PhD Gaëlle Dechamp-Goy
email: gaelle.dechamp@univ-st-etienne.fr

PhD Bérangère Szostak
email: berangere.szostak@univ-lyon2.fr

IS DESIGN A SOLUTION FOR THE SMALL ANDMEDIUM ENTERPRISES' FUTURE? THE "DESIGN CONCEPT" CONTEST

Keywords: Emergent strategy for innovation, design, Neo-Institutional Theories, case study

 that institutions can sustain an emergent strategy in a given field. Ordinarily considered as stable elements of that field, these institutions may be subject to change. This theoretical approach is the object of a case study set in the framework of a contest. Organized by the General Council of the Loire and aimed at SME located in its constituency, the contest goal is to encourage innovation through design. By design, one must understand a creation produced by Man for industrial and commercial use. An emergent strategy is defined as new when situated within a defined context and a specific period of time.

, this analysis has been elaborated to illustrate how an emergent strategy can be successfully incorporated. Several empirical questions subsequently follow: "What are the characteristics that allow business managers settled in the Loire district to adopt a design strategy? Which fields of activity in the Loire area are the most inclined to be compatible with the design strategy? Which business projects are the most eligible for partnership with designers? How will the General Council choose the subjects for the contest in order to initiate change within institutions?

Introduction :

It is a known fact that the theoretical developments anchored in Neo-Institutional Theories highlight the importance of these institutions in order to understand the homogenization of forms within an organizational field. However, [START_REF] Desreumaux | Théorie néo-institutionnelle, management stratégique et dynamique des organisations[END_REF] likes to remind us that, today, many questions remain unanswered regarding change in institutions 1 [START_REF] Desreumaux | Les théories institutionnelles des organisations : une perspective internationale[END_REF]. The role of the actor is emphasized once again. On the other 1 Sometimes initiated by an institution hand, this questions the relationship the said actor has with referential rules and ideas [START_REF] Beckert | Agency, entrepreneurs and institutional change. The role of strategic choice and institutionalized practices in organizations[END_REF].

However, what happens if the actor is an institution setting rules and norms within the organizational field? In other words, if an agent is considered a source of stability in a given field, can he encourage the other organizational actors to change, more particularly to innovate, by incorporating an emergent strategy? Washington and Venstresca (2004), who focus their attention on visibility strategies, give a positive answer to this question in their article. According to these authors, "institutions" may be defined as "those shared rules and typifications that identify categories of social actors and their appropriate activities or relationships" (Barley and Tolbert 1997, p. 96).

The above research insists on the "positive effects" the institutions may have on how organizations change. This approach, however, may seem paradoxical when compared to the definition of these institutions. [START_REF] Scott | Institutions and Organizations, 2 nd édition -1994 la première[END_REF] explains that institutions form a framework, and it is within this framework that organizations generally carry out their action: Not only are they the sum of interactions between people and organizations, but they also serve as points of reference which help understand the actors' and organizations' actions.

However, [START_REF] Washington | How organizations change: the role of institutional support mechanisms in the incorporation of higher education visibility strategies: 1874-1995[END_REF] point out three mechanisms liable to provide institutional support for the organizational incorporation process within an emergent strategy: (1) the prevailing logic2 of the organizational field 3 and its capacity to resolve ambiguities, (2) the nature of the characteristics that are liable to initiate a new strategy within the field and (3) competitiveness between the organizations in a given field. This research brings a new light on Neo-Institutional Theories. It therefore becomes interesting to study these institutions' approach by regarding the legitimization of emergent strategies as a source of change within this field.

According to Yin (1994), it is possible to illustrate this theory by studying the action carried out by the Loire General Council. Since 2007, the latter desires to encourage SMEs settled in its constituency to incorporate a strategy for innovation based on design. This action is thus in line with Washington and Ventresca's approach (2004) which puts forward the existence of rules and norms that validate innovation through design as an emergent strategy, viewing them as legitimate as the usual strategies often used by these generally subcontracting companies. This action also implies new relationships between the field actors, and in this case, between SMEs and designers. What is the nature of the process initiated by the Loire General Council to encourage the incorporation of design? What relation is there with the three different mechanisms put forward by [START_REF] Washington | How organizations change: the role of institutional support mechanisms in the incorporation of higher education visibility strategies: 1874-1995[END_REF]? What other tracks are still to be explored?

After having explained how design can be considered an emergent strategy, the present article will put forward the case of the DOING Company4 who, supported by the Loire General Council's initiative, successfully incorporated the design strategy. Because Washington and Ventresca 's studies (2004) are conducted at a mesoscopic scale, that is to say based on the interaction between organizations, our work studies the relationship between the following field actors: the DOING Company and the design agencies. This qualitative research will also allow us to share with co-workers our first comments on the theoretical and managerial implications of such an approach.

HOW THE LOIRE SMALL AND MEDIUM BUSINESSES VIEW DESIGN

AS AN EMERGENT STRATEGY FOR INNOVATION.

The aim of the first part of this paper is to clarify the premise of our research which upholds the idea that "the incorporation of design within the strategy of the Loire small and medium businesses qualifies as an emergent strategy for innovation".

DEFINING THE CONCEPTS OF "DESIGN" AND "EMERGENT STRATEGY"

Instead of a unique definition for "design"; we prefer to proceed by presenting "touchstones" in order cover the wide range of designations peculiar to each designer. Design is above all a "state of mind" [START_REF] Brun | Stratégie de développement de nouveaux produits et compétitivité des PME : du design management au design comme aide au management[END_REF]. According to the latter, this implies "considering the elements of design not as an accumulation, but as an entirety. By considering design in this way, it is possible to portray the goals of enterprises as a whole. This is achievable because it allows the interpretation of factors of all kinds from technical and semiological" [START_REF] Brun | Stratégie de développement de nouveaux produits et compétitivité des PME : du design management au design comme aide au management[END_REF].

These considerations find an echo in the etymological definition of the word design: it comes from the Latin word "designare" which leads to the words "designer" (to intend) and "dessiner" (to draw) in French. Therefore, for many specialists, the concept of design has a double objective: i) a design in that it implies an intention, a process; ii) a drawing in that it gives life to a project through a sketch, a pattern, i.e. a visual creation. In this article, design is consequently referred to as an activity of creation produced by Man for industrial and commercial use.

When using the term "emergent strategy", we refer to [START_REF] Washington | How organizations change: the role of institutional support mechanisms in the incorporation of higher education visibility strategies: 1874-1995[END_REF] approach. They use the concept of institutional support to highlight how the mechanisms mentioned in the introduction (1) create conditions favorable to change and (2) define the elements eligible to be incorporated. In their attempt to illustrate the concept of "emergent strategy", [START_REF] Washington | How organizations change: the role of institutional support mechanisms in the incorporation of higher education visibility strategies: 1874-1995[END_REF] article develops arguments similar to Straw and Epstein's (2000) work. Moreover, they point out that their work enhances general research on the emerging sociology of strategy 5 . Their aim is to use neo-institutional theories to explore how "new" strategies, also referred to as "emergent" strategies, become relevant typified solutions easy to relay on a wide scale because recognized as such. As a result, a strategy is qualified as emergent when applied to a particular context featuring characteristics that enable to distinguish between what is "normal" and what is "new". Furthermore, the concept of "emergent strategy" can only apply to a given situation: the initial context appropriately demonstrates how the incorporation of a strategy is innovative. In addition, we are led to adopt an open-minded approach to the definition of organizational strategy. In order to qualify design as an emergent strategy for innovation for the small and medium businesses of the Loire, we must define their current strategic situation.

-DESIGN: AN EMERGENT STRATEGY FOR INNOVATION FOR THE SMALL AND MEDIUM BUSINESSES OF THE LOIRE.

According to a recent study carried out by the local Chamber of Commerce, only 18% of small and medium businesses settled in the Loire use design. According to the General Council, the fact that this figure is largely below the nation's average may be explained by the important amount of sub-contractors.

The economic context of this district has been shaped by important historical events: in the 60's, prosperity emanated from industries linked to coal, clothing, metalworking and weaponry. The result was the creation of many competitive enterprises, albeit sub-contractors to principal firms, such as ManuFrance, GIAT France and Creusot-Loire. However, industrial 5 Cf text p.93 restructuring led to the gradual disappearance of these firms who were the Loire small and medium businesses' principal clients. Although 60 000 jobs were lost, the present economy may still be described as harboring enterprises as competitive as ever. However, a large majority of them are sub-contractors.

Today, institutions such as the General Council, the Chamber of Commerce and the Agency for Development all come to the same conclusion: very few SMEs in the Loire are liable to become principal firms. Hardly any possess departments dedicated to research, development and design. In this context, design may therefore be viewed as an emergent strategy for innovation in that it is of small importance, if of any importance at all, to a majority of the Loire's small and medium businesses. However, this pessimistic assessment may be tempered when considering the nature of the Loire small and medium businesses' environmental strategies. Multiple networks link these companies together [START_REF] Szostak | Le soutien des PME innovantes ligériennes par les réseaux[END_REF]. The networks in question are viewed as institutions by those at the source of these geographical groupings. As a result, the "clusters" organize the Loire enterprises into groups according to industrial sectors such as the mechanical, medical or digital industries. They are specified as Local Productive Systems (SPL)6 and include the following entities: Mécaloire, Pôles des Technologies Médicales (PTM), Inter Forêt Bois 42, Loire Numérique7 . The Loire General Council financially supports their actions in favor of the local economic fabric. In this way, the Loire General Council will encourage the incorporation of the design strategy qualified as emergent because it is considered innovative in this particular context (see the infra case study).

HOW THE DOING COMPANY INCORPORATED DESIGN AS A STRATEGY FOR INNOVATION

This research is based on a qualitative approach. Given its exploratory nature, it is also based on a case study. The study of a case that has the characteristic of being unique allows one to better understand a particular question [START_REF] Hadly-Rispal M | Une stratégie de recherché en gestion : l'étude de cas[END_REF], and is perfectly justified when particularly critical, revealing or extreme (Yin, 1994). Furthermore, design as a new rule favoring innovation and the creation of new relationships between field actors (subcontracting companies; design agencies) reveal an unprecedented situation that requires the exploration, rather than the exploitation, of data. For this reason, we have opted for a case study so as to better detail and understand this unmatched situation.

The DOING case study therefore aims at deepening the impact of new rules and relationships between actors who make it possible for design to be incorporated as a strategy for innovation. The department of Innovation and Economic Competitiveness of the Loire General Council is well aware of the growing importance of design in revitalizing the Loire district. As a result, it invited companies belonging to 5 regional clusters to take part in a contest in which they would collaborate on an innovative project with designers.

THE DESIGN CONCEPT CONTEST OR THE MATERIALIZATION OF THE INSTITUTION

Underlying this case study is a contest named "Design Concept" whose principal initiator is the Loire General Council. The latter noted that although innovation has an intrinsic influence on a company's strategy, implementation is less effective where resources are limited. Such is the case for many small and medium businesses located in the Loire.

Consequently, various policies helped them innovate. These policies are based on the principle according to which the dynamics of companies and territories interact with actors within a delimited geographical area. As mentioned above, the actions carried out within clusters answer to the same logic.

The General Council (in cooperation with partners) consequently decided to launch a program entitled "Innovation and Competitiveness" aimed at developing an "innovating territory". It decided to organize projects around transversal themes such as the digital field, design and economic intelligence. At the source of this method was the intention to gather companies, researchers and stable structures around these themes in order to introduce business managers to innovating practices. The project on design was the first to be launched under the banner of the "Design Concept" contest.

After having drafted a first selection of the most innovating projects 8 , the guild in charge of the contest settled on 5 of them: all in all, 15 companies, grouped into aggregations, were to work with 3 to 5 design agencies each, the work specifically related to design being directly financed by the General Council. Each aggregation is associated with a territorial cluster: Loire Numérique, Mécaloire, Pôle Optique Rhône-Alpes, Club ERF (Entreprendre en Roannais Forez), and Sporaltec. The contest lasted for over a year, to the submission of 9 "innovating ideas" projects (5 were selected) to the choice of the 3 winners potential influence of institutions on the development of innovation and the importance of design in this process. Our choice is based not only on the success met by the project, but also on the fact that the company in question succeeded in appropriating both the new rules of "design" and the new partnership with the design agencies. We believe that major ideas will stem from the study of this case and allow one to understand how an institution is responsible for its success. Directed by the DOING Company, the case in question consists of a RFID prepaid card with access to various services offered by the city of Saint-Etienne (see methodology below).

Methodology for the analysis of the "RFID project"

This qualitative study is based on three kinds of material. The General Council forwarded all the data it possessed concerning the contest in general. It also sent us information related to the work undertaken by the aggregation of enterprises concerned by the project. The above structure (the innovation department) also transmitted its personal analysis of the project during two meetings between researchers working on the assignment. Furthermore, we attended the selections that took place in May and July. Finally, we carried out semi-directive interviews with the six people concerned by the project for an overall of 6H25.

-The DOING company: M-V Gellet (1h20) and Laurence Cote (1h) -Loire Numérique: S. Nait-Idir (1h) -Designers' Guild : X. Charquet & E. Lair (1h45) and A. Paquelet (1h20)

The interview guide was adapted to each interviewee (whether enterprises, institutions or designers. However, the main themes remained the same: (1) Presentation of the person and the organization he/she belongs to, (2) His/her idea of innovation/design, (3) Description of the project (how the project is viewed, description of the encounters between actors, how the project unfolded, personal opinions on the conclusion/benefits/limits of their work).

Each interview was entirely recorded. The themes chosen for analysis were: (1) Description of the initial situation: the actors the sector, (2) Defining the actors' roles, launching the project, (3) The meetings organized around the monitoring of the project, how the actors communicated throughout the project, (4) The results, whether or not design was successfully adopted as a new rule, whether or not new partnerships with design agencies were successfully established. The validity of the analytical scale is being tested on the study of 4 other projects currently in process.

CASE STUDY: THE LOIRE NUMERIQUE PROJECT ENTITLED RFID AND CONDUCTED BY THE DOING COMPANY.

Loire Numérique (LN) is an association grouping companies specialized in the digital, computing (IT) and communication fields. LN's role is to federate the skills of its 120 current members and assign these particular competences to major projects. DOING has existed since 1992 and was created by G. Moulet, an analyst-programmer. The growing importance of the Internet is at the source of the company's rapid expansion in the late 90's, until the beginning of 2000. However, the founder didn't feel capable of continuing the venture: "no, managing a company is really not my cup of tea, I prefer to resign". This crisis could have triggered the company's downfall. But the determination of a certain amount of employees who refused to let go. As a result, M-V Gellet became manager and decided to search for another shareholder in order to wipe out the company's debt and gain stability. In 2001 the arrival of a new shareholder, Neyrial, involved strategic changes. This consisted in the suppression of a SBU 10 : retailing was to be exclusively assigned to Neyrial, whereas DOING was to remain in charge of programming and development. The company currently 10 Strategic Business Unit employs eight people and is specialized in the creation of data bases in association with a variety of websites. DOING's competencies serve a strategy of differentiation in that the company proposes tailored websites with special specifications.

The company wanted to create a multiservice "city card" which would apply to public transport or parking and decided, in October 2007, to submit the project, in association with Loire Numérique, to the jury of the "Innovating Ideas and Design Concept" contest. Until then, the incorporation of design as an instrument of innovation had not yet occurred11 . They therefore seized the opportunity to test design: DOING views design as new way to espouse a strategy of innovation.

Laurence Cote, in charge of the development of Fidelium, recounts: "In October 2007, we submitted to the jury our multiservice card project and it was chosen. This enabled us to work on the project with people from a different professional circle than ours, and with a point of view centered on design." The question here was to rely on the interaction of complementary competences to initiate the project. In May 2008, DOING presented the progression of its project (the name had been changed to TWIZY) to the Jury who decided it would stand amongst the finalists.

Those in charge of the project chose to work with two design agencies specialized in graphics: KALK and Mademoiselle E. They also contacted a product design agency: Paquelet Design. Originally, DOING was thinking of working on the material for the card and whether that material should be recyclable or not. "How can one optimize a smart card by making it original and practical?" Thus was the challenge the designers, with a strategy of innovation in mind, were to respond to.

The three principal project managers for DOING were: the company director, the person in charge of trade development (L. Cote) and the technical director. The Economic Intelligence representative for LN (S. Naît Idir) also closely followed the project as SPL correspondent. In this way, the institutions all collaborated in an effort to give design as much legitimacy as the other strategies of innovation used by DOING (mainly technical).

The collaboration with the designers lasted for four months. Each gathering provided the opportunity for project actors to share with each other their findings or ideas according to their specializations: technical feasibility research was assigned to DOING, adaptability research relating to the conception and utilization of the product was assigned to the designers who are collaborated partners on the project. The latter came up with a truly original idea which consisted in "dematerializing" the product by turning into a patch: small, original, and capable of sticking to various objects. One of the designers explains that: "It was necessary to create this product, but why materialize it into another object?" This is how the concept was born: a patch that could be placed onto a personal device, a telephone, a bracelet… It resembles a stamp that just needs to be "repackaged". DOING explains: "The only difficulty we experienced was adapting how we visualized the final product, to the solution the designers finally proposed. This meant that we had to accept a different point of view and the possibility of adapting it despite our technical constraints. However, we can't really say we encountered real "difficulties".

According to DOING, the project resulted in 4 proposals:

1) A scenario centered on communication and the use of TWIZY on a daily basis 2) The idea of a "repositionable patch" that can be incorporated into the object of one's choice.

3) The graphic conception destined to enhance and present the product. 4) A generic designation easy to memorize ("tout ici" or too easy). The project is regarded successful at various levels. At an industrial level, the project enabled DOING to incorporate design and therefore enhance the value of its product thanks to two features: its "dematerialized" packaging and its name (TWIZY). DOING emphasizes the fact that the project would not have reached such a high standard if it hadn't been for the designers, further admitting "we should have done this earlier". As for Loire Numérique, the project provided the opportunity to gather various enterprises specialized in digital technology around a common venture in collaboration with designers. In doing so, Loire Numérique fully met the General Council's requirements.

The designers also viewed the project as successful, praising the protagonists for their open-mindedness and their simplicity. They appreciated the fact that they were listened to, that their ideas were selected and that they were given a role in the industrial procedure: "we had the satisfaction of feeling part of a whole". The designers' main satisfaction was to know that DOING had chosen their concept, therefore enabling them to become an example for other firms who can learn from their experience in incorporating design as a legitimate strategy. Until the "Design Concept" contest, this kind of relationship had not existed. As a result, a new agreement was settled between them, enacting the first step towards the institutionalization of their relationship {small and medium sub-contractors; design agencies}. DOING team assert that "What we find interesting in the process of incorporating design is that we were able to examine our project under various angles. Because this approach is more creative, we were able to give a concrete expression to the product. This is all the more true with TWIZY because we had to deal with a virtual "no contact" product: there was an even stronger need to visualize it in spite of the nature of the concept. Being the manufacturer, our technical visualization is perhaps a little too close to the subject. The design approached allows us to be a little more detached and therefore reach a more "presentable" result; like a jewel case that adds value. If we were to compare our product to a car, we could say that the designers provided TWIZY's body. How could we possibly do without them?" Today, poor on resources, DOING depends on subsidies (the Loire General Council, OSEO…) for the creation of a prototype of TWIZY (still being discussed end of 2009) in order to test its functionality and commercialize it. In 2010 the company continues to collaborate with the design agencies.

ANALYSING THE CASE STUDY AND DEFINING RESEARCH

PERSPECTIVES

In this last section, we suggest areas for further exploration. The General Council used the contest to encourage SMEs to incorporate design into the process of innovation. It also wanted to help them understand the subject by referring to major structures from different organizational fields. In the DOING case study the objectives seem to have been reached for the most part: the interviews reveal that the DOING and Loire Numérique protagonists have successfully established a link between design, creativity and innovation. As a result, they no more associate design with products found in magazines. They now understand that design transcends the object itself, implying that companies adopt a more wide-ranging approach to innovation. "Design is a combination between business and pleasure, with Man in the middle" (manager of Doing); according to DOING personnel, it has become easier for them to consider design agencies as a typical actor in the innovation process. This category of actors is now in a stable relationship with the DOING Company recommending them, when necessary, to the other firms belonging to the same cluster.

Furthermore, the relationships that grew between the firms and design agencies during the contest still exist at the present time. The recent contacts we had with DOING indicate that they intend initiating other projects with the "design agency" actor. This success finds an explanation in the three mechanisms put forward by [START_REF] Washington | How organizations change: the role of institutional support mechanisms in the incorporation of higher education visibility strategies: 1874-1995[END_REF] and mentioned in the introduction. In our case study, the logic of innovation applied to the digital sector may be defined, above all, as a "technical conception".

If design is integrated in the process, it is only to "dress" the product. However, trying to stay in line with this logic, DOING had trouble finding a solution that would make its multiservice card truly competitive: the prevailing logic was a shortcoming. This context encouraged institutional support for the integration of design as an emergent strategy for innovation. Indeed, the integration of the designers at the outset of the project resulted in a creative, innovative and competitive solution.

Beside the fact that the project success is clearly illustrated by the theoretical approach, we instinctively believe that this case underlines what is at stake when a SME integrates design in a strategic attempt to innovate: created and implemented by stable structures (General Council, Loire Numérique), the Design Concept contest created a partnership between DOING and other professionals that wouldn't have existed otherwise.

The designers helped the company discover new perspectives. In fine, these perspectives are essential: today, DOING not only owns an innovative product (a card that isn't really a card!) but it has also succeeded in integrating design as a full-fledged strategy for innovation.

To be more precise, the analysis of this case reveals the factors that boosted the successful integration of design within small and medium businesses. Concerning TWIZY, the designers explain that the principal reason for success was "the capacity of each actor to communicate and work together on a clearly defined idea". Although this sentence corroborates several of our observations, it needs to be validated by other case studies.

First of all, it seems that the integration of design within a business is possible only if the actors possess (or successfully define) a common language. In DOING's case, the manager had studied arts and communication in college and this background obviously helped the actors to understand each other. She even explains how she served as an "interpreter" to the engineers and technicians of her company and adds that, without her help, they wouldn't have been able to work directly with the designers. In the same line of thought, we have the intuition that belonging to the same social network also encourages the integration of an emergent strategy. This is corroborated by the fact that one of the project designers was also a member of Loire Numérique, thus establishing from the outset a confidence-building atmosphere.

As a conclusion to the findings of this case study, one has to keep in mind that the objectives of the General Council were to encourage SME with specific qualifications to innovate through the integration of design. This structure relies on mimetic isomorphism [START_REF] Dimaggio | The iron cage revisited: institutional isomorphism and collective rationality in organizational field[END_REF]) in order to typify the "renegade" behavior of certain businesses and establish it as a new norm in the field (Kondra and Hinig, 1998).

CONCLUSION

The functions of small and medium businesses and the theme of organizational change are major issues of management science. In their article, [START_REF] Washington | How organizations change: the role of institutional support mechanisms in the incorporation of higher education visibility strategies: 1874-1995[END_REF] claim that an institution, on the contrary, can sometimes encourage change and even sustain the integration of an emergent strategy. To illustrate this hypothesis, our paper analyses the existing case of an institutional initiative (the "Design Concept" contest) that aims to legitimize the emergence of innovation based on design within organizations.

Finally, there are two other possible prospects of research we would like to explore: 1) because certain factors are known to encourage the legitimization of design, it is pertinent to ask oneself whether any business manager can integrate an emergent strategy via design, and whether there are industrial fields, if any, that are more or less liable to use design to innovate. The resulting observations would serve to reveal the extent to which institutional efforts to introduce changes in a given field are successful. 2) The second observation relating to the analysis of the DOING case highlights the necessity to provide designers with the opportunity to provide a platform for their creative skills. The latter's function is to propose creative and original ideas -in the end, the firm can decide to choose the ones it wants to keep. If the specifications are too restrictive, creativity is less free to express itself [START_REF] Michlewski | Uncovering Design attitude: inside the culture of designer[END_REF]. The aim of this reflection is to funnel institutional actions, as early as possible, on design projects where co-construction is more feasible. Thus, the following research prospect becomes conceivable: Which business projects are the most receptive to an innovation effort to co-construct with designers? WHITLEY R., 1992, The comparative study of business systems in Europe: issues and choices, in "European business systems, Firms and markets in their national contexts", Sage, p. 71-80 YIN R., 1994, Case study research: design and method, Sage publication, 2 nd edition.

Diagram 1 -

 1 Department of Loire in France and in Rhône-Alpes (4773 square kilometers, 73000 habitants)

Finally

  , it appears that in an attempt to initiate change within institutions, the contest integrated a variety of economic actors: public and private, design agencies, sub-contracting companies, the General Council, clusters or the "Designer+" guild. The sequence of events according to which the contest obeyed may be illustrated by the following diagram: the colored areas point out the phases of collaboration; the arrows show the incentives the actors exerted on each other.Diagram 2: Schematization of the "Design Concept" contest viewed according to neo-institutional theories.Within the framework of a research convention with the General Council, we carried out semi-directive interviews with each actor participating in the contest. We chose the project led by the Loire Numérique 9 (LN) cluster to illustrate our comments concerning the 9 Translate « digital »

Diagram 3 :

 3 A depiction of the TWIZY project (in French) [translation : RFID card holder / Direct communication via an internet connection / TWIZY website /Database server]

A prevailing logic is a system that encompasses coherent and inter-related beliefs, norms, laws and values.[START_REF] Scott | Institutions and Organizations, 2 nd édition -1994 la première[END_REF]

An organizational field is the totality of relevant actors implied in institutional realm (competitors, suppliers, consumers, regulation organizations….).

A research is currently being conducted on the Loire General Council's initiative (the initiative in question is described further in the article) and concerns several companies. The above article has chosen to focus on one of them.

"Système Productif Local"

Loire numerique's website features a good illustration: http://www.loire-numerique.com

The projects selected where those that featured an important collective dimension and were the most likely to develop into a specific product.

It should be noted that DOING had previously employed a graphic designer to work on the presentation of the software related to the Fidelium-Net card


Nabil Belgasmi
email: belgasmi.nabil@gmail.com

Lamjed Ben Saïd

Khaled Ghédira
email: khaled.ghedira@isg.rnu.tn

Evolutionary Multiobjective Optimization Of The Multi-Location Transshipment Problem

Keywords: Multi-Location Transshipment Problem, Multiobjective Optimization Problems, Multiobjective Evolutionary Algorithms, Pareto optimality

We consider a multi-location inventory system where inventory choices at each location are centrally coordinated. Lateral Transshipments are allowed as recourse actions within the same echelon in the inventory system to reduce costs and improve service level. However this transshipment process usually causes undesirable lead times. In this paper, we propose a multiobjective model of the multi-location transshipment problem which addresses optimizing three conflicting objectives: (1) minimizing the aggregate expected cost, (2) maximizing the expected fill rate, and (3) minimizing the expected transshipment lead times. We apply an evolutionary multiobjective optimization approach using the Strength Pareto Evolutionary Algorithm: SPEA2, to approximate the optimal Pareto front. Simulation with a wide choice of model parameters shows the different trades-off between the conflicting objectives.

Introduction

Practical optimization problems, especially supply chain optimization problems, seem to have a multiobjective nature much more frequently than a single objective one. Usually, some performance criteria are to be maximized, while the others should be minimized.

Physical pooling of inventories has been widely used in practice to reduce cost and improve customer service [START_REF] Herer | The multi-location transshipment problem[END_REF]]. Transshipments are recognized as the monitored movement of material among locations at the same echelon. It affords a valuable mechanism for correcting the discrepancies between the locations' observed demand and their on-hand inventory. Subsequently, transshipments may reduce costs and improve service without increasing the system-wide inventories.

The study of multi-location models with transshipments is an important contribution for mathematical inventory theory as well as for inventory practice. The idea of lateral transshipments is not new. The first study dates back to the sixties. The twolocation-one-period case with linear cost functions was considered by [START_REF] Aggarwal | Inventory control aspect in warehouses[END_REF]]. [START_REF] Krishnan | Inventory control in N warehouses[END_REF]] studied with N-location-one-period model, where the cost parameters are the same for all locations. [START_REF] Jonsson | Analysis of a Two-Echelon Inventory Control System With Complete Redistribution[END_REF]] incorporated non-negligible replenishment lead times and transshipment lead times among stocking locations to the multi-location model. The effect of lateral transshipment on the service levels in a two-location-one-period model was studied by [START_REF] Tagaras | Effects of pooling on the optimization and service levels of two-location inventory systems[END_REF]]. In all works only minimization of the expected total cost is considered. Transshipment lead times were often assumed to be negligible despite its direct impact on service levels. This is a noticeable limitation.

The contribution of this paper is twofold. We, first, propose a multiobjective multilocation transshipment (MOMT) model which minimizes the aggregate cost and transshipment lead times while maximizing the global fill rate. Second, we apply a recent multiobjective evolutionary algorithm named SPEA2, to find Pareto optimal solutions of the considered problem.

The remainder of this paper is organized as follows. In Section 2, we formulate the multiobjective transshipment model. In Section 3, we give a brief description of the multiobjective evolutionary optimization, and we present the SPEA2 algorithm. In Section 4, we show our experimental results. In Section 5, we state our concluding remarks.

Model

Model description

We consider the following real life problem where we have n stores selling a single product. The stores may differ in their cost and demand parameters. The system inventory is reviewed periodically (figure 1). At the beginning of the period and long before the demands realization, replenishments take place in store i to increase the stock level up to S i . Stores are then able to meet the unknown demand D i which represents the only uncertain event in the period. The joint distribution over demand realizations is common knowledge. Once demands are observed, they are automatically fulfilled with the local available inventory. However, after demand observation, some stores may be run out of stock while others still have unsold goods. In such situation, it will be possible to move these products from stores with surplus inventory to stores with still unmet demands. This is called lateral transshipment within the same echelon level. It means that stores in some sense share the stocks. The set of stores holding inventory I + can be considered as temporary suppliers since they may provide other stores at the same echelon level with stock units. Let τ ij be the transshipment cost of each unit sent by store i to satisfy a one-unit unmet demand at store j. In this paper, the transshipment lead time is considered non-negligible. The shipped quantity T ij will be received by store j after a deterministic lead time L ij . This lead time depends on many factors, such as (a) physical distances between the different stores, (b) availability of transportation vehicles and their capacities, (c) the traffic jam, and possible breakdowns that may arise. After the end of the transshipment process, if store i still has a surplus inventory, it will be penalized by a per-unit holding cost of h i . If store j still has unmet demands, it will be penalized by a per-unit shortage cost of p j .

In each period, we must determine the replenishment and transshipment quantities. The shipped quantities T ij depend on the policy in force and its control parameters. The replenishment quantities S i depend on the higher level decision maker goals. For example, if we aim to minimize the number of unmet demands, we should supply each store i with a large quantity of stock S i .

Figure.1 Sequence of events in a period

Fixed cost transshipment costs are assumed to be negligible in our model. [START_REF] Herer | The multi-location transshipment problem[END_REF]] prove that, in the absence of fixed costs, if transshipment are made to compensate for an actual shortage and not to build up inventory at another store, there exists an optimal base stock policy S* for all possible stationary policies. To see the effect of the fixed costs on a two-location model formulation, see [Herer and Rashit (1999a)].

Modeling assumptions

Several assumptions are made in this study to avoid pathological cases:

 Assumption 1 (Lead time): All transshipment lead times are both positive and deterministic. The whole transshipment process is supposed to take place within the same period. In other words, all lead times L ij are less then the duration of the period. This may avoid shipped inventory at period t to arrive at period t+1. Replenishment lead times are negligible between the central warehouse and all the stores.

 Assumption 2 (Demand): Customers' demands at each store are fulfilled either by the local available inventory or by the shipped quantities that may come from other stores. In addition, since the transshipment lead times are not negligible, we assume that customers would wait until the end of the transshipment process. Unmet demands after transshipments realization are lost.

 Assumption 3 (Transshipment policy): The transshipment policy is stationary, that is, the transshipment quantities are independent of the period in which they are made; they depend only on the available inventory after demand observation. In this study, we will employ a transshipment policy known as complete pooling. This transshipment policy can be described as follow [Herer and Rashit (1999b)]: "the amount transshipped from one location to another will be the minimum between (a) the surplus inventory of sending location and (b) the shortage inventory at receiving location". The optimality of the complete pooling policy is ensured under some reasonable assumptions detailed in [Tagaras (1999)].

 Assumption 4 (Replenishment policy): At the beginning of every period, replenishments take place to increase inventory position of store i up to S i taking into account the remaining inventory of the previous period. The optimality of the order-up-to policy in the absence of fixed costs is proven in [START_REF] Herer | The multi-location transshipment problem[END_REF]].

Model formulation

Cost function

Since inventory choices in each store are centrally coordinated, it would be a common interest among the stores to minimize aggregate cost. At the end of the period, the system cost is given by:

                   I i I j j j j i i i D S K S D p D S h D S C , , (1)
The first and the second term on the right hand side of (1) can be respectively recognized as the total holding cost and shortage cost before the transshipment. However, the third term is recognized as the aggregate transshipment profit since every unit shipped from i to j decreases the holding cost at i by h i and the shortage cost at j by p j . However, the total cost is increased by τ ij because of the transshipment cost. Due to the complete pooling policy, the optimal transshipment quantities T ij can be determined by solving the following linear programming problem:

             I i I j ij ij j i T T p h D S K ij  max , (2) Subject to         I i D S T I j i i ij , (3)         I j S D T I i j j ij , (4) 0  ij T (5)
In (2), problem K can be recognized as the maximum aggregate income due to the transshipment. T ij denotes the optimal quantity that should be shipped from i to fill unmet demands at j. Constraints (3) and ( 4) say that the shipped quantities cannot exceed the available quantities at store i and the unmet demand at store j.

Since demand is stochastic, the aggregate cost function is built as a stochastic programming model which is formulated in (6). The objective is to minimize the expected aggregate cost per period.

                               I i I j j j j i i i S S D S K S D p D S h D S C , min , min (6)
Recall that the demands joint distributions are known in advance. The expected aggregate cost can be given by:

          S K S C D S C AT BT S S    min , min (7)
where BT C denotes the expected cost before the transshipment, called Newsvendor 1 cost, and AT K denotes the expected aggregate income due to the transshipment. This decomposition shows the important relationship between both the newsvendor and the transshipment problem. By setting very high transshipment costs, i.e. τ ij > h i + p j , no transshipments will occur. Problem K AT will then return zero. Consequently, we can deal with both multiobjective transshipment and newsvendor problems.

Fill Rate function

One of the most important performance measures of inventory distribution systems is the fill rate at the lowest echelon stocking locations. The fill rate is equivalent to the proportion of the satisfied demand. We extend the fill rate formulation given in [Tagaras (1999)] to n locations model. Let F be the aggregate fill rate measure after the transshipment realization.

         j j i ij j j D T S D D S F , min , (8)
Notice that the whole system fill rate would be maximized if we order very large quantities at the beginning of every period. However, this may results in global holding cost augmentation. If we order very little quantities S i , we certainly avoid holding costs, but the different locations will often be unable to satisfy customers' demands. This badly affects the system fill rate. Thus, we need to find good solutions taking into account the balance among costs and service level.

Lead time function

The fill rate measure is widely used service criteria to evaluate the performance of inventory distribution systems. However, it does not take into account the lead times caused by the transshipment process. In other words, we can have a perfect fill rate value while making customers waiting for long time. In our attempt to integrate the lead time in our Transshipment model, and following [START_REF] Pan | Allocation of order quantity among suppliers[END_REF]], we suggest this aggregate performance measure

         I j I i L T D S L j i ij ij , , , , (9)
Where T ij L ij denotes the lead time caused by the shipping T ij units from i to j. Although S and D variables are not visible in the lead time function formulation, they are present in the K linear programming problem which leads to computing T ij values.

Multiobjective problem formulation and estimation

As we have mentioned before, the main purpose of this research is to study the multilocation transshipment problem taking into account the optimization of three conflicting objectives: cost (1), fill rate (8) and lead times (9) where the decision variables are the order quantities S=(S 1 ,…,S N ).

In our case, all the objectives are stochastic because of the demand randomness modelled by the continuous random variables D i with known joint distributions. The stochastic nature of the problem leads us to compute the expected values of each objective function. In addition, an analytical tractable expression for problem K given in (2) exists only in the case of a generalized two-location problem or N-location with identical cost structures [START_REF] Krishnan | Inventory control in N warehouses[END_REF]]. In both cases, the open linear programming problem K has an analytical solution. But in the general case (many locations with different cost structures), we can use any linear programming method to solve problem K. In this study, we used the Simplex Method. The mentioned properties of our problem are sufficient to conclude that it is not possible to compute the exact expected values of the stochastic functions given in (1), ( 8) and ( 9). The demand randomness and the absence of a tractable expression for problem K are the only important. The most common method to deal with noise or randomness is resampling or re-evaluation of objective values [H.-G. [START_REF] Beyer | Evolutionary algorithms in noisy environments: Theoretical issues and guidelines for practice[END_REF]]. With the resampling method, if we evaluate a solution S for N times, the estimated objective value is obtained as in equation ( 8) and the noise is reduced by a factor of N . For this purpose, draw N random scenarios D 1 ,…,D N independently from each other (in our problem, a scenario D k is equivalent to a vector demand

D k =(D 1 1 ,…,D N N ). A sample estimate of f(S), noted E(f(S,D)), is given by   N S f Var D S f N S f D S f N k k           )] ( [ ) , ( 1 ) ( ) , ( 1 (10)
We remark that the approximation quality is as good as N is big.

 

) ( lim ) ( ) , ( S f S f D S f N    (11)
In summary, the optimization problem (P) to be solved in this study is the following:

(P):              S L S F S C min max min (12)
where C , F and L are respectively the approximations of the expected global cost, fill rate and lead time; S=(S 1 ,…,S N ) is the a vector of positive order quantities.

Multiobjective Optimization

Most real world problems have several (usually conflicting) objectives to be satisfied.

A general multiobjective optimization problem has the following form:

  ) ( ),..., ( ), ( min 2 1 S f S f S f k (13)
Subject to the m inequality constraints and the p equality constraints:

m i S g i ,..., 2 , 1 , 0 ) (   (14) p i S h i ,..., 2 , 1 , 0 ) (   (15)
The most popular approach to handle multiobjective problems is to find a set of the best alternatives that represent the optimal tradeoffs of the problem. After a set of such trade-off solutions are found, a decision maker can then make appropriate choices. In a simple optimization problem, the notion of optimality is simple. The best element is the one that realizes the minimum (or the maximum) of the objective function. In a multiobjective optimization problem, the notion of optimality is not so obvious. In other words, there is no solution that is the best for all criteria, but there exists a set of solutions of solutions that are better than other solutions in all the search space, when considering all the objectives. This set of solutions is known as the optimal solutions of the Pareto set or nondominated solutions. This is the most commonly adopted notion of optimality, originally proposed by Francis [Ysidro Edgeworth (1881)], and later generalized by [Vilfredo Pareto (1896)].

We say a vector of decision variable S* is Pareto optimal if there does not exist another S such that

         j one least at for S f S f and k i S f S f j j i i *), ( ) ( , , 2 , 1 *), ( ) (  (16)
In words, this definition says that S* is Pareto optimal if there exists no feasible vector of decision variable S that would decrease some criterion without causing a simultaneous increase in at least one criterion. This concept almost always gives not a single solution, but rather a set of solutions called the Pareto optimal set. The plot of the objective functions whose nondominated vectors are in the Pareto optimal set is called the Pareto front.

Evolutionary Multiobjective Optimization

There are two approaches to multiobjective optimization: classical methods and evolutionary methods. Classical methods convert the separate objective functions into a single objective function (weighted sum method, weighted metric methods, value function method, and goal programming methods). These methods have the drawbacks of modelling the original problem in an inadequate manner, giving a single solution and limiting the choices available to the designer. However, the last few years have shown the introduction of a number of non-classical, unconventional search algorithms [K. [START_REF] Deb | Multiobjective Optimization Using Evolutionary Algorithms[END_REF]]. Of these, we mention the evolutionary algorithms that mimic the nature's evolutionary principles to drive its search toward an optimal solution. Since a population of solution individuals is processed in each generation, the outcome of an evolutionary algorithm is also a population of solutions. If the optimization problem has a single optimum, all evolutionary algorithm population individuals can be expected to converge to that optimum. This ability to find multiple optimal solutions in one single simulation run makes evolutionary algorithms suitable in solving multiobjective optimization problems.

SPEA2: Strength Pareto Evolutionary Algorithm

Many multiobjective evolutionary algorithms have been proposed in the last few years. Comparative studies have shown for large number of test cases that, among all major multiobjective EAs, Strength Pareto Evolutionary Algorithm (SPEA2) is clearly superior. The key results of the comparison [E. [START_REF] Zitzler | SPEA2: Improving the strength Pareto Evolutionary Algorithm for Multiobjective Optimization[END_REF]] were: (1) SPEA2 performs better SPEA on all test problems, (2) SPEA2 and NSGA-II show the best performance overall. But in higher dimensional spaces, SPEA2 seems to have advantages over PESA and NSGA-II. In addition, it was proven that SPEA2 is less sensitive to noisy function evaluations since it saves the non-dominated solutions in an archive. In this study, we used SPEA2 to solve instances of the proposed multiobjective transshipment problem. At the beginning of the optimization process [E. [START_REF] Zitzler | SPEA2: Improving the strength Pareto Evolutionary Algorithm for Multiobjective Optimization[END_REF]], an initial population is generated randomly.

Optimization Results

In this section, we report on our numerical study. We first report a study conducted to analyze the shape of the cost, fill rate and lead time functions. Than, the resulting objective and solution spaces are considered. The corresponding Pareto fronts are analyzed and discussed. Secondly, we describe the experimental design which serves as the base for our experiments. We describe and analyze the results obtained for this basic experiment. This leads to understand the importance of our multiobjective model.

A detailed example

The first exemplary inventory model consists of 2 locations with the following parameters:

Table 1. Multi-location system configuration Parameter Value Holding cost (h i ) 3 Shortage cost (p j ) 2 Lead time (L ij ) 5 Transshipment cost (τ ij ) 0.5 Demand distribution (D i ) N(100,20)
To construct the shape of each objective function, we generated 30.000 samples of each function with respect to the setting given in Table1. Each sample consists of a random value of S = (S 1 , S 2 ).

Objectives sampling

Figure 2 (left) illustrates the convexity of the aggregate cost function. Figure 2 (right) shows that the area around the optimum is very flat as mentioned in [J. [START_REF] Arnold | Evolutionary Optimization of the a Multi-location Inventory Model with Lateral Transshipments[END_REF]]. Figure 2 (middle) illustrates the projection of the aggregate cost function on the (S 1 , S 2 ) plane. Notice that for higher inventory levels (S i > 250) the cost function grows linearily since it is proportional to the system holding costs.

Figure 3 (left) shows the form of the aggregate fill rate function. We notice that most of the solution area ensures high fill rate values.

Figure 4 (left) illustrates the aggregate lead time function. It has a more complicated shape when compared to the cost and fill rate functions. Higher transshipment lead time values exist when one location orders high stock quantity S i while the other orders very low stock quantity. This is evident because in that case, transshipment occurs frequently to move unsold units from surplus locations to locations with unmet demands. However, negligible lead time values result when all the ordered quantities are either very high or very low.

Figure2. Aggregate cost function

Figure3. Aggregate fill rate function

Figure4. Aggregate lead time function

Notice that all the objective functions of this studied case are symmetric relatively to the plane S 1 =S 2 . This is evident since all the considered locations have identical cost and demand structures.

Obviously, an individual consists of 2 genes only, each for one location. The multiobjective evolutionary optimization process was started with the parameters in Table2. To show the results of the evolutionary optimization, we have experienced 4 multiobjective problems detailed in the sections below. For each problem, we describe the objective sampled using 12000 points. Both Pareto fronts and its corresponding solution spaces are presented and analyzed.

Table2. SPEA2 parameters

Parameter

Cost vs. Fill Rate problem

Assume that decision makers' aims are minimizing aggregate cost while maximizing the fill rate in a multi-location system with lateral transshipment. This is a biobjective problem which we note C/F problem (Cost/Fill rate problem).

In figure 5 (left), the objective space of the C/F problem is shown. It is clear that cost and fill rate are correlated. There are not many dominated solutions. This proves that the transshipment ensures high service level while keeping the aggregate cost nearly optimal.

Cost vs. Lead time problem

This section deals with a bi-objective problem that minimizes both aggregate cost and transshipment lead time simultaneously. We notate it as the C/L problem. Studying this problem is interesting since it allows us to examine the trade-off between cost and lead time in a system based on lateral transshipment.

In figure 6 (left), the objective space is shown. Notice the presence of a local optimum in the objective space. This should be escaped by the evolutionary algorithm SPEA during the optimization process. Notice that in figure 6 (middle) the Pareto front is concave. As shown in section 3, standard multiobjective methods (i.e. aggregation method) are unable to identify a non-convex Pareto front. Consequently, the use of an evolutionary multiobjective algorithm is again well justified. When comparing the resulting Pareto front to the objective space, we clearly see that many dominated solutions were found out and eliminated by SPEA2.

Figure6. Cost/Lead time bi-objective problem (C/L)

Fill rate vs. Lead time problem

The bi-objective F/L problem concerns the maximization of the fill rate and the minimization of the transshipment lead time simultaneously. Figure 7 (middle) proves that there does not exist a Pareto front for the F/L problem, but only an ideal point that achieves a maximal fill rate (100%) and no transshipment lead time. To explain more this we refer to figure 7 (right). It is shown that the ideal point is obtained when we order high inventory levels in all the locations (i.e. S i > 200). The consequences are evident because, in one hand, high inventory levels increases the aggregate fill rate, on the other hand, it causes a general inventory excess which significantly decreases the transshipment frequency. It is also evident this solution is not practical as it considerably raise the aggregate holding. However, this problem may become interesting when production. This is known as the capacitated production model. In this case, we can not order large quantities. The ideal point may become unreachable. Instead, a Pareto front may emerge.

Cost vs. Fill rate vs. Lead time problem

The C/F/L multiobjective problem deals with the simultaneous optimization of the aggregate system cost (C), fill rate (F) and lead time (L).

Varying cost and demand structures

To show the effect of varying the multi-location system setting on the Pareto front characteristics, we have experimented with different cost structures and demand variances. System S 1 illustrates the case where holding inventory is very expensive. In system S 2 the shortage cost is costly. This may happen when there are many competitors with good service level. In system S 3 and S 4 we study the effects of the high and low demand variance on the Pareto front. N(100,05) 1 2 0,5

Table3. Systems settings

System

From figure 9, we conclude that all systems S 1-4 have a considerable effect on the final Pareto front spread. Notice that for systems S2 and S4, the entire C/F Pareto front is localized in an area where both cost and fill rate are nearly optimal. This is can be explained as follow: for system S2, having a relatively high shortage cost makes the global inventory level increase which ameliorates the fill rate. As for system S4, the demand standard deviation is very low. In other words, customer demands can be easily forecasted. Good ordering decision can be easily made to directly fill the observed demand. This has two important effects: a significant fill rate augmentation and a notable transshipment lead time as shown in the C/L and C/F/L Pareto fronts of system S4 (figure 9). When the holding cost is high (system S1), the minimizing the aggregate cost is ensured by decreasing the global inventory level. Thus, the fill rate is somewhat affected. Consider system S3, it is clear that the C/L Pareto front is very large. We conclude that cost and lead time are very correlated and conflicting when demand variance is high. In other words, high demand instability causes the global system to frequently face shortage and excess inventory situations. Thus, transshipments take place repeatedly as recourse actions to balance the inventory level. As a result, lead times increase considerably.

Figure9. Effects of system settings on the optimal Pareto fronts

Conclusion

This research proposes a multiobjective model for the multi-location transshipment problem. The model incorporates optimization of the aggregate cost; fill rate and transshipment lead time. The SPEA2 multiobjective evolutionary algorithm was applied to solve some instances of the proposed multiobjective transshipment problem. Different Pareto fronts were successfully generated in relatively short computation time. The result obtained confirms the conflict of cost, fill rate and lead time, and also demonstrates the need to integrate these objectives in the decision making process. Future work should deal with the application of appropriate noisy multiobjective methods and comparison of the obtained results.

Figure5.

  Figure5. Cost/Fill Rate bi-objective problem (C/F)

Figure7.

  Figure7. Lead time/Fill Rate bi-objective problem (F/L)

  Figure 8 (left) illustrates the objective space of the C/F/L problem. Figure 8 (middle) shows the resulting Paretofront. When comparing it to the objective space, we notice that during the optimization process, many dominated solutions where detected and omitted. In figure8(right), it is shown that inventory choices are well spread over the solution space.

Figure8.

  Figure8. Cost/Fill Rate/Lead time multiobjective problem (C/F/L)

The following notation is used in our model formulation:

	τ ij	Unit cost of transshipment from i to j
	T ij	Amount transshipped from i to j
	L ij	Unit transshipment lead time from i to j
	I +	Set of stores with surplus inventory (before transshipment)
	I -	Set of stores with unmet demands (before transshipment)
	n	Number of stores
	S i	Order quantities for store i
	S	Vector of order quantities, S = (S 1 , S 2 , …, S n ) (Decision variable)
	D i	Demand realized at i
	D	Vector of demands, D = (D 1 , D 2 , …, D n )
	h i	Unit inventory holding cost at i
	p j	Unit penalty cost for shortage at j

  In our multi-location problem, an individual is a base stock decision S = (S 1 , S 2 , …, S n ) consisting of n genes S i . At each generation, all the individuals are evaluated. A fine-grained fitness assignment strategy is used to perform individuals' evaluation. It incorporates Pareto dominance and density information. In other words, good individuals are the less dominated and the well spaced ones. The good individuals are conserved in an external set (archive). This is called the environmental selection. If the archive is full, a truncation operator is used to determine which individuals should be removed from the archive. The truncation operator is based on the distance of the k-th nearest neighbour computation method [B.W.[START_REF] Silverman | Density estimation for statistics and data analysis[END_REF]]. In other words, an individual is removed if it has the minimum distance to the other individuals. This mechanism preserves the diversity of the optimal Pareto front. The archived individuals participate in the creation of other individuals for the coming generations. These steps are repeated for a fixed number of generations. The resulting optimal Pareto front is located in the archive. The main loop of the SPEA2 algorithm is as follow:

	Input: N P (population size) N A (archive size) T (number of generations)
	Output: A (nondominated set)
	1) Initialize Population
		Create an initial population P 0
		Create empty external set A 0 ("archive")
	2) For t = 0 to T
		Evaluate fitness of each individual in P t and A t
		Copy all nondominated individuals in P t and A t to A t+1
		If the A t+1 size exceeds archive size N A reduce A t+1 using
		truncation operator
		If the A t+1 size is less than archive size then use dominated
		individuals in P t and A t to fill A t+1
		Perform Binary Tournament Selection with replacement on A t+1 to
		fill the mating pool
		Apply crossover and mutation to the mating pool and update A t+1
	End For

The newsvendor model is the basis of most existing transshipment literature. It addresses the case where transshipments are not allowed[START_REF] Porteus | Stochastic Inventory Theory[END_REF]].