Keywords: linear inverse problems, Bayesian estimation, maximum a posteriori, conditional mean estimation, penalized least squares

.

Conciliation d'a prioris sans préjugé

Rémi Gribonval * & Pierre Machart * * INRIA, Centre de Rennes -Bretagne Atlantique, prenom.nom@inria.fr Résumé. Il existe deux grandes familles de méthodes pour résoudre les problèmes linéaires inverses. Tandis que les approches faisant appel à la régularisation construisent des estimateurs comme solutions de problèmes de régularisation pénalisée, les estimateurs Bayésiens reposent sur une distribution postérieure de l'inconnue, étant donnée une famille supposée d'a priori. Bien que ces approchent puissent paraître radicalement différentes, des résultats récents ont montré, dans un contexte de débruitage additif Gaussien, que l'estimateur Bayésien d'espérance conditionnelle est toujours la solution d'un problème de régression pénalisée. Nous prsentons deux contributions. D'une part, nous étendons le résultat valable pour le bruit additif gaussien aux problèmes linéaires inverses, plus généralement, avec un bruit Gaussien coloré. D'autre part, nous caractérisons les conditions sous lesquelles le terme de pénalité associé à l'estimateur d'espérance conditionnelle satisfait certaines propriétés désirables comme la convexité, la séparabilité ou la différentiabilité. Cela permet un éclairage nouveau sur certains compromis existant entre efficacité computationnelle et précision de l'estimation pour la régularisation parcimonieuse, et met à jour certaines connexions entre estimation Bayésienne et optimisation proximale.

Mots-clés. problèmes linéaires inverses, estimation Bayésienne, maximum a posteriori, estimateur d'espérance conditionnelle, moindres carrés pénalisés

Abstract. There are two major routes to address linear inverse problems. Whereas regularization-based approaches build estimators as solutions of penalized regression optimization problems, Bayesian estimators rely on the posterior distribution of the unknown, given some assumed family of priors. While these may seem radically different approaches, recent results have shown that, in the context of additive white Gaussian denoising, the Bayesian conditional mean estimator is always the solution of a penalized regression problem. We present two contributions. First, we extend the additive white Gaussian denoising results to general linear inverse problems with colored Gaussian noise. Second, we characterize conditions under which the penalty function associated to the conditional mean estimator can satisfy certain popular properties such as convexity, separability, and smoothness. This sheds light on some tradeoff between computational efficiency and estimation accuracy in sparse regularization, and draws some connections between Bayesian estimation and proximal optimization.

Introduction

Let us consider a fairly general linear inverse problem, where one wants to estimate a parameter vector z ∈ R D , from a noisy observation y ∈ R n , such that y = Az + b, where A ∈ R n×D is sometimes referred to as the observation or design matrix, and b ∈ R n represents an additive noise.When n < D, it turns out to be an ill-posed problem. However, leveraging some prior knowledge or information, a profusion of schemes have been developed in order to provide an appropriate estimation of z. In this abundance, we will focus on two seemingly very different approaches.

Two families of approaches for linear inverse problems On the one hand, Bayesian approaches are based on the assumption that z and b are drawn from probability distributions P Z and P B respectively. From that point, a straightforward way to estimate z is to build, for instance, the Minimum Mean Squared Error (MMSE) estimator, sometimes referred to as Bayesian Least Squares, conditional expectation or conditional mean estimator, and defined as:

ψ MMSE (y) := E(Z|Y = y). (1)
This estimator has the nice property of being optimal (in a least squares sense) but suffers from its explicit reliance on the prior distribution, which is usually unknown. Moreover, its computation involves an integral computation that generally cannot be done explicitly.

On the other hand, regularization-based approaches have been at the centre of a tremendous amount of work from a wide community of researchers in machine learning, signal processing, and more generally in applied mathematics. These approaches focus on building estimators (also called decoders) with no explicit reference to the prior distribution. Instead, these estimators are built as some optimal trade-off between a data fidelity term and some term promoting some regularity on the solution. Among these, we will focus on a particularly widely studied family of estimators ψ that write in this form:

ψ(y) := argmin z∈R D 1 2 y -Az 2 + φ(z). (2)
For instance, the specific choice φ(z) = λ z 2 2 gives rise to a method often referred to as the ridge regression [START_REF] Hoerl | Ridge regression: applications to nonorthogonal problems[END_REF] while φ(z) = λ z 1 gives rise to the famous Lasso [START_REF] Tibshirani | Regression shrinkage and selection via the lasso[END_REF]. Do they really provide different estimators? Regularization and Bayesian estimation seemingly yield radically different viewpoints on inverse problems. In fact, they are underpinned by distinct ways of defining signal models or "priors". The "regularization prior" is embodied by the penalty function φ(z) which promotes certain solutions, carving an implicit signal model. In the Bayesian framework, the "Bayesian prior" is embodied by where the mass of the signal distribution P Z lies.

The MAP quid pro quo A quid pro quo between these distinct notions of priors has crystallized around the notion of maximum a posteriori (MAP) estimation, leading to a long lasting incomprehension between two worlds. In fact, a simple application of Bayes rule shows that under a Gaussian noise model b ∼ N (0, I) and Bayesian prior

P Z (z ∈ E) = E p Z (z)dz, E ⊂ R N , MAP estimation 1 yields the optimization problem (2)
with regularization prior φ Z (z) :=log p Z (z). By a trivial identification, the optimization problem (2) with regularization prior φ(z) is now routinely called "MAP with prior exp(-φ(z))". With the ℓ1 penalty, it is often called "MAP with a Laplacian prior". As an unfortunate consequence of an erroneous "reverse reading" of this fact, this identification has given rise to the erroneous but common myth that the optimization approach is particularly well adapted when the unknown is distributed as exp(-φ(z)).

In fact, [START_REF] Gribonval | Should penalized least squares regression be interpreted as maximum a posteriori estimation[END_REF] warns us that the MAP estimate is only one of the plural possible Bayesian interpretations of ( 2), even though it certainly is the most straightforward one. Taking one step further to point out that erroneous conception, a deeper connection is dug, showing that in the more restricted context of (white) Gaussian denoising, for any prior, there exists a regularizer φ such that the MMSE estimator can be expressed as the solution of problem [START_REF] Gribonval | Reconciling "priors" & "priors" without prejudice?[END_REF]. This result essentially exhibits a regularization-oriented formulation for which two radically different interpretations can be made. It highlights the important following fact: the specific choice of a regularizer φ does not, alone, induce an implicit prior on the supposed distribution of the unknown; besides a prior P Z , a Bayesian estimator also involves the choice of a loss function. For certain regularizers φ, there can in fact exist (at least two) different priors P Z for which the optimization problem (2) yields the optimal Bayesian estimator, associated to (at least) two different losses (e.g.., the 0/1 loss for the MAP, and the quadratic loss for the MMSE).

Contributions

Main result A first major contribution of our recent paper [START_REF] Gribonval | Reconciling "priors" & "priors" without prejudice?[END_REF] is to extend the result of [START_REF] Gribonval | Should penalized least squares regression be interpreted as maximum a posteriori estimation[END_REF] to a more general linear inverse problem setting (i.e. y = Az + b). In a nutshell, it states that for any prior P Z on z, the MMSE estimate with Gaussian noise P B = N (0, Σ) is the solution of a regularization-formulated problem (though the converse is not true).

Theorem 1 (Main result). For any non-degenerate prior2 P Z , any non-degenerate noise covariance Σ and observation matrix A, we have: 1. ψ MMSE is injective. 2. There exists a C ∞ function φ MMSE , such that for all vector y ∈ R n , ψ MMSE (y) is the unique global minimum and stationary point of z → 1 2 y -Az 2 Σ + φ MMSE (z). 3. When A is invertible, φ MMSE is uniquely defined, up to an additive constant.

For further details about the characterization of φ MMSE (z), see [START_REF] Gribonval | Reconciling "priors" & "priors" without prejudice?[END_REF]. It is worth noting that its construction uses techniques going back to Stein's unbiased risk estimator [START_REF] Charles | Estimation of the mean of a multivariate normal distribution[END_REF].

Connections between the MMSE and regularization-based estimators Some simple observations of the main theorem can shed some light on connections between the MMSE and regularization-based estimators. For any prior, as long as A is invertible, there exists a corresponding regularizing term. It means that the set of MMSE estimators in linear inverse problems with Gaussian noise is a subset of the set of estimators that are produced by a regularization approach with a quadratic data-fitting term.

Second, since the corresponding penalty is necessarily smooth, it is in fact only a strict subset of such regularization estimators. In other words, for some regularizers, there cannot be any interpretation in terms of an MMSE estimator. For instance, as pinpointed by [START_REF] Gribonval | Should penalized least squares regression be interpreted as maximum a posteriori estimation[END_REF], all the non-C ∞ regularizers belong to that category. Among them, all the sparsity-inducing regularizers (e.g. ℓ 1 norm) fall into this scope. This means that when solving a linear inverse problem (with an invertible A) under Gaussian noise, sparsity inducing penalties are necessarily suboptimal (in a mean squared error sense).

Relating desired computational properties to the evidence Let us now focus on the MMSE estimators (which also can be written as regularization-based estimators). As reported in the introduction, one of the reasons explaining the success of optimizationbased approaches is that one can have a better control on the computational efficiency of the algorithms via some appealing properties of the functional to minimize. An interesting question then is: can we relate these properties of the regularizer to the Bayesian priors, when interpreting the solution as an MMSE estimate?

For instance, when the regularizer is separable, one may easily rely on coordinate descent algorithms [START_REF] Nesterov | Efficiency of coordinate descent methods on huge-scale optimization problems[END_REF]. Even more evidently, when solving optimization problems, dealing with convex functions ensures that many algorithms will provably converge to the global minimizer [START_REF] Boyd | Convex Optimization[END_REF]. As a consequence, it is interesting to characterize the set of priors for which the MMSE estimate can be expressed as a minimizer of a convex or separable function.

The following lemma precisely addresses these issues. For the sake of simplicity and readability, we focus on the specific case where A = I and Σ = I. Lemma 1 (Convexity and Separability). For any non-degenerate prior P Z , Theorem 1 in [START_REF] Gribonval | Reconciling "priors" & "priors" without prejudice?[END_REF] says that ∀y ∈ R n , ψ I,I,P Z (y) is the unique global minimum and stationary point of z → From this result, one may also draw an interesting negative result. If the distribution of the observation y is not log-concave, then, the MMSE estimate cannot be expressed as the solution of a convex regularization-oriented formulation. This means that, with a quadratic data-fitting term, a convex approach to signal estimation cannot be optimal (in a mean squared error sense). One may also note that the properties of the regularizer explicitly rely on properties of the evidence p Y rather than these of the prior P Z directly. This is reminiscent of former interesting results in [START_REF] Raphan | Learning to be bayesian without supervision[END_REF].

Worked example : the Bernoulli-Gaussian model

It is worth noting that the results of this section (and further details about them) can be found in our research report [START_REF] Gribonval | Reconciling "priors" & "priors" without prejudice?[END_REF]. However, they are currently unpublished. The Bernoulli-Gaussian prior corresponds to the specific case of a 1-D mixture of a Dirac (with a weight p) a Gaussian. This prior is often used as marginal distribution to model high-dimensional sparse data, as the value z = 0 is drawn with a probability p > 0. Naturally, this prior is not log-concave for any p > 0. However, due to its smoothing effect, the evidence p Y can still be log-concave as long as the noise level is high enough.

We obtain Figure 1 depicting the maximal signal-to-noise ratio (SNR) ensuring that the evidence p Y is log-concave, as a function of the sparsity level p. We notice that when p → 0 (i.e., the signal is not sparse), the maximal SNR goes to +∞. This means that for any level of noise, the evidence (which becomes a simple Gaussian) becomes log-concave. On the other hand, when p → 1 (i.e. the signal is very sparse), the maximal SNR goes to -∞. Moreover, the curve is monotonically decreasing with p. In other words, the higher the sparsity level, the lower the SNR (hence the higher the noise level) needs to be to ensure that the evidence p Y is log-concave. Furthermore, one can note that even for a relatively low level of sparsity, say 0.1, the evidence p Y cannot be log-concave unless the SNR is smaller than 9dB. As a consequence, when using penalized least-squares methods with a convex regularizing term, the resulting estimator cannot be optimal (in a mean squared error sense) unless the observations are very noisy, which basically means that the performances will be poor anyway.

Figure 1 :

 1 Figure 1: A plot of the maximal SNR so that p Y is log-concave (hence φ is convex)

  1 2 y -Iz 2 + φ I,I,P Z (z). Moreover, the following results hold: 1. φ I,I,P Z is convex if and only if p Y (y) := p B ⋆ P Z (y) is log-concave, 2. φ I,I,P Z is additively separable if and only if p Y (y) is multiplicatively separable.

which is the Bayesian optimal estimator in a 0/1 loss sense, for discrete signals.

We only need to assume that Z does not intrinsically live almost surely in a lower dimensional hyperplane. The results easily generalize to this degenerate situation by considering appropriate projections of y and z. Similar remarks are in order for the non-degeneracy assumptions on Σ and A.


Thècle Alix
email: thecle.alix@ims-bordeaux.fr

Bruno Vallespir
email: bruno.vallespir@ims-bordeaux.fr

A framework for product-service design for manufacturing firms

Keywords: Product-service systems, service value, service engineering

Manufacturers propose services around the products they deliver to increase their competitiveness and reach objectives of profitability satisfying specific customer needs. Loyalty can be obtained under the condition that isolated offerings are replaced by integrated value adding solution composed of a product and of one or more product-service. The design of such solution requires to take account of four narrowly overlapping dimensions: the product, the product-service, the process and the organization. A challenge is to propose a model to support the firm core competence widening taking account of all the dimensions together, analyzing how they are interlinked and how they allow to design the coherent value adding solution. In this paper the two first stages of a methodology for new product-service development for manufacturing firms are presented that take account of firm's environment, core competence, processes as well as the benefits expected by service delivery and the service value.

Introduction

Service activities have become since few years a current way to differentiate from competitors and make customers loyal. Manufacturers propose services around the main product they deliver and customer loyalty can be obtained under the condition that isolated offerings are replaced by integrated value adding solution composed of the product and associated product-service [START_REF] Furer | Le rôle stratégique des services autour des produits[END_REF]. Consequently they must be thought and designed together before being sold as an integrated offer.

Even if currently the way of doing of industrialists is far from a co-design productservice system concept [START_REF] Baines | State-of-the-art in product-service systems[END_REF], a survey performed during the summer 2008 [START_REF] Alix | Product-service value analysis: two complementary points of view[END_REF] has shown that most of the services proposed by big manufacturing companies are dedicated to the core product and that they are developed accordingly. For the most part, they are completely integrated in the product offer (for 75% of them) and performed by the manufacturing company (for 95%). Underlying objective of profitability can be reached under the condition that firms manage all the changes that are necessary to deliver a service, as well as the transition allowing to reach the stable condition of product-service high value solution provider.

Changes to control can be split in: (i) Strategic changes due to the necessity to define common organization, management and control principles, (ii) Marketing changes as the analysis and understanding of the customers requirement to provide the good service (high value) is crucial, (iii) Commercial changes to determine the differentiation potential regarding competitors to valorize the offer and make it worth in the eyes of the customer, (iv) Economical changes as the product functionalities centric discourse had to be changed in an integrated value centric one to convince the customer and (v) Cultural modifications of firm employee's skills and focus that must be less technical and back office and more commercial and front office. The design and delivery of an integrated solution requires to take account of four narrowly overlapping dimensions related to: (i) the product (object that corresponds to the firm core competence, initial object of the selling), (ii) the product-service (service supplied in addition to the product and increasing its value for the customers), (iii) the processes (used to create the product and/or the product-service) and the organization (the context in which the process unfold is launched); while managing the value, risks and knowledge inherent to new development (Fig. 1).

Fig. 1.

From manufacturing business to product-service solution providers business.

Service research is wide and integrates different communities who have already responds to some problematic [START_REF] Berry | Relationship marketing of services -growing interest, emerging perspectives[END_REF], [START_REF] Fisk | Services Marketing Self-Portraits: Introspections, Reflections, and Glimpses from the Experts[END_REF], [START_REF] Lovelock | Marketing des services[END_REF], [START_REF] Zeithaml | The behavioral consequences of service quality[END_REF] but as Wild et al. mentioned it "each discipline involved in service research appears to have their own dogma and mythology, and all too often end up with minimal interaction with relevant areas" [START_REF] Wild | A framework for Cross Disciplinary Efforts in Services Research[END_REF]. A cross disciplinary approach could be useful to combine the points of views, analysis methodologies and tools to properly cover all the aspects of service delivery and to help characterize the stable condition abovementioned.

The challenge is then to propose a method to support firm core competence widening taking all the dimensions and changes into account, analyzing how they are linked and how they allow to design the coherent value adding solution using the most appropriate methodologies and tools whatever the discipline is concerned. To reach this objective, we propose to analyze new product-service development using a project management centric view as it encompasses the firm's environment, core competence, process, organization as well as benefits, risks and value.

Based on the previous hypothesis, we assume that the project of product-service development can be split as any project of product design in four main steps (Fig. 2.): -The first common step consists in a starting sequence and allows to analyze customer expectations and to explore the positioning of the firm. This is a sort of strategic analysis based among other things on the study of environmental factors and criteria allowing to determine the strengths, weaknesses, opportunities and threat of the new development and to choose between several different ones. This step is discussed in section 3.

-The second step is a definition sequence that allows to precise the specifications of the product-service to deliver and its value for both the customer and the manufacturer. Based on a functional analysis and a value engineering approach, value results can be gathered in a matrix that can be used as a strategic tool to analyze the relevance of a product-service offer that integrates the costs of design and delivery as well as the mercantile strategy. This step is developed in section 4.

-The third step corresponds to the realization sequence whose objective is, in that particular case, to define the process from the design of the service to its delivery. The definition and modeling of the processes is out of the scope of this contribution.

-The fourth and final step is the closing sequence. It corresponds to the real service delivery to the customer and capitalization of project experience. This aspect is also out of the scope of this paper.

Support activities concerning delay, cost, risk, organization, communication and knowledge management specific to the project are mandatory to ensure the new development success. Main aspects of their concern are skimmed over in Fig. 2.

Fig. 2. Sequences and activities of a project of new product-service development

This project must also come within the scope of the firm and be coherent with the core product development, existing process and organization. This implies that all the data related to these 3 items have to be compiled with data coming from the operational and support activities as sort of control.

Starting sequence

As outlined in section 2, the starting sequence proceeds to a strategic analysis that consists in a diagnosis and strategic segmentation [START_REF] Alix | New product development: material versus immaterial[END_REF]. The diagnosis can be performed using the SWOT matrix.

The SWOT matrix to diagnose and position the firm

The SWOT analysis (Strengths, Weaknesses, Opportunities and Threats analysis) is a tool for auditing an organization and its environment. It can help managers to determine if their objective -in term of new development for example-is attainable or not by the identification of internal and external key factors useful to achieve them. The SWOT analysis gathers key pieces of information in two main categories: -Internal factors cover strengths and weaknesses internal to the organization that are helpful or harmful to achieve the objective. Usually, they include the 4P's of mix marketing (Product, Price, Place, Promotion); as well as personnel, finance, manufacturing capabilities, etc. The customer's requirements in term of service associated to the product are taken into account by the way of the mix marketing study that will reveal the components of the value for the customers. Note that in that case the first P stands for product-service.

-External factors concern opportunities and threats that are helpful or harmful external conditions to achieve the objective. They include macroeconomic matters, technological change, legislation, and socio-cultural changes, as well as changes in the marketplace or competitive position.

All these factors gathered in a matrix permit to define the risks and benefits of a new product development strategy. If the objective is attainable, the SWOTs can be used as inputs to the creative generation of possible further strategies.

List of internal factors: strengths and weaknesses

The identification of strengths and weaknesses can be done regarding inside the firm and analyzing its culture and main economic functions in term of organization, product and process and their interrelations. Then, taking account of the changes mentioned in section 1, internal factors may stem from: -Firm culture and organization: enterprise identity, brand image, organisation structure mode; industry specialization; project experience, membership, sales office; -Marketing and commercial ins and outs aspects: market share, Product-service / Price / Place / Promotion coherence; -Human resources ins and outs: skills; motivation, involvement, project team, project manager, top management commitment, contact personnel training, contact personnel quality, sales team; -Financial ins and outs: results, benefits, possibilities of investment and investors; -Technical ins and out as a product-service can be material or not and/or technologically complex in particular if it uses TIC. Then factors coming from design (technological innovation potential, R&D opportunities) and production (Capacity/load ratio; Delay; Partners relationship; Resource competencies, stock level Production, service definition, process definition identified procedures) are relevant to analyze product-service development.

The justification of each factor and sub factor is given in [START_REF] Alix | Product-service value analysis: two complementary points of view[END_REF].

List of external factors: opportunities and threats

External factors stem from the study of the micro-, macro-and meso-environment of the firm. The Macro-environment picture can be obtained by the way of a PEST analysis (Political (and legal), Economic, Social, Technological). The PEST factors can be used to assess the market for a business or organisational unit strategic plan [START_REF] Armstrong | A handbook of Human Resource Management Practice[END_REF]. The micro-environment can be studied by analysing the firm' strength and weakness regarding the five strengths of its sector of activity: the relationship with its customers, with its suppliers, the competitor's pressure, the threat of new competitors and the substitute products [START_REF] Porter | The Competitive Advantage: Creating and Sustaining Superior Performance[END_REF]. The Meso-environment focuses on person that could influence the economical relations in a market. The list of external factors and sub factors of interest is detailed in [START_REF] Armstrong | A handbook of Human Resource Management Practice[END_REF].

Definite list of factors

The factors abovementioned can be gathered by aggregation and according to their relevance in the following set: Project team, Manufacturing resources, Technological potentiality, Operations/ process, Partners relationship, Brand image, Cost base, Cash flow, Sales team, Distribution, Political environment, Economic outlook, Cultural changes, Technical context, Customers position, Suppliers position, Competitors position, Substitute, Product to integrate [START_REF] Alix | Product-service value analysis: two complementary points of view[END_REF]. Note that we do not mention if an internal factor is a strength or a weakness as there is a continuum between both; id. for the threats and opportunities. The project team leader will first have to determine the consequences of a factor: whether it is a benefit (strength or opportunity) or a risk (weakness or threat). Subsequently, the relevance of each internal factor as well as the probability of occurring of each external factor will be defined. Finally the impact of each factor on the organisation could be discussed and results plotted in a chart (see © Copyright MarketWare International 2001-2004). A visual representation of the risks and benefits of a new product-service development could be obtained and compared to other ones. The position of the firm will result from the comparison that takes parameters relative to the product, organisation and processes into account by the way of the factors.

The definition sequence consists, once the development direction is chosen, in defining the solution that will be profitable for both new manufacturer and customers; to determine its position in the portfolio of the firm and its legitimacy to be proposed and enhance firm competitiveness and profitability.

This second stage rests on the use of the value analysis methodology and compares the value of the offer for the manufacturer taking account of its expected benefits and the value of the same offer for the customers defined by the way of expected quality criteria. All these developments are based on the assumption that the value can be defined by the ratio between the performance of some functions and their cost [START_REF] Goyhenetche | Le marketing de la valeur, Créer de la valeur pour le client[END_REF].

Currently two functions are defined: (i) "basic function" which correspond to anything that makes the product work or sell and (ii) "secondary functions" or "supporting functions" that describe the manner in which the basic function(s) are implemented

Product-service value analysis: from the manufacturer point of view

We assume that the functions which participate to the definition of the value for the provider focus on the expected benefits of a product-service proposal. Based on [START_REF] Baglin | Le developpement d'offres de services dans les PMI[END_REF] and a literature review in the management area, benefits usually mentioned concern: (i) the construction of a customer loyalty by the building of dependency relationships between a consumer and a provider that can lead toward profitability, (ii) the search for differentiation that allows retaining and attracting consumers, (iii) the increase and stabilizing of firms' turnover due to the possibility to generate regular income and to have cash flow disposal, (iv) the corporate image reinforcement linked to technological advanced, product quality... (v) the occupation of an existing or new market to participate to market share division, (vi) the possibility to create alliance with service providers and to share risks, (vii) the possibility to increase the quickness of a design or production process using product-service based on information and communication technologies, (viii) the possibility to shorten sales delay or negotiation phase using financial services and (ix) the search for a product-service system that is designed to have a lower environmental impact than traditional business models [START_REF] Alix | Product-service value analysis: two complementary points of view[END_REF].

Each benefit can be defined as expected performances that stem from a strategy and have priorities one to the other. Quantifiable criteria can be associated to each one whose level also stem from the strategy. The level really measured, that reflect the performance of the function, compared to the global cost of the service allows to determine the value of the service for the firm.

Costs to take into account can be divided in direct and indirect costs. Regarding product-service characteristics, several costs can be addressed that depends (i) on its degree of tangibility, (ii) on the degree of interaction that is necessary between the firm contact personnel and the customer to deliver it and, (iii) on the degree of standardization of the product-service delivery process. They can encompass component costs, cost of labor, and overheads.

The description of the functions from the manufacturer point of view and the consciousness of the product-service costs allow to build a value analysis matrix [START_REF] Alix | Product-service value analysis: two complementary points of view[END_REF].

Product-service value analysis: from the customer point of view

According to [START_REF] Hermel | La qualité de service[END_REF], customers challenge the overall value of an offer to its complete cost. The overall value refers to the different advantages obtained, supported by the firm brand image. Advantages may gather both benefits expected on technical functionalities and subjective criteria as lots of studies have shown that customers are waiting for something from the exchange with the firm. [START_REF] Zeithmal | Delivering quality service[END_REF] has proposed a list of criteria and dimensions allowing to evaluate the quality of a standard service These criteria can be associated to implicit functions whose fulfillment can lead to customer loyalty and value increase.

Then, the list of functions of a product-service expected by customers consists in: (i) the product-service raison d'être: help choosing, acquiring or using the main product [START_REF] Furer | Le rôle stratégique des services autour des produits[END_REF], (ii) secondary functions linked to its interactions with the contact personnel, users and means necessary to realize it, the partners, environmental and legislative constraints and the realization constraints as mentioned previously and, (iii) the implicit functions coming from quality criteria discharged from the functions that refers to the delivery process: to obtain a tangible service.

The value determined by the firm from the customer point of view will be determined by putting in opposite the previous list of function and the distribution of the above mentioned costs via another value analysis matrix.

Synthesis

Using aggregation operator, it is possible to deduce the whole value of the productservice proposed by a manufacturing firm. This one can have two positions: high or low and can be analyzed regarding two dimensions: the customer dimension and the firm dimension Fig. 3.

Firm value

High Low

Customer value

High

The product service is profitable for the firm and satisfies customers. It might accompany the product

To make the customer loyal, firm may propose the service but found solution to increase its value by decreasing its price if it is worth in the eye of the consumer or adding others services located in the high/high value.

Low

This position is synonymous of customer loyalty if the customer participates or if the cost of the offer is not too important. Otherwise, he won't be interested by this list of sales point.

The abandon of the product-service or not will depend on the cash that is necessary to provide it or on the delivering difficulties The value analysis of each product-service coherent with the firm position from the two points of view will provide a synthetic view of the equilibrium of the global offer. To ensure firm global profitability, the portfolio of product-services has to be shared out between all categories (High/low).

Conclusion

We have proposed in this contribution the two first steps of a methodology in four steps to support manufacturing firm core competence widening by the furniture of product-service taking account of the changes that are necessary to become a "service" as well as the product, the organization and its process. The first step developed here provides keys to choose an orientation for product-service new development. The second step allows to analyze the relevance of a product-service offering based on its value analysis. Further works include the definition of tools to help characterize the two last steps as well as a refinement of the two first one.

Figure 3 :

 3 Figure 3: Value matrix

Process


Mounir Badja
email: mounir.badja@ims-bordeaux.fr

Wael Touzi
email: wael.touzi@ims-bordeaux.fr

Thècle Alix
email: thécle.alix@ims-bordeaux.fr

Contribution to the definition and modeling of service and service activities

Keywords: Service characteristics, Service modeling, Process modeling

For a long time, it was highlighted that the service is intangible or immaterial; these characteristics are mainly used to distinguish the service, making it incomparable with good. The set of proposed definitions and characteristics that led to debates between specialists in economics for several years and gave place to a variety of visions and approaches are still not consensual and science engineers challenge. Goal of this paper is to present, on the one hand, the existing literature proposed by economists concerning services (definitions and specificities) and, on the other, arguments proposed by science engineers that challenge them. That study allows us to propose a generic definition of what a service is and a preliminary model of a service activity.

Introduction

Services have been recently powerful engines of economic growth in many economies with such sign that today, a developed economy, would be a "tertiarized" economy [START_REF] Edvardson | Service portraits in service research: a critical review[END_REF]. Economists, Marketers, Human Resource Managers have studied the service economy, service marketing and service relation for a long time [START_REF] Berry | Relationship marketing of services -growing interest, emerging perspectives[END_REF], [START_REF] Fisk | Services Marketing Self-Portraits: Introspections, Reflections, and Glimpses from the Experts[END_REF], [START_REF] Zeithaml | The behavioral consequences of service quality[END_REF]. All have proposed definitions, associated different characteristics and defined specific tools for management. Now that services represent a way to innovate in any sector of activity and since they have spread, particularly in the manufacturing area to differentiate from competitors and offer advantages, it becomes obvious to increase service efficiency and to cross disciplinary efforts to enrich services research [START_REF] Wild | A framework for Cross Disciplinary Efforts in Services Research[END_REF]: -Academics belonging to the manufacturing community are interested in investigating this sector and propose methods and tools to help modeling and controlling firms that are redeployed in product-service systems.

-Industrialists, for their concern, aims at developing coherent tools to manage efficiently service offers and service innovations that are synonyms of profitability and customers' loyalty.

Defined by these latest in a rather negative sense and considered as residual, dependent on manufacturing, technologically backward and not very innovative for a long time, services activities and services in general receive now a better echo. Studies led concern service delivery systems analysis, service operation management, business process modeling, service quality evaluation and performance measurement, service value, service engineering, etc. and meet the studies already performed.

All these investigations that are necessary to deliver high value to the customer and to reach firms' objectives in terms of profitability and durability rest on the understanding of what a service is conceptually and on the analysis of the differences and similarities between products and services to help manufacturers understand what is specific to service delivery and what might be adapted. On the basis of a literature review presented in the following part and, on a qualitative survey presented in the third part of this paper, a definition and modeling principles are proposed in the fourth part before concluding.

2

Definitions and characteristics of services in the literature review

Service definitions

A general consensus exists regarding the definition and execution of industrial production activities; it is less certain for the questions related to services, service activities and service execution. This is mainly due to the structural change of the service sector and to the historical tradition to consider services as a homogenous residual of a more "productive" manufacturing. Indeed, service is a complex and subjective matter, which allows individual interpretation and perception.

Nevertheless, it is useful to present some literature definitions to structure our approach and to better define the different characteristics of services that will be used thereafter for the model. The ones that are proposed here are the most cited in the literature: -"A service may be defined as a change in the condition of a person, or of a good belonging to some economic unit, which is brought about as the result of the activity of some other economic unit, with the prior agreement of the former person or economic unit" [START_REF] Hill | On Goods and Services[END_REF].

-"Service is a transformation of existence mode and/or dispositions of the person himself, of his body and his mind. While goods modify the existence conditions, services modify the existence modes, where goods are only supports" [START_REF] Zarifian | Evénement et sens donné au travail[END_REF].

-"A service is an act (or a succession of acts) of duration and localization defined, achieved thanks to human and/or material means, implemented for the benefit of an individual or collective customer, according to processes, codified procedures and behaviors" [START_REF] Dumoulin | Entreprise de service: 7 facteurs clés de success[END_REF].

These definitions have in common the notion of activity or process, the notion of time and the concept of interaction between a supplier and a customer. They all gather characteristics that led to the definition of specific tools and methods of analysis and management.

Characteristics of services

Researchers started to enumerate distinctive characteristics of services in order to distinguish them from goods [START_REF] Lovelock | Marketing des services[END_REF] [10] [START_REF] Alix | Gathering production Process of services and goods: towards the mixed enterprise[END_REF]:

-A service is not owned, but there is a restricted access.

-Services have intangible results.

-Customers are involved in the service production process.

-Other persons than the customer can be involved in the service process.

-Quality in service is difficult to control while increasing productivity.

-Quality in service is difficult to apprehend.

-Service cannot be stored.

-Service delivery delay is crucial.

-Service delivery integrates physical and electronic way.

Based on these assertions, four characteristics named IHIP characteristics (i.e. Intangibility, Heterogeneity, Inseparability and Perishability characteristics) have merged to exemplify a service.

As related by the management literature, there are also some key characteristics that are common of all service activities. The main features of the service activity stems from the specific role played by the customer source of other attributes such as a co-production with the firm contact personnel and an uncertainty concerning the service outcome link to the conditions of the interpersonal exchange [START_REF] Hill | On Goods and Services[END_REF].

Qualitative survey

A new community coming from the engineering science is investigating the service domain. In order to cross the points of view and enrich our understanding on services, a survey was carried out by the way of several interviews of engineers. Performed in facing each other, they focused on three main themes: an individual definition of services and associated characteristics, an analysis of the link existing between a product and a service and finally a comparison of the key elements to manage to produce a product and a service or more specifically a comparison between the model of production of a product and the "servuction" model.

Presentation of the qualitative survey

About eleven engineers were questioned during the survey carried out by two persons in the following way: a document presenting the results of the literature review was performed and sent to the interviewed persons by e-mail. Appointments were taken and conversations on the above-mentioned themes were recorded.

Processing and analysis of interviews

During the interviews, each interviewee expressed his own opinion on a service definition. Gathering and analysing these definitions, we have noted some key elements: -The service is an answer to a need, -The human factor impacts the production of the service, -The service process impacts its as well as all the elements which play a role during its execution, -An ontology of service might be defined because of the multiplicity of terms used and underlying concepts.

Concerning the characteristic of inseparability and perishability, there was a total convergence of views. Interviewees were also in agreement with the fact that a service is produced at the same time it is consumed. Concerning the intangibility and heterogeneity characteristics, the points of view diverge.

Indeed, regarding the intangible nature of service (in the sense of impalpable), 80% of respondents supports this hypothesis but affirm that the value and effect of service is tangible and that the service should be supported by substantial resources.

Regarding the heterogeneity of services, opinions are more divided. 20% think that service is homogenous and 30% of respondents have a shared view on the subject. Note that, here, heterogeneity is defined by the fact that "... a same service has a different result according to the person who provides it, the customer who receives it and the moment when this exchange is done" [START_REF] Eiglier | Servuction: Le Marketing des Services[END_REF]. This difference in opinion stems from the fact that some think that service is heterogeneous with a generic base, and also depend from a deference between customer view (perceived service) and supplier view (delivered service).

Regarding the characteristic of storability, although opinions are divided, the majority thinks that service is non-storable due to the impossibility of their storage (the service being an interaction between customer and provider). Some others think that a service is storable and affirm that it can be viewed as a sort of pass for press.

For perishability, the concept of time could be a common discriminator between a product and a service as a service might meet a need during a limited time (e.g. transport).

The observed divergences and the interviewee responses depend narrowly on their initial service definitions and their research topic. The gathering of definition and points of views allow us to propose our definition of services taking account of the duality between goods and services.

Service definition proposition

The definition proposal is not an aim in itself, but is an essential step without which we cannot claim to seriously work on service. Based on the previous literature review and the results of the survey interpretations, we propose to define the service as the execution or the instantiation of an activity generating, an artifact and/or a state change of the artifact or the input agent, consuming entities (capacity to serve) grouped in resources, inputs and controls; attempting to satisfy customer needs.

To make explicit the proposed definition, it is necessary to define the meaning of each term that is used and illustrate the definition using some conceptual diagrams.

We define the service as an execution activity, without taking account of the activity output nature (material/immaterial) and without distinguish the service provider from the service customer (self-service/customer-provider). From an operational and modeling point of view the execution activity can be seen as the instantiation of an activity done by affecting a value to the activity, resources, inputs, controls and outputs.

Service meta-model

We assume that the service consumes and produces entities classified as artifacts or agents (Fig. 1). "An artifact may be defined as an object that has been intentionally made or produced for a certain purpose" [13][14]. The artifact intentionality is a fundamental element [START_REF] Vieu | Artefacts and Roles: Modelling Strategies in a Multiplicative Ontology[END_REF], thus natural entity become artifact by attributing an intentionality (a pebble used like a paperweight is an artifact). We distinguish physical and no physical artifacts [START_REF] Kassel | Vers une ontologie formelle des artefacts[END_REF], where the firsts are the only ones having direct spatial dimensions and functions, these functions provide no physical artifacts. An agent is an entity having the capacity to accomplish actions using some competency and to provide no physical artifacts [START_REF] Kassel | Vers une ontologie formelle des artefacts[END_REF].

These entities take part in a service as an inputs, outputs, resources and controls. The entity serve capacity depends on its capability to provide no physical artifacts (broken car has no transport serve capacity), the entity with low serve capacity needs to consume a service to increase this capacity and be able to participate in the supported service (broken car needs mechanical repair service to be able to perform transport).

According to serve capacity possible values, we can define several entity states; the transition between two entity states can be induced by consuming service or by participating to service providing. The serve capacity evolution of service participating entities depends on the entity nature (a software developer increases his competency and developing serve capacity when he participates to development service) (a knife deceases its cutting serve capacity when it's used in a service).

If we assume that in our view the entity is not all the time participating in service, then the transition between two entity states can also be induced by other factors such as events or the time.

The service consumption responds to entity need, artifact need is different from agent need. The artifact need is closely linked to its serve capacities and needs services to be able to provide other services. An artifact with no functions will certainly disappear. The agent need for its concern includes two views: the first one is similar to the artifact need i.e. where the agent consumes services to provide other ones (a machine operator needs to consume formation service to provide a service on a specific machine). The second view is to consider the intrinsic human needs, which "… arrange themselves in hierarchies of pre-potency…" where "… the appearance of one need usually rests on the prior satisfaction of another …" [START_REF] Maslow | A Theory of Human Motivation[END_REF].

Service modeling

We gather considered concepts using UML class diagram (Fig. 1) [START_REF] Fowler | UML Distilled: A Brief Guide to the Standard Object Modeling Language[END_REF] within which three class groups coexist, representing three views: (i) the functional view (Service, Activity, Entity, Process and Service-Concept), (ii) the interaction view (Service, State, Transition, Need and Entity) and (iii) the dynamic view (Activity, Entity, Process and Synchronization-connector).

The functional view allows to model the service, its inputs, its outputs and its activity using a mix of IDEF0, IEM [START_REF] Spur | Integrated Enterprise Modelling[END_REF] languages and integrating UML instantiation notion (Fig. 2). The activity represents a proposed response for the service-concept gathering customer needs, and the service an instantiation of this response. Based on the UML state machine diagrams [START_REF] Fowler | UML Distilled: A Brief Guide to the Standard Object Modeling Language[END_REF], the interaction view allows modeling the entities states and the transitions between them (fig. 3). The service here consumes serve capacities (and/or entities) inducing entity state change (and/or producing entities) according to the need. The dynamic view allows to describe the sequences that are mandatory to execute the service. This view is based on BPMN [START_REF] Omg | Business Process Modeling Notation[END_REF].

The definition proposal and the IHIP

After having proposed a definition and a modeling of the service, we check the IHIP characteristics and there link with the proposed point of view. The service defined as an execution activity is: -Intangible; the execution being an order of actions, it is immaterial but can act on physical or no physical entities. -Heterogeneous; the service being an activity instantiation each instance is different, with a common base (activity description).

-Inseparable; the execution gathers the provider and the customer during the execution duration (self-service/customer-provider).

-Perishable; the execution taking a finite time, the service only exists during its execution.

Conclusion

In the current economic context, the problem of service becomes a key issue. This article points both the contributions of the economic literature and the recent developments in service theory. We have proposed a definition and a service model that takes into account the service nature and characteristics and the links service/resources, which are considered as serve capability container. This view of service allows a better action on service.

Various questions suggest new fields of investigation, and future pathways of research to the evaluation of performance in services, study the quality of services, the definition of a production typology for material product and/or immaterial product, the formalization of public services, and new typology of services.

Fig. 1 .

 1 Fig. 1. Proposed service meta-model.

Fig. 2 .

 2 Fig. 2. Service functional view.

Fig. 3 .

 3 Fig. 3. Service interaction view.


Michel Ravelomanantsoa

Yves Ducq

Bruno Vallespir

Integration of requirements for Performance Indicator System definition and implementation methods

Keywords: Performance measurement, Framework, GERAM

The topic of Performance Measurement and Management has been investigated for more than twenty five years leading to more than thirty five methods around the world, developed either by researchers or more pragmatically by practitioners, in order to define and implement indicators. Most of them are more oriented for the definition and few for the implementation. Other are simply a list of recommended PI's. Several studies have been done to compare some of these methods and to explain the reasons of PI's implementation failures. The objectives of this paper is to go deeper in detail in the comparison and in a second time to define a generic framework that could help to detect what should contain a generic method for Performance Indicator System definition and implementation and what is the knowledge that must be included in this kind of method to be more efficient.

Introduction

The topic of Performance Measurement and Management has been investigated for more than twenty five years leading to more than thirty five methods around the world, developed either by researchers or more pragmatically by practitioners, in order to define and implement indicators. Most of these methods are dedicated to the Performance Indicator (PI) definition and few of them are for the implementation. All these methods have been developed independently based on system theory, production management theory or accounting methods, according to the background of developers. Among all these methods, more or less used and well known, one can cite the famous ones or the most used or disseminated around the world as Balanced Score Card [START_REF] Kaplan | The Balanced Scorecard[END_REF], the Performance Prism [START_REF] Neely | The performance Prism -The scorecard for measuring and managing Business Success -Edition[END_REF], ECOGRAI [START_REF] Ducq | Definition and aggregation of a Performance Measurement System in three Aeronautical workshops using the ECOGRAI Method[END_REF], IPMS [START_REF] Bititci | Integrated Performance Measurement System: a development guide[END_REF], Medori [5] or DPMS [START_REF] Ghalayini | An integrated dynamic performance measurement system for improving manufacturing competitiveness[END_REF].

Several studies were performed to compare methods for PMS from several points of views. For instance, [START_REF] Kihn | Comparing performance measurement approaches -PMA Conference[END_REF] classifies these methods according to three categories: financial, goal centred and behavioural, concluding that each one has its own advantages to obtain a consistent PIS. In [START_REF] Franco | Towards a definition of a business performance measurement system[END_REF] seventeen definitions of what a Business Process Measurement System is, are analysed through methods available or theoretical articles. This analysis was made on the main features of a PIS, on its role in an organisation and on the process of use it. The main conclusions are that a PIS must be multi-dimensional (financial and non-financial), must include strategic objectives, performance targets and supporting infrastructure. [9] uses systematic review to analyse few methods in order to detect why some of them are more useful to manage organisations through measure, i.e. to obtain an efficient PIS. The most important aspect is that a method for PIS must help to the definition of detailed action plans extracted from measures, to measure progress, to have a vision (a perspective as a strategic map) and to have cause and effect relationships (links between indicators).

In conclusion of these studies, it is noticeable that several recurrent points exist in each method such as a methodological approach to build the PIS, some basic concepts to define performance indicators as objectives, action means, etc. However, each of them has also some lacks in order to obtain an efficient PIS, easy to build and easy to use for decision makers. So, the conclusion is that each method, even the most famous ones, can be improved based on qualities of other ones.

So, The objective of this paper is to go further not only in the comparison of methods but also in the definition of a generic framework that could help to define what should contain a method to define and implement Performance Indicator System. The objective is not to define a new method by itself but to build the base for the future combination of methods to collect, and to manage in order to use at the best the enterprise knowledge required to build an efficient PIS. So, in a first part, the paper will explain the difference between a method and a framework and why it is obvious to start from GERAM framework to perform this work. In a second part, a complementary analysis will be presented, highlighting what are the concepts and the components required for a method for PIS design and implementation. In a third time the paper will present GERAM framework developed by IFAP/IFIP taskforce. In a fourth time, GERAM is adapted to the domain of PIS and the base for the framework for PIS methods is presented. Then, perspectives for future works are proposed.

A framework dedicated to PIS methods

Why and what is a framework

As mentioned previously, the few analyses conducted to compare PIS methods show that even if all these methods were based on theoretical or practical points of view, none are complete and none can ensure to collect the whole required knowledge to obtain an efficient PIS for a single enterprise or a supply chain. The objective of this work is to "set in order" the various existing methods. Indeed, the goal of the framework is to answer to the large diversity of objectives pursued by all PIS methodologies, and then to federate them.

A lot of experiences, led in the domain of modelling for Information Systems with Unified Modelling Language [START_REF] Omg | Object Management Group. -Unified Modeling Language Specification -Version 1[END_REF] or in the domain of enterprise modelling with Unified Enterprise Modelling Language [START_REF] Berio | Requirements analysis: initial core constructs and architecture, UEML Thematic Network -Contract[END_REF], have shown the necessity to work at a generic level of modelling instead of the level of methods in order to obtain coherent models leading to implement efficient systems. This generic level may be constituted of meta-model (such as for UEML), frameworks, etc. This is why it was decided to develop a framework, a kind of meta-model or meta-structure which will help to define the required content of a method for PIS definition and implementation. In our point of view, a method is composed of: a set of concepts called also structural framework in [START_REF] Folan | Providing for Inter-Organisational Performance Measurement: Challenges and Concepts -Proceedings of the 4 th international IFIP workshop on performance measurement "implementation of performance measurement systems for supply chains[END_REF] which must be identified in the enterprise in order to build the PIS, some formalisms to represent the PIS at work, and a structured approach, called also procedural framework in [START_REF] Folan | Providing for Inter-Organisational Performance Measurement: Challenges and Concepts -Proceedings of the 4 th international IFIP workshop on performance measurement "implementation of performance measurement systems for supply chains[END_REF].

A framework is a generalised architecture composed of elements, recommended in PIS engineering and integration, and thereby sets the standard for the collection of related tools and methods. The objective is to allow any enterprise to more successfully tackle initial PIS design, implement and make it evolve during enterprise operational lifetime. This framework does not impose any particular set of tools or methods, but defines the criteria to be satisfied by any set of selected tools and methods.

The main advantage of the framework is not only to present the elements but also the links between these elements. It is clear that the final objective of this framework is also to allow, in the future, to improve each existing method and to inform the practitioners about what to add to these methods.

In order to define this kind of framework, the authors propose to follow the same approach that was used in the domain of enterprise modelling methods and which led to develop GERAM (Generalised Enterprise Reference Architecture and Methodology). GERAM was first selected for two main reasons. The first one is the genericity of the framework that can be applied for each enterprise modelling method.

The second reason is the domain of enterprise modelling (EM) which is very closed to the domain of PIS in the sense that EM is the art of externalising enterprise knowledge that adds value to the enterprise (single, extended or virtual organisation). This knowledge is related to the representation of the structure, the behaviour and the organisation of the enterprise according to different points of views: functional, decisional, business, IT… This knowledge is also required to design and implement a PIS.

The interest of this approach linked to GERAM is to avoid to start from scratch when analysing the methods and to define relevant criteria for comparison being specific enough to keep only those interesting for PIS methods. The interest to work at a generic level is to have a global view on the requirements for a PIS without being polluted by a specific context or by a specific function of the enterprise which led to consider only one kind of PI or one decision level. Moreover, the modules are not defined independently in the sense that they are linked together, each one being required to go from user specifications to the implemented Performance Indicator System. For instance, concepts need an architecture to put them in coherence, the architecture need an engineering method to be implemented to define the PIS, which requires a software tool to be used and updated.

Methodology of work

The methodology used to develop the framework is presented figure 1.

After a state of the art of existing PIS methods, as exhaustive as possible, a state of the art of existing framework was performed, and GERAM was chosen due to reasons mentioned previously. Then, the various methods were "disassembled" and compared, and commonalities were identified. These commonalities were compared with GERAM modules exposed hereafter. Then, a first version of the framework for PIS methods was elaborated. framework was developed by the IFIP-IFAC Task Force on Architectures for Enterprise Integration [13]. This generalised architecture was developed from the evaluation of three existing enterprise integration architectures (CIMOSA, GRAI and PERA) and concluded that each of them had something to offer. To do so, a generalised architecture is required. It defines a tool-kit for designing and maintaining enterprises for their entire life-history and it has the potential for application to all types of enterprises. The set of components identified in GERAM is briefly described in the following:

-GERA (Generic Enterprise Reference Architecture) defines generic concepts recommended for use in enterprise engineering and integration projects. They can be categorised as: human, process and technology oriented concepts.

-EEMs (Enterprise Engineering Methodologies) describe the processes of enterprise engineering and integration in the form of a process model or structured procedure with detailed instructions.

-EMLs (Enterprise Modelling Languages) define the generic modelling constructs adapted to the need of people creating and using enterprise models.

-GEMCs (Generic Enterprise Modelling Concepts) define and formalise the most generic concepts of enterprise modelling which may be defined in various way: natural language (glossaries), meta-model, ontological theories defining the meaning (semantics) of modelling languages.

-PEMs (Partial Enterprise Models) are reusable, paradigmatic, typical models which capture characteristics common to many enterprises within or across one or more industrial sectors.

-EETs (Enterprise Engineering Tools) support the processes of enterprise engineering and integration. They should provide for analysis, design and use of enterprises models.

-EMs (Enterprise Models) particular may consist of several models describing various aspects or views of the enterprise.

-EMOs (Enterprise Modules) are physical elements (resources) which can be used in the implementation of the enterprise.

-EOSs (Enterprise Operational System) particular support the operation of a particular enterprise. The implementation is guided by the particular enterprise model which provides the system specifications.

GERAM framework is presented in the figure 2 below:

Figure 2: GERAM Framework

GERAM can be more considered as a set of requirements than as a real practical enterprise modelling method but all the existing methods can consider GERAM to evaluate their completeness.

The Framework for PIS methods

Based on the disassembling of the set of PIS methods and based on the components of GERAM, the following elements are proposed to be included. It means that, in comparison to GERAM, some components are kept because they correspond to PIS methods as for EM methods, other components were removed and then other were added to complete the framework.

GEPISA: GEneral Performance Indicator System Architecture

GEPISA is a crucial component because it aims to structure the future PIS. This contains guides and rules for designing PIS. This is closed to the structural framework as defined by [START_REF] Folan | Providing for Inter-Organisational Performance Measurement: Challenges and Concepts -Proceedings of the 4 th international IFIP workshop on performance measurement "implementation of performance measurement systems for supply chains[END_REF]. GEPISA aims also to describe the way of running for the PIS. GEPISA can contain the different architecture included in the studied methods:

-architectures based on audit methods to seek areas to improve (audit led), -architectures based on enterprise models (model led), -architectures based on perspectives (need led). PISEM: Performance Indicator System Engineering Method PISEM describes the process to design and to implement PIS. It is expressed in the form of a structured procedure composed of steps as the procedural framework in [START_REF] Folan | Providing for Inter-Organisational Performance Measurement: Challenges and Concepts -Proceedings of the 4 th international IFIP workshop on performance measurement "implementation of performance measurement systems for supply chains[END_REF] or the structured approach of ECOGRAI [START_REF] Ducq | Definition and aggregation of a Performance Measurement System in three Aeronautical workshops using the ECOGRAI Method[END_REF].

GEPISC: GEneral

COPIS: Conceptual Performance Indicator System

COPIS consists is PI's description at the conceptual level, i.e. using description tools as specification sheets, maps… At this stage, the PIS is not concrete nor implemented.

OPIS: Operational Performance Indicator System

OPIS consists in the PIS at the operational level. In this case, the PIS is implemented and composed of customised/parameterised PISET for the particular enterprise.

It is also possible to define other modules that GERAM does not propose. For instance, based on the literature and on the practice of PIS implementation, it seems necessary to have a module dedicated to the choice and implementation of PISET. This module would aim to define the steps and tools for the parameterisation and implementation of PISET to obtain PIS at the operational level.

Conclusions and perspectives

The comparison of methods led to the conclusions that each of them has advantages and points to improve, either in the definition or in the implementation of PIS. It was then necessary to determine the required elements of such methods to be efficient. The interest of a framework is to work at a meta level of comparison and then to avoid to start from scratch when analysing the methods, to define relevant criteria for

Figure 1 :

 1 Figure 1: The methodology of work

  PPIS concerns the use of reference PIS which enables to save time in the definition of PI's. It provides referential PIS reusable according to a specific context (bank, industry, construction …sectors). It is materialised for instance by a list of PI's as in[13]. The interest of PPIS is also to allow benchmarking as in ENAPS European Project.

	Performance Indicator System Concepts
	GEPISC defines all required concepts to design and implemented PIS as objectives,
	decision variables, customer…
	PPIS: Partial Performance Indicator System

PISET: Performance Indicator System Engineering Tool

PISET concerns the setting up of a technological infrastructure in order to process various aspects such as data collection, coherence, aggregation and consolidation of data, development and presentation of indicators etc…EIS, OLAP, ROLAP, datawarehouse, datamart, datamining, ETL, etc… belong to PISET. The use of decisional computing technology is essential for the implementation of PIS.

comparison but to be enough specific to keep only those interesting for PIS methods. The modules are linked together, each one being required to start from user specifications towards the implemented Performance Indicator System. In conclusion, the authors will insist on the necessity to continue the survey of existing methods to define and implement performance indicator systems and the detection of required generic modules.


Mahmoud Moradi
email: mahmoud.moradi@ims-bordeaux.fr

Mounir Badja
email: mounir.badja@ims-bordeaux.fr

Bruno Vallespir
email: bruno.vallespir@ims-bordeaux.fr

Knowledge Based Enterprise Engineering (KBEE): a modeling framework for enterprise knowledge capitalization

Keywords: Enterprise modeling, Knowledge modeling, Enterprise Engineering, Knowledge Engineering

The main objective of this paper is to study the complementarity nature of enterprise modeling and knowledge management within the framework of enterprises. To do so, we evaluate some important methodologies in each domain and then several modeling points of view are explained. By reviewing CommonKADS, MASK, CIMOSA, and GIM methodologies and their modeling views we propose a generic framework to model knowledge in all its aspects. This framework has four modeling views namely, intent modeling, context modeling, content modeling and evolution modeling. These views are classified into several sub-elements brought together by developing meta-model in UML class diagrams. KBEE may possibly be useful both for the practitioners and scientific to deal with knowledge and its modeling in enterprises.

Introduction

Knowledge is widely recognized as being the key capital of enterprises that contributes to enterprise competitiveness and provides the basis for long term growth, development and existence. Therefore, one of the major questions is how to make more efficient use of knowledge in the enterprise (in terms of sharing or acquiring). It is a well known fact that much of existing information and knowledge, which is extremely valuable, is not made explicit, externalized or formalized and is consequently not available for use by other individuals, and sometimes it can even be lost for the enterprise. Therefore, how can informal enterprise knowledge be captured, formalized, organized, spread and reused?

From the hypothesis that modeling of knowledge and enterprise are imperative tools to manage knowledge in the organizations especially in externalization and integration of knowledge and also for the engineering context, we will propose in this paper a method for engineering the enterprise based on knowledge. This method is a result of synthesis of four main frameworks in Enterprise Modeling (EM) and Knowledge Management (KM). This method put in a shared context approximately all of the aspects concerning knowledge in the enterprises and looks at the knowledge from several point of views and entitled KBEE (Knowledge Based Enterprise Engineering). For the comparison of methods we propose a framework to classify all views into four mains categories as context modeling, intent modeling, content modeling, and evolution modeling. These components together are the basic foundation of reviewed methods. KBEE is a model based enterprise engineering framework that aims at modeling knowledge in all shapes and all sources in the enterprises in the perspective to provide an integrated and multifaceted knowledge base.

As a starting point, we draw on the CommonKADS, MASK, CIMOSA, and GRAI/GIM methodologies which all are intended for supporting and representing several views to model enterprises. These methods together provide an integrated view in enterprise context modeling (Fig. 1).

Knowledge Based Enterprise Engineering

Meta-modeling

Meta-modeling is the act of modeling applied to languages. The study of intersections between languages for their unification is largely facilitated by meta-modeling. Accordingly, we will use a meta-modeling approach to describe the selected enterprise modeling and knowledge management methods. Each method must be defined through a meta-model. In addition, the meta-modeling language being used is the UML class diagram [START_REF] Omg | Object Management Group[END_REF] because it seems sufficient to deal with our problem which is, mainly, to describe the conceptual aspects of the methods. Indeed, for each method, a meta-model is built with a class diagram. With these meta-models, we can compare the constructs of the various methods. However, it is important to note that the meta-models which we want to build here are not meta-models on the software science point of view. Thus, these meta-models have to be understandable for analysts of the enterprise modeling domain. They have to be clear and not necessarily to be the "best" meta-models, optimized and with the lowest number of classes. Moreover, meta-models are not comprehensive model of methods. This means meta-models developed here are approximately completed ones. Last point about meta-models is that they do not cover all the concepts and formalisms exist in the methods. We use simplified meta-model for the reason which it will cover basic concepts and elements.

From modeling point of view, the tools and techniques that help to model knowledge in the enterprises context are the main approaches to share and transfer knowledge. In one part the CommonKADS knowledge engineering methodology and MASK method are two methods that help knowledge sharing and transfer by applying knowledge engineering and knowledge capitalization tools with developing a number of formalisms. In another part CIMOSA and GRAI/GIM methodology are two wellknown enterprise modeling framework with several views and formalisms. A point should to be taken into account is that we did not choose these methods for the reason by which they are comprehensive methods in the field.

CommonKADS views knowledge engineering as a modeling activity, where each model is "a purposeful abstraction of some part of reality" [START_REF] Schreiber | Knowledge engineering and management: The CommonKADS methodology[END_REF]. Each model focuses on certain aspects of the knowledge and ignores others. It proposes six models at successively deeper levels of detail: knowledge engineers are encouraged to model the organization in which the system will be introduced; the task (business process) which the Knowledge Based System (KBS) will support; the agents who are or will be involved in the process; required communication between agents during the process; the knowledge which is applied to performing the knowledge-based process; and the design of the proposed KBS. Fig. 2 illustrates meta-model of views of CommonKADS.

MASK (Method of Analysis and Structuring Knowledge) offers a flexible environment that allows to success knowledge capitalization projects [START_REF] Barthelmé | An architecture for knowledge evolution in organisations[END_REF] and [START_REF] Ermine | La gestion des connaissances[END_REF]. Modeling tools as defined in MASK are generic enough and respond to expert's workspace and cognitive vision. These tools have an important role in knowledge extraction and formalization. They help to structure knowledge under: systemic, ergocognitive, psycho-cognitive, historical, and evolution views [START_REF] Matta | How to capitalize knowledge with the MASK method ?[END_REF]. These views together construct knowledge modeling in MASK. Detail meta-model of views in MASK is depicted in fig. 3.

CIMOSA (CIM Open System Architecture) provides guidelines, architecture and an advanced modeling language for enterprise modeling covering several aspects of the enterprise [START_REF] Vernadat | Enterprise modeling and integration: principles and applications[END_REF]. The concept of views allows working with a subset of the model rather than with the complete model providing especially the business user with a reduced complexity for his particular area of interest. CIMOSA has defined four different modeling views: Function, Information, Resource and Organization [START_REF] Abdmouleh | Distributed client/server architecture for CIMOSA-based enterprise components[END_REF]. See fig. 4.

GRAI/GIM (GRAI Integrated Methodology) is a methodology for design and analysis of production systems based on the GRAI method [START_REF] Doumeingts | A methodology supporting design and implementation of CIM systems including economic evaluation[END_REF]. It includes modeling languages and focuses on decision system analysis of the enterprise. In GRAI/GIM, an enterprise consists of a physical system, a decision system and an information system. An enterprise can be described using four views: Functional, Physical, Decisional, and Informational [START_REF] Vallespir | GIM: a technico-economic methodology to design manufacturing systems[END_REF].

Comparison of EM and KM

Now with a comprehensive look at the methods in modeling both in KM and EM field there are several views. Some of them are common view in all methods like activity and task and some view are unique to each method. Because one of the main objectives of this research is to show and the use the complementary nature of KM and EM here we propose a generic classification to integrate the modeling views and develop the building block of enterprise knowledge modeling (see Fig. 6).

Intent

Fig. 6. Views of methods

Both CIMOSA and GRAI/GIM have excellent approach to model organizational context and could provide basic description of operational knowledge context. But they do not provide appropriate explanation of the knowledge being used in the enterprise. Moreover, they do not have any view to model evolution on knowledge and organization. They do not focus on actor or agent directly as a principal source of knowledge. As a matter of intent and intentionality, they provide partial views. For example GRAI/GIM models decision making and CIMOSA partially models the objectives of domain, process, and activities.

Both CommonKADS and MASK provide inclusive views to model knowledge in organization. They provide also advanced approach to content modeling. One weakness of these methods is context modeling. They do not have complete and integrated view to model enterprise context as aforementioned in GRAI/GIM and CIMOSA in meta-model.

Knowledge Based Enterprise Engineering (KBEE) 6.1 KBEE views

We propose four generic view of KBEE. These dimensions assist to model knowledge in the organization from multiple points of view;

Context modeling. One of the important issues to model knowledge is to model the context in which knowledge exists. Several methods in both EM and KM develop views and languages to describe the context. This context includes tasks, activities, and business processes in the enterprises. Moreover, the communication view considered as a dimension of context. Although context modeling is the common point of these two fields but one can find more in detail context modeling in EM methods and there are several good languages to model context in EM domain.

Intent modeling. In the literature of both EM and KM, there are several papers that describe the essential of intentionality of top management to launch a global project in the enterprise. However, only in GIM there is a clear decision modeling. Also some sort of organizational modeling in CommonKADS and CIMOSA exist but there is not a clear modeling of strategy and leadership support for the methods. The concepts like mission, vision, and strategy in the enterprises are the source of knowledge and describe global direction of each organization.

Content modeling. Content is the heart of our classification of knowledge modeling. This dimension includes several aspects that should be modeled. Agent modeling is an important view to model knowledge in enterprise. We know that knowledge exists in some form and somewhere in the organization but a very important part of knowledge is tacit knowledge and this knowledge is with the human and so employees in the enterprises. Inference and concept modeling as other important parts of knowledge exist in KM methods. KM methods take care of information implicitly in throughout of modeling.

Evolution modeling. Even though in the EM context, the researchers talk about evolution management in the company and maturity models but there is the absence of languages or modeling view dealing with evolution modeling in detail. This aspect is well defiled in MASK methodology in two different models; one for pragmatic dimension as historic modeling and another one for the evolution of sense and signification as lineage modeling.

KBEE meta-model

Three main elements of KBEE are actor, activity, and artifact (Fig. 7). Artifact includes all elements being used by actor and activity or produced by an activity intended to define what to do. Global objective of the enterprise is the direction of this element. The activity must do by an actor and this actor use the knowledge and some kind of artifact to accomplish that activity. The elements and concepts being used to KBEE as the results of unification of four methods is described in fig. 8. This conceptual meta-model represents essential components of knowledge modeling in the organization. The classed of concepts labeled by green color show the intent concerning concepts. Classes like system, domain, organization and role describe element of context. Communication view and knowledge view in CommonKADS, cognitive task in MASK, and resource view in CIMOSA represent content view in KBEE. Actor, Activity and Artifact here represent the knowledge context for KBEE. Finally evolution view in MASK that originally was intended to model maturity of concepts in the domain is applied to all the classes of KBEE. It means the entire concepts in the context of KBEE will be the object of evolution. To do so, we show evolution as the relation between all the classes that will be subject of evolution.

Conclusion and perspectives

The key idea of KM is to provide a way whereby knowledge contents are created, shared, and utilized in an efficient and effective manner. Therefore, it is critical to analyze these knowledge requirements. Managers need tools to analyze knowledge contents needed in business processes and decision-making. This paper presents the rationale for knowledge modeling as a foundation for successful KM projects. A method is proposed for building an effective knowledge model. As a modeling language of the method, the unified modeling language (UML) has been chosen. KBEE to be completed and comprehensive need further works. The formalism and proper languages or tools for the dimension and classed are needed. In this paper we developed the conceptual dimensions of KBEE and we did not enter the detail level of the KBEE view. Another research direction is to propose the common ontology of concepts, elements and views. How to gather the knowledge and information is the next perspective of this research. This perspective will determine the knowledge sources in the organization, implementation methodology and techniques to collect knowledge in an appropriate way.

Fig. 1 .

 1 Fig. 1. Theoretic Foundation

Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .

 2345 Fig. 2. Meta-model of CommonKADS

Fig. 7 .Fig. 8 .

 78 Fig. 7. Three basic components of KBEE

Context Content Evolution Historic Lineage Mission Vision Strategy Objective Decision Organization Domain Process Activity Communication Resource Actor Information Knowledge Inference Concept Cognitive task Intent Context Content Evolution Historic Lineage Mission Vision Strategy Objective Decision Organization Domain Process Activity Communication Resource Actor Information Knowledge Inference Concept Cognitive task Context Content Evolution Historic Lineage Mission Vision Strategy Objective Decision Organization Domain Process Activity Communication Resource Actor Information Knowledge Inference Concept Cognitive task