expertise Institution and is now considered in the calculation of the profitsharing of the workers of the Institute. Action 8 "To implement a Company Displacement Plan" that is seen as one of the most beneficial actions (rank 2) needs investments. This action has been given overwhelming support by the French Government, who considers action 8 as an interesting strategy to reduce the CO 2 emissions during the home-to-work commute.

Action 14 that consists of the development of a solidarity social economy (e.g., provide services to the Institute workers like caretaker's lodge) was at first considered as insignificant, but the ranking has shown that this action does not need a lot of investment, and can have an important impact for working conditions within the Institute.

Action 12 "To control energy consumption of institute buildings" was considered as a leading 2008-2009 action for the implementation of the eco-responsibility principle. The "Facility Manager" in the Institute is in charge of the implementation of this action. The following section is an illustration of the MCAP chosen to deal with an operational problem.

Use of Choquet Integral MCAP for the ranking of operational actions for the execution of the SD action 12 "To control energy consumption of institute buildings"

The Institute has launched a project for the rehabilitation of the inheritance built within the site of Verneuil (Picardy region in France) where a great part of the buildings are old (60 years or more). In 2008, an audit based on thermograph analysis has revealed that the buildings present an important thermal loss (between 150 and 500 kW/m²). Thus the Institute must establish an energy control policy (action 12), regarding French thermal Regulation promulgated in 2005, that has an ambitious energy objective, by reducing more than 30% of the consumption due to the use of heating.

The actors involved in the implementation of action 12 are working at an operational level. They have heterogeneous quantitative information about different actions that they think are interesting to implement (Category B see section 1.3). They would like to set a priority order on a set of 20 actions (see Table 4) that they have previously been identified. The Buildings n°3 and 10 are the most concerned by the implementation of SD action 12. An expert consulted within the Institute has noticed that due to the age, shape and high level of workers that work in these two buildings, they are at the first rank concerns of restoration.

Due to the fact that all the actions listed below cannot be implemented in the same year considering the fixed budget, it becomes necessary to give a decision aid support to the Division Manager in order to define a plan of works to be done, considering different points of view and criteria.

Set of attributes and partial assessment of the actions

Four criteria were identified by analyzing the audit report of 2008 and by considering experts' opinions and the expectations of the final Decision Maker (DM) who is an expert in energy. These criteria (attributes) are both qualitative and quantitative:

Efficiency (Eff). Legitimacy of the work to be done by comparing the investment cost with respect to the effective gain resulting from the action (score from 1 to 4).

Energy saving (Energy).

Estimation of percentage of the total energy saving (in %).

Carbon emission avoided (CO2).

Estimation of the "equivalent carbon" avoided after the end of the work (in Kg).

Hardness of the work (H).

Considering the duration of the work, its scope and its impact on the activity of the employees, the DM attributes a score from 1 to 4.

The DM would like to obtain a global score on each action. The analyst has then decided to use Choquet integral where the final score is calculated going from partial utility assessment of the action on each criterion to a global utility function.

MACBETH methodology [START_REF] Bana | On the Mathematical Foundation of MACBETH[END_REF] was used to determine the utility functions on each criterion. We first ask the DM to provide two significant levels for each criterion. For the criteria Energy and CO2, the DM considers the current situation unacceptable if there is no energy saving and if the avoided carbon emission is equal to 0 kg. A score equal to 1 for the criteria H and Now that the utility functions are defined, the next steps consist of defining the parameters of the Choquet-like aggregation function and of obtaining a ranking on the actions according to the Choquet integral.The identification method has been implemented within the Kappalab package [START_REF] Grabisch | kappalab: Non additive measure and integral manipulation functions[END_REF] for the GNU R (Development Core Team. R., 2005) statistical system where actions are presented as vectors with their partial utility score on each criterion.

From a partial to a global assessment of the actions

The global utility function of any action a was given by the following:

where were called the utility functions and F, non-decreasing in its arguments, was called the aggregation function.

, ,

Eff Energy CO H a a a and a were the scores (evaluations) given to each action over each criterion.

The overall utilities computed using the Choquet integral were presented in the table below where LS was calculated according to the least squares identification routine based on quadratic programming and HLS was based on the heuristic least squares identification routine. The Shapley values of the solutions (the Shapley value of i can be thought of as an average value of the marginal contribution

{ } ( ) ( ) T i T µ µ ∪ -
of criterion i to a subset T not containing it) and the interaction index's matrices (see figure 8) are given in the following tables: As one can see, both of the two solutions give the criterion Eff as the most important. In fact, the cost of an action must be justified. The criterion CO2 is less important for both models. HLS gives the importance of criterion H in second position, slightly weaker than criterion Eff. On the contrary, the LS model gives quasi identical importance to H and Energy. This difference can be explained by the small amount of data.

Both models give rise to the three most important criteria. CO2 does not seem to affect the global evaluation of an action. Concerning the interactions, we can see that Eff and Energy are complementary, whereas Eff and H are redundant. The rest of the pairs are quasi-independent.

According to these observations, we have finally explicated the global score e of an action a in the case of a 2-additive capacity where the variables

a a a and a are the scores on each

= + + + + ∧ + ∨ + ∨ + ∧ + ∧ + ∧
The 20 actions were ranked from the least important to the most important (see Table 7).

Table 7. Ranking of the 20 actions from the least important to the most important

The expected planning of works (ranking on actions) (see Table 7) was almost respected and accepted, except for actions 4, 9 and 3. In fact, the decision aid process applied using Choquet integral has offered the opportunity to the DM to reconsider some of his preferences on actions.

Discussion and conclusion

The Sustainable Development (SD) principle is difficult to implement within an Organization. SD principle seeks for more participation and more accountability in framing decision and choosing short and long terms actions to reach sustainability. There is rarely an optimal solution in SD but most frequently a need to build compromises between conflicting aspects such as economic, social and environmental ones and different expectations of stakeholders. Moreover, information is rarely available and precise. In this paper we have used a Multi-Criteria Decision Aid (MCDA) methodology to cope with these difficulties.

MCDA methodology offers the opportunity to avoid monetization of the different dimensions of the SD. These dimensions are not substitutable for one another and all have a role to play. MCDA is a branch of decision theory where actions or alternatives are chosen considering several points of view or criteria, assuming that the decision maker (DM) has all the information at his disposal concerning the alternatives, i.e., they are fully described by a vector of attributes which is supposed to be known without uncertainty. Two main features of this kind of problem make it difficult to solve. The first one is that attributes describing alternatives are heterogeneous, i.e., they represent different physical (or economical, subjective . . .) entities like price, size, color, weight, etc. and may be numerical or not. Hence a first difficulty is to make them commensurable in some sense. The second feature is that points of view or criteria are more or less important to make a decision, and most often they are conflicting or interacting in some way, so that it is not obvious how to combine them for reaching a final overall opinion.

There are several possible aggregation procedures in MCDA methodology. We have proposed a method to choose an adequate aggregation procedure for SD problems. Outranking approach (i.e., ELECTRE) easily solves the commensurateness problem by making pair wise comparisons. Monocriterion synthesis approaches (i.e., MAUT approaches) rely on the construction of utility functions, which can be fairly difficult because of incommensurability problems, but then easily reach a final decision by combining utilities or scores of all criteria.

In this paper we have implemented two aggregation procedures to rank SD actions within a public Organization: ELECTRE III at a strategical level of decision and MAUT method based on the Choquet integral at an operational level of decision within an expertise Institute. Both methods present advantages and difficulties in a real life situation. The implementation of the ELECTRE III method for the ranking of 22 SD actions offer the opportunity to discuss incomparability situations (R) where the actors involved can discuss their different visions and opinions about the implementation of the SD actions. However, the interest of the relation R is lost when dealing with more than 100 actions. That is due to the difficulty to read the final graph with all the comparison situations (I, P, Q, R). The Analyst is then obliged to use the final pre-order to communicate the results. But let us note that this method is easy to understand and communicate, perhaps due to the fact that the actors involved were familiar with this method that was used in daily situations for risk management and risk analysis problems (i.e., pesticide ranking, industrial accident scenario ranking, etc.). Nevertheless, it is difficult to explain to the DM that the final pre-order can change if new SD actions are introduced. Even if actors understand that this result is due to a pair wise comparison, they still consider that it is due to the non robustness of the method.

The implementation of the MAUT method based on Choquet integral was very helpful at an operational level. First, the engineer culture within the Institute is familiar with numbers and they appreciate the results of this method that offer the possibility of having a final score on actions that respect the incommensurability between the criteria. Second, this method offers the possibility of building a real interaction between the Analyst and the DM and testing the coherence on the action ranking. However, the main inconvenience is to request the DM to give a preliminary desired global score on the actions. This can be possible if the DM has a limited set of actions and if he knows the actions that he has to rank well.

One year after the implementation of the SD plan, the Ministry of Finance and Industry and the Ministry of Environment were both attracted by the ability of the MCDA methods to reach the goal of more transparency, more accountability and more participation in the way public funding are spent and the goal of sustainability is achieved. The Institute is now engaged in a sharing methodological process within the 60 public Organizations that are members of the SD French club.

In 2011, The Institute has started framing its second SD Plan for the period 2012-2015. The experience feedback learned from the implementation of the 1 st SD plan was that even if the participative process (including the 600 workers of the Institute and the other large set of stakeholders) was long, hard and expensive one, it has reach the objectives of being effective, legitimated by and transparent to all stakeholders. All the actions identified in the SD action plan were implemented and followed each year by the staff of Directors. Let us notice that even if one of the challenges of the SD plan was to open the scope of sustainability to social and economical dimensions, the first set of actions that was implemented was the one with the more environmental expected benefit (see table 1). We do think that this is due to the fact that these actions were the more strongly regulated by the environmental legislation.

2

To increase the percentage of products coming from biological agriculture in the collective restoration services.

3

To check the sources of origin of wooden products.

4

To use eco-labeled products for building cleaning.

5

To control the use of paper.

6

To inform and raise awareness among the staff about ecodriving during work displacements.

7

To only have vehicles (private cars) with less than 130g of CO2/km. 8

To implement a Company Displacement Plan. 9

To control waste management.

10

To have a reasonable management of Parks and of the arborical patrimony within the Institute. 11 To remove ink-jet printers for 2010. 12 To control energy consumption of institute buildings. 13 To implement durable policy of sourcing. 14 To contribute to the development of a solidarity social economy.

15

To consolidate the partnerships with the different actors of the SD.

16

To develop new managerial practices with respect to SD principles.

17

To develop better career management and to improve the well being in the Institute.

18

To invest the Institute in the social responsibility by taking care of our responsibility in handicap integration.

19

To implement a strategic watch in the field of SD to support project leaders and managers within the Institute.

20

To develop the exchanges of knowledge and know-how with our foreign partners and to capitalize the good practices.

Highlights

There is rarely an optimal solution in Sustainable Development (SD).

MCDA methodology offers the opportunity to avoid monetization of the different dimensions of the SD.

We have proposed a method to choose an adequate aggregation procedure for SD problems.

We have implemented two aggregation procedures to rank SD actions within a public Organization: ELECTRE III and MAUT.

Figure 1 .

 1 Figure 1. Sustainable Development principle

Figure 2 .

 2 Figure 2. The Organization and its environment (a) and 3 levels of decision in the Organization (b)

Figure 3 .

 3 Figure 3. Multi-criteria decision aid methodology: the link between the Analyst and the Decision Maker

Figure 4 .

 4 Figure 4. Multi-criteria decision aid method applied to the implementation of the SD principle

  application of the SD principle within an Organization (ex. company, plant, …) is largely different from a territory (ex. national, regional, …) mainly because of the number of DMs: one main in the case of the Organization (ex. the General director), and several when dealing with territories (ex. Mayors, all the general directors of the Organizations within the territory, local administrative authorities, …). It is also different because a territory is an open system (where coexist different levels of responsibility in terms of decisions and where the borders of what is in and what is out is not delimited legally speaking) and the Organization a more closed one[START_REF] Merad | Aide à la décision et expertise en gestion des risques[END_REF].

  Institute in the field of industrial environment and risks INERIS is a public institute in the field of industrial environment and risks, and works as a technical support for the French ministry of environment. As a public institute, INERIS must be exemplary when it comes to the implementation of the SD principle. In 2008, INERIS signed, with other public organizations, the Sustainable Development Charter. This one reinforces the engagement of the Institute in favor of the SD principle. In a letter addressed to INERIS on April 6, 2009, the French Ministry of Environment invited the Institute to frame a Sustainable Development Plan (SDP). In this SDP, the Ministry asked to: identify some strategic objectives, list a set of actions respecting 3 priorities (responsible sourcing, eco-responsibility, social responsibility) and identify a set of indicators to follow the execution of the actions at an operational level.

Figure 5 .

 5 Figure 5. Set of benefit criteria b) Set of expense (cost) criteria: The implementation of the 22 actions will represent an expense for the Institute. As presented below, three criteria will be used to estimate the surplus of expenses involved for the implementation of the SD actions: internal expenses (work done by the Institute staff), external expenses (e.g., scientific and technical subcontracting) and

Figure 6 .

 6 Figure 6. Set of cost criteria

Figure 8 .

 8 Figure 8. Shapley values and interaction index's matrices

Figure 1 .Figure 2 .Figure 3 .Figure 4 .Figure 6 .

 12346 Figure 1. Sustainable Development principle

Figure 7 .

 7 Figure 7. Details on the procedure used to define utilities * "Jugements consistants": consistant judgments. **"Rejet de carbone évité": carbone rejection avoidance.

Table 1 .

 1 List of 22 SD actions for INERIS

Table 3 .

 3 Ranking of the actions according to two sets of criteria This table has helped to start a debate between staff of Directors. Indeed, actions5, 7, 8, 11, 12 and

Table 4 .

 4 List of 20 actions for the buildings energy control at INERIS

Table 5 .

 5 A partial assessment of the actions

Table 6 .

 6 Rankings on the 20 actions

Table 1 .

 1 List of 22 SD actions for INERIS

		Eff	Energy	CO2	H	LS	Eff Energy	CO2	P	HLMS	Eff Energy	CO2	P
	LS	1.50	0.89	0.71	0.87	Eff	NA	0.23	-0.19 -0.29	Eff		NA	0.10	-0.18 -0.16
	HLS 1.29	0.80	0.69	1.21	Energy		NA	0.08	0.05	Energy		NA	0.10	0.08
						CO2			NA	-0.08	CO2			NA	-0.08
						P				NA	P			NA
					Figure 8. Shapley values and interaction index's matrices
	Id. Description							Environmental	SD domains Social	Economic
		Office automation: for 2010, 60% of the newly bought materials
	1	must have performance equivalent to the TCO Swedish reference, and comprise a minimum percentage of recycled
		materials.

21

  To reinforce the links between INERIS and NGOs. 22 To develop a SD culture within the Institute.

Table 2 .

 2 Impacts SD Dashboard

		Expected benefits			Expected costs
	Id. SD Actions	C Env	C Soc	C Eco	D Int	D Ext	Inv

Table 5 .

 5 A partial assessment of the actions

		u	Eff	u	Energy	CO u	2	u	H	Global score given by the DM
	Ac.12-1	4.5		0.26	0.95	0	2
	Ac.12-2	4.5		0.92	1.73	0	2.25
	Ac.12-3		9		5.12	9.59	20	11.5
	Ac.12-4		9		6.57	7.84	15	11
	Ac.12-5	18		6.94	8.05	7.50	12.25
	Ac.12-6	18		4.70	9.15	15	12
	Ac.12-7	18		20	14.02	17.5	16
	Ac.12-8	18		20	5.13	20	17.75
	Ac.12-9		9		3.93	20		15	11
	Ac.12-10		9		8.99	9.17	11.25	10.25
	Ac.12-11		9		9	13.63	11.25	10.75
	Ac.12-12	4.5		9	20		7.50	11
	Ac.12-13	16		9.01	13.63	15	13.75
	Ac.12-14	16		9	13.08	15	13.75
	Ac.12-15	16		9	8.81	15	12.75
	Ac.12-16	16		8.99	9.15	15	13
	Ac.12-17	18		20	8.94	20	19
	Ac.12-18	18		20	2.40	20	17.5
	Ac.12-19	18	12.80	4		11.25	14.75
	Ac.12-20	18		12	4		7.50	14.5

Table 6 .

 6 Rankings on the 20 actions

		Desired
		global	LS	HLS
		assessment
	Ac.12-1	2	2.43	2.15
	Ac.12-2	2.25	2.73	2.31
	Ac.12-3	11.5	11.73	12.66
	Ac.12-4	11	10.30	10.74
	Ac.12-5	12.25	12.58	12.18
	Ac.12-6	12	12.27	12.56
	Ac.12-7	16	17.69	17.42
	Ac.12-8	17.75	17.93	17.55
	Ac.12-9	11	11.75	11.57
	Ac.12-10	10.25	9.89	9.98
	Ac.12-11	10.75	10.95	10.66
	Ac.12-12	11	10.40	10.73
	Ac.12-13	13.75	13.04	13.53
	Ac.12-14	13.75	13.04	13.45
	Ac.12-15	12.75	13.02	12.83
	Ac.12-16	13	13.03	12.87
	Ac.12-17	19	18.24	18.02
	Ac.12-18	17.5	17.72	17.20
	Ac.12-19	14.75	14.49	13.86
	Ac.12-20	14.5	13.73	13.08

Table 7 .

 7 Ranking of the 20 actions from the least important to the most important Myriam Merad* , Nicolas Dechy* 4 , Lisa Serir**, Michel Grabisch***, Frédéric Marcel* * INERIS-BP 2 -F60550 Verneuil-en-Halatte (France) (e-mail : myriam.merad@ineris.fr, tel: +33 (0) 3 44 55 69 25) ** Département Automatique et Systèmes Micro-Mécatroniques, TEMIS, 24 r Alain Savary, F-25000 Besançon (France) *** Centre d'Économie de la Sorbonne, 106-112, Bd de l'Hôpital, 75013 Paris (France)

		Id.	Building n°3	Building n°4	Buildings Building n°5 Building n°7	Building n°10	Building n°79
	Least important	Ac.12-1

N. Dechy was at INERIS during the study and is now working at IRSN.

N. Dechy was at INERIS during the study and is now working at IRSN.

Eff are considered unacceptable. Then, the DM considers a score equal to 4 for the criteria H and Eff completely satisfactory, equivalent to respectively 30% economy saving and more than 15t of carbon emission avoided.

The analyst wanted to obtain a utility level between 0 and 20 because this range of information was meaningful for the DM (see figure 7). This way, the information about what is unacceptable and suitable on each criterion was quoted as following:

0 0 15000 20

and ( ) ( ) The MACBETH procedure was used according to M_MACBETH software. The DM was asked to express his preferences on each criterion among all the actions. The DM was also asked to provide a global score (see Table 5) on each action between 0 and 20. Although it was unrealistic to consider that this range of information can always be given, we have assumed that the DM was able to provide it (Table 6). This last information helps the Analyst in defining the expected results viewed by the DM.