David Romero
email: david.romero.diaz@gmail.com

Sergio Cavalieri
email: sergio.cavalieri@unibg.it

Barbara Resta
email: barbara.resta@unibg.it

Green Virtual Enterprise Broker: Enabling Build-to-Order Supply Chains for Sustainable Customer-Driven Small Series Production

Keywords: Glocalization, Mass-Customization, Sustainability, Build-to-Order Supply Chains, Small Series Productions, Green Virtual Enterprise, Brokerage

Global businesses are moving towards 'glocalization' and 'masscustomization' strategies to serve in a more personal and sustainable way their customers. Advances in ICT and green manufacturing technologies are enablers of this phenomenon. This paper explores a new business model, and its related supply chain model, the Green Virtual Enterprise Broker, which is fully customer-driven and aware of the environmental footprint of products and services to serve customized and small series production demands.

Introduction

To satisfy the consumers' desire for personalized products, many manufacturing enterprises have nowadays diversified their product lines to appease every consumer taste. Nevertheless, this approach to product diversification has backfired, resulting in failed product launches, huge overstock and significant upfront costs, since a greater variety of product options usually leads to more dissatisfied consumers, due to raised expectations and unattainable perfection [START_REF] Markwart | Emerging Consumer Trends -Customization[END_REF]. This reality has left many manufacturing enterprises with negative economic, social and environmental footprints that can be translated into capital losses on new product development investments, unsatisfied consumers in target customer segments, and wasted resources related to unsold products [START_REF] Romero | Forward -Green Virtual Enterprises and their Breeding Environments: Sustainable Manufacturing, Logistics & Consumption[END_REF]. As a result, new business models, and their related supply chains, are required to support in a sustainable way the emerging consumer trends of mass-customization (small series production) and personalization (single product) to individual customers or communities [START_REF] Molina | Virtual Enterprise Brokerage: A Structure-Driven Strategy to Achieve Build to Order Supply Chains[END_REF], relying on novel production paradigms characterized by flexible open manufacturing networks of small production units. Furthermore, Internet sales, both B2C & B2B, have made any product globally accessible for purchase, but its delivery and provisioning of life cycle services is a different challenge for traditional business solutions. In this sense, the notion of a Glocal Networked Enterprise presents a promising hybrid agile and lean supply chain and business model that can effectively and efficiently support highly customized and service-enhanced products along their lifecycle by involving manufacturers, customers, communities, third-party logistics providers and local service suppliers in a business ecosystem.

This paper explores a new business model, and its related supply chain model, the Green Virtual Enterprise Broker, which is fully customer-driven and aware of the environmental footprint of products and services along their lifecycle.

Sustainable Customer-Driven Business Models

New sustainable and customer-driven business models will continue emerging in the coming years due to the rapid advances in information and communication technologies, as well as in green manufacturing technologies, that have the potential to support a new generation of supply chain models. Such models will be characterized by the customer involvement in the supply chain as co-inventors (e.g. Quirky), codesigners (e.g. mi Adidas), or even as part of the assembly and delivery activities (e.g. IKEA); retailers as virtual business brokers; independent manufacturers as product development networks; and independent suppliers as logistics and product servicing networks. As a result, future business scenarios are based on collaborative and participatory business models and networked enterprises [START_REF] Romero | Forward -Green Virtual Enterprises and their Breeding Environments: Sustainable Manufacturing, Logistics & Consumption[END_REF].

Sustainable Business Models

Sustainable business models seek to go beyond delivering economic value -in accordance with a triple bottom line approach. According to Lüdeke-Freund [START_REF] Lüdeke-Freund | Towards a Conceptual Framework of Business Models for Sustainability[END_REF] a sustainable business model seeks to create balanced social, environmental and economic value through integrating sustainability more fully into its business model and value proposition(s). Furthermore, Short et al. [START_REF] Short | Business Model Innovation for Embedding Sustainability -A Practice-Based Approach Introducing Business Model Archetypes[END_REF], define a sustainable value proposition as a long-term shareholder value created as a scalable source of competitive advantage by embracing opportunities and managing the risks/benefits associated with their economic, environmental and social developments.

Moreover, Stubbs and Cocklin [START_REF] Stubbs | Conceptualizing a "Sustainability Business Model[END_REF] state that sustainable business models use both a system and firm-level perspective, built on the triple bottom line approach, to define a supply chain model with a wider range of stakeholders. Sustainable business models require collaboration between companies, governments, communities and households; people and their communities play a critical role to bring such a change if provided with the smart thinking to increase efficiency and improve the usage of environmental resources, waste reduction and communal use of products or services (where possible) [START_REF] Bartolomeo | Eco-Efficient Services -What are they, How do they Benefit Customers and the Environment and How likely are they to Develop and be Extensively Utilized[END_REF]. As a result, next generation supply chain models will be based on sustainable business models capturing economic value, while protecting the environmental and generating social value for the customer by improving his/her quality of life through highly customized value propositions.

Customer-Driven and Community-Driven Business Models

Customer preferences are an important element in any business model and supply chain, since economic value is captured from customers [START_REF] Bowman | Value Creation versus Value Capture: Towards a Coherent Definition of Value in Strategy[END_REF]. Customer value refers to what the customer wants with certain limitations related to his/her purchasing power [START_REF] Pynnönen | Customer Driven Business Model -Connecting Customer Value to Firm Resources in ICT Value Networks[END_REF]. Therefore, in this context a customer-driven business model can be defined as a business model that echoes the voice of the customer and aims to meet or exceed his/her personal preferences based on main basic judging elements, such as: product functional features, service mix and quality, total cost of ownership, social and environmental impact.

Such customer-driven viewpoint, which can be seen as an on-demand manufacturing approach, can offer customers the opportunity for customizing or personalizing their products and manufacturing enterprises to increase their manufacturing resources productivity by avoiding unsold products.

In addition, to create new sources of value, several industrial sectors are striving to provide integrated product-service solutions, breaking down the traditional barriers between products and services. Product-Service Systems (PSS) prevail as a systemic approach for enabling a strategic and managerial transition from selling the pure artefacts to deliver a customized and result-oriented solution providing a unique and positive experience to the user throughout his/her journey with the adopted solution [START_REF] Cavalieri | Product-Service Systems Engineering: State of the Art and Research Challenges[END_REF].

With result-oriented solutions customers get the ownership benefits with less personal burden, cost savings and lower impact on environment, hence showing more captivating alternative to standard and traditional buying and ownership styles. The focus is not limited to the communal use of products and services, but the primary objective is to promote and encourage the active role of consumers towards sustainable communities. Collaborative lifestyles are ideas based on people with similar interests coming together to share and exchange less tangible assets such as time, space, skills and money. As a result, customer-driven models are escalating towards community-driven models, considering that the choices of the single customers are not taken on an individual base but rather with their explicit awareness of the benefits or the rebound effects that their decisions could exert on the community they belong to. Collaborative business models like: sharing, lending, exchange, swapping, and bartering are now able to operate again on a large scale, across geographic boundaries, thanks to the advent of modern technology [START_REF] Botsman | What's Mine Is Yours: The Rise of Collaborative Consumption[END_REF].

Capturing sustainable value in small series productions and/or personalized products in a global marketplace requires the interplay of various collaborative networks (e.g. a business ecosystem), such as product development and servicing networks, including customers and local stakeholders, co-creating highly customized and serviceenhanced products [START_REF] Camarinha-Matos | Collaborative Business Scenarios in a Service-enhanced Products Ecosystem[END_REF] [START_REF] Camarinha-Matos | Interplay of Collaborative Networks in Product Servicing[END_REF].

In the following sections, different production approaches will be explored to offer highly customized products to single customers or community of customers in a sustainable way.

Small Series Production (Special Edition Items)

A Small Series Production (SSP) is characterized by a small run (small lot size) and a low number of repetitions (frequency a product run is repeated) [START_REF] Lödding | Handbook of Manufacturing Control: Fundamentals, Description, Configuration[END_REF]. From a marketing perspective, a small series production is known as a special edition, and represents a restricted number of products being produced every once in a while (e.g. season) with some extra materials of some kind included and/or certain level of customization. For example: textiles, clothing and footwear seasons collections. Small series productions, or special editions, call for a Configure-to-Order (CTO) production approach offering customers a standard customization based on a predefined number of customization alternatives (e.g. a solution space1 ) aiming to satisfy their demand. Special editions are customized based on standard product designs, have a slightly higher cost, a limit variety, and are produced only when an order is placed.

Table 1 presents some of the production and supply chain management (SCM) characteristics and challenges of a CTO operational model to support global small series productions.

Table 1 -Production & Supply Chain Management Challenges in SSPs

Process

Characteristics Challenges

Design & Engineering • Standard customization.

• Medium customer-driven design.

• Designs based on common parts and modular subassemblies.

Production

• Pull order system.

• Medium volume.

• Medium flexibility.

• Medium to Short cycle time.

• Medium inventory costs.

• Medium total costs.

• Inventory management across the supply chain.

Logistics & Distribution • Medium to Short cycle time.

• High supply chain management and integration.

One-Time Production (Limited Edition Items)

A One-Time Production (OTP) is characterized by a small run; i.e. only one small lot is produced and the product is not manufactured again (repetitions = zero) [START_REF] Lödding | Handbook of Manufacturing Control: Fundamentals, Description, Configuration[END_REF]. From a marketing perspective a one-time production is known as a limited edition, and represents a restricted number of products being produced for a unique time with a particular design. For example: exclusive sport and luxury cars production. On-time productions, or limited editions, call for a Make-to-Order (MTO) production approach offering a high level of customization (one of a kind) and high quality. Limited editions are tailored (an exclusive design), have a high cost, a limit number of units, and are produced only when an order is placed.

Table 2 presents some of the production and SCM characteristics and challenges of a MTO operational model to support global on-time productions.

Personalized Production (Deluxe Item)

A Personalized Production (PP) is characterized by a one item production according to single customer requirements [START_REF] Lödding | Handbook of Manufacturing Control: Fundamentals, Description, Configuration[END_REF]. From a marketing perspective, a personalized production is known as a deluxe item, and represents a unique engineering design or significant customization according to be produced according to specific customer's requirements. For example: a personalized competition sportswear or equipment for a professional athlete.

Table 2 -Production & Supply Chain Management Challenges in OTPs

Process

Advantages Challenges

Design & Engineering

• One of a kind customization.

• Tailored customization.

• None customer-driven design.

• Low standard parts ratio.

• Customization extent is high.

Production

• Pull order system.

• Medium to low volume.

• Medium flexibility.

• Medium cycle time.

• Low inventory costs.

• Medium total costs.

• Demand quantity is small.

• Production planning based on order. • Manufacturing is trigger by customer orders. • Medium delivery time.

Logistics & Distribution

• Medium cycle time.

• None supply chain integration.

Personalized productions, or deluxe items, call for an Engineer-to-Order (ETO) production approach offering a complete involvement of the customer in the item (product) design and engineering (e.g. unique design, set of part numbers, bill of materials, routing, etc.). Deluxe items are developed from scratch for each single customer, and therefore have a high cost and are produced only when an order is placed.

Table 3 presents some of the production and SCM advantages and challenges of an ETO operational model to support global personalized productions.

Table 3 -Production & Supply Chain Management Challenges in PPs

Process

Advantages Challenges

Design & Engineering

• High customization (personalization). • High customer-driven design (full involvement).

• High product complexity.

Production

• Pull order system.

• Low volume.

• High flexibility.

• Large cycle time.

• None inventory costs.

• High total costs.

• Long delivery time.

Logistics & Distribution

• Large cycle time.

• Long delivery time.

Collective Production (Shared Item)

A Collective Production (CP) is characterized by the production of a bundle of products and services according to the requirements of a close community of customers. From a marketing perspective, a collective production could be termed as shared item, since design, engineering and delivery requires a significant customization according to the specific local and cultural needs of the community sharing the common solution. For example: energy management systems, local mobility systems, healthcare systems. This kind of solutions call for a novel Participatory-Engineering-to-Order (P-ETO) production approach, since the whole community, through a participatory mechanism, needs to be involved in the definition of the requirements and the engineering of the shared solution. A top-down approach (without the involvement of the community since the beginning) would inhibit its widespread adoption.

Table 4 -Production & Supply Chain Management Challenges in CPs

Process

Advantages Challenges

Design & Engineering

• High customization (personalization). • High customer-driven design (full involvement).

• Long design and engineering time. • Contradictory requirements. Production • Pull order system.

• Very low volume.

• High flexibility.

• Large cycle time.

• None inventory costs.

• High total costs.

• One-of-a-kind supply chain.

Logistics & Distribution

• High service costs.

• Long delivery time.

Some of the related challenges that can be foreseen are: (a) engineering and delivering community-driven solutions requires a variety of professional skills, including among others sociologists and urban planners; and (b) given the complexity and the local features of the solution, deriving from an integration of more products and services, the configuration of the supply chain would be one-of-a-kind, specifically designed and scarcely repetitive.

Table 4 presents some of the production and SCM advantages and challenges of a P-ETO operational model to support global personalized productions.

Green Virtual Enterprise Broker/Brokerage and their Glocal Networked Enterprises

Global businesses are moving towards glocalization (globalized but localized) [START_REF] Hesselbach | Glocalized Solutions for Sustainability in Manufacturing -Preface[END_REF] and mass-customization strategies to serve in a more personal and sustainable way their customers [START_REF] Romero | Collaborative Networked Organisations and Customer Communities: Value Co-creation and Co-innovation in the Networking Era[END_REF]. Authors define a Green Virtual Enterprise Broker (GVE-Broker)

as a new business model where a focal enterprise2 creates sustainable value by mobilizing and managing processes and resources rather than owning them. A GVE-Broker business model relies on a Glocal Networked Enterprise (GNE) composed by a network of enterprises, with global presence as network, but with locally available skills or core-competences and resources at the localities of their member enterprises to better serve customers worldwide.

A GNE is a breeding environment 3 for the dynamic creation of Build-to-Order (BTO) supply chains [START_REF] Molina | Virtual Enterprise Brokerage: A Structure-Driven Strategy to Achieve Build to Order Supply Chains[END_REF], named: virtual manufacturing and/or service enterprises [START_REF] Romero | Forward -Green Virtual Enterprises and their Breeding Environments: Sustainable Manufacturing, Logistics & Consumption[END_REF], to meet the specific requirements of customers, and at the same time adopt, under case by case bases (the business opportunity characterization) the proper supply chain strategy/model (e.g. agile, lean, flexible) to cope with the uncertainties faced by the demand and sustainable and competitive supply of small series productions and personalized products, and their related services [START_REF] Hau | Aligning Supply Chain Strategies with Product Uncertainties[END_REF]. By associating the right business partners in a Green Virtual Enterprise (VE), BTO supply chains [START_REF] Molina | Virtual Enterprise Brokerage: A Structure-Driven Strategy to Achieve Build to Order Supply Chains[END_REF] [16] can face the challenges of a customer-or community-driven and sustainable supply chain with global added value product-service systems as customized 'value propositions'; at the same time they would achieve a sustainable competitive advantage through the efficient use of locally available resources and competences in glocal networked member enterprises to reduce costs, lead time, environmental footprint and social negative impacts.

GVE-Brokers activities will be performed by means of a web-based collaborative solution platform (e.g. an e-marketplace) for the realization of sustainable business ecosystems for the co-creation, manufacturing and delivery of customized productservices in distributed markets.

This web-based collaboration solution platform (see Table 5) will have a threefold service support offer for: (a) services for customers based on user toolkits 4 for masscustomization, personalization and participatory engineering of value propositions, where customers can access to a solution space for co-innovating, co-creating and/or co-developing his/her own products and services [19] [20] [21] [START_REF] Hermans | A Model for Evaluating the Solution Space of Mass Customization Toolkits[END_REF], (b) services for GVE-brokers based on GVE creation tools named: opportunity identification and characterization, GVE rough planning, GVE partners search and suggestion, GVE composition, GVE partners negotiation, detailed GVE planning, GVE partners contracting, and GVE set-up [START_REF] Romero | Green Virtual Enterprises Breeding Environment Reference Framework[END_REF] [24] [START_REF] Wang | An Ontological Intelligent Agent Platform to Establish an Ecological Virtual Enterprise[END_REF], and (c) services for GVE coordinators based on GVE management tools such as: project planning and decision support, project execution and monitoring, and customer follow-up [START_REF] Romero | Green Virtual Enterprises Breeding Environment Reference Framework[END_REF] [START_REF] Negretto | VO Management Solutions -VO Management e-Services[END_REF].

User toolkits as virtual tools build an interface between manufacturers and service providers and their customers. User toolkits can be employed by manufacturers and service providers to get an exact purchase order and therefore produce customized products just when the customers need them and only in the quantity they are needed. Hence, user toolkits offer two advantages: (a) allow users to exactly specify their design preferences reducing the possibility of unsold products and increasing customer satisfaction, and (b) improve customer relationship [19] [20] [21] [START_REF] Hermans | A Model for Evaluating the Solution Space of Mass Customization Toolkits[END_REF]. GVE creation tools will support GVE-brokers to find glocally (globally and locally) the right GVE partners considering the availability of their green capabilities and capacities, cost, and localization in order to build the best supply chain possible with the shortest lead time, cost and environmental footprint. Within the GVE creation tools, those related to GVE partners search and suggestion will play a vital role to help GVE-brokers to find and evaluate different feasible GVE configurations with respect to customer-, economic-, social-and environmental-oriented criteria (e.g. customer preferences, production cost, delivery cost, lead time, footprint, green technologies, etc.) [START_REF] Romero | Green Virtual Enterprises Breeding Environment Reference Framework[END_REF] [24] [START_REF] Wang | An Ontological Intelligent Agent Platform to Establish an Ecological Virtual Enterprise[END_REF].

Thus, GVE-brokers capability to dynamically create BTO supply chains, tailored within a glocal networked enterprise, seems to be the most promising sustainable strategy to support 'glocal markets' and respond to the quality-, time-, cost-and environmental-frames demanded by the consumers of customized and small series production products that want a premium customer service (attention) and the feel of proximity (near-by store) when it comes to the services associated to their products. In this scenario (see Fig. 1), glocal networked enterprises are an encouraging organizational model to enable agile, lean, and reasonably priced production and services activities glocally-wide [START_REF] Hartel | Virtual Organization of After-Sales Service in the One-of-a-Kind Industry[END_REF]. networks to strengthen a structure for 'glocal operations'5 that responds to individual and niche customers' needs on a global scale with the shortest lead time, cost and environmental footprint possible [23] [26]. GVE coordinators will formulate 'glocal strategies' to incorporate the adaptation of the network glocal core-competences and resources, business opportunities characteristics, and location of the glocal networked member enterprises to suit the requirements of a local customer and attain a new competitive advantage. GVE coordinators will utilize the glocal network experience for customizing products and services in such way that appeal to local/niche markets (small series productions) and single customers (personalization) [START_REF] Dumitrescu | The Glocal Strategy of Global Brands[END_REF] [29] [START_REF] Johanisson | Building a "Glocal" Strategy -Internationalizing Small Firms through Local Networking, 39ème Conférence Mondiale de[END_REF].

Conclusions and Future Work

Glocal Networked Enterprises are becoming a needed reality in a globalized marketplace (e.g. e-commerce), aided by an emerging consumer trend for customized products, and supported by the progress in information, communication and production technologies (e.g. Big Data, Internet of Things, 3D printing). Furthermore, future glocal networked solutions will have to face the constraints to achieve an economically, socially and environmentally sustainable industrial landscape and marketplace in a global perspective [START_REF] Hau | Aligning Supply Chain Strategies with Product Uncertainties[END_REF].

Green Virtual Enterprise Brokers and their Glocal Networked Enterprises offer an encouraging organizational model for managing 'glocal operations' by means of the cooperation of manufacturing and service enterprises to fulfill world-wide various production and service provision needs. Hence, new markets are opening up for customized and small series production products and their related services but require new collaborative supply chain and business models [START_REF] Johanisson | Building a "Glocal" Strategy -Internationalizing Small Firms through Local Networking, 39ème Conférence Mondiale de[END_REF].

Further work is needed to develop not only new collaborative supply chain and business models but also new methods and (ICT) tools to enable 'BTO supply chains for sustainable customer-driven small series productions'.

Fig. 1 .

 1 Fig. 1. Glocal Networked Enterprise World-Wide Operations GVE management tools will support GVE coordinators in their main activity of orchestrating the glocal networked enterprise's product development and servicing

Table 5 -

 5 The Green Virtual Enterprise Broker and its Solution Platform Overview

	Building Blocks	Types
	Value Proposition(s)	• Mass-customized • Personalized • Shared
	Customer Segments	• Individual customers • Customer niche • Customer community
	Customer Relationships	• Customer-driven (co-innovation, co-creation, co-development)
	Channels	• e-Marketplace
	Key Partners		Glocal Networked Enterprise:
	(stakeholders)	• Manufacturers • Service Providers • Customers & Communities • Brokers
		Front-end	Intermediary	Back-end
		User toolkits for:	Broker toolkit for:	Networked Enterprise
		mas-customization,	• Opportunity	toolkit for:
		personalization and	characterization	• Monitor activities
		participatory	• Partners search and	• Monitor finance
		engineering	selection	• Monitor KPIs
	Key Activities &		• Topology set-up	• Measure indicators
	Resources		• Schedule activities	• Manage exceptions
			• Assign tasks	• Monitor risks
			• Allocate budget	• Liability (guarantees)
			• Define KPIs
			• Identify risks
		e-Marketplace Platform: An interactive environment for
		value co-creation and collaborative supply chain management.
	Cost Structure	• Costing models (e.g. variables costs + economies of scope).
	Revenue Streams

• Profit models (e.g. subscription fees + brokerage fees).

A solution space encompasses all the possible designs a toolkit can produce.

A focal enterprise "is the initiator of an international business transaction, including multinational and small/medium size enterprises, that conceives, designs, and produce

A focal enterprise "is the initiator of an international business transaction, including multinational and small/medium size enterprises, that conceives, designs, and produce the offerings (goods and services) intended for consumption by customers worldwide"[START_REF] Cavusgil | International Business Strategy, Management and New Realities[END_REF].

A virtual enterprise breeding environment is a long-term strategic alliance of enterprises aimed at offering the necessary conditions to support the rapid and fluid configuration of virtual manufacturing and/or service enterprises[START_REF] Romero | Forward -Green Virtual Enterprises and their Breeding Environments: Sustainable Manufacturing, Logistics & Consumption[END_REF].

A user toolkit is a technology that allows users to design a novel product via trial-and-error experimentation and deliver them an immediate (simulated) feedback on the potential outcome of their design ideas[START_REF] Von Hippel | Perspectives: User Toolkits for Innovation[END_REF].

Glocal operations can be defined as strategies for providing a global offer while taking local related issues into account and therefore meeting certain local/particular needs or preferences, at lower costs due to the global edge of the networked enterprise[START_REF] Johanisson | Building a "Glocal" Strategy -Internationalizing Small Firms through Local Networking, 39ème Conférence Mondiale de[END_REF].


Muhammad Khakim Habibi

Olga Battaïa

Van-Dat Cung

Alexandre Dolgui
email: dolgui@emse.frvan-dat.cung@grenoble-inp.fr

Muhammad Khoirul

Khakim Habibi

Integrated Procurement-Disassembly Problem

Keywords: Vehicle routing, disassembly, line design and balancing, inventory control, End-of-Life product

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Electronic and electrical manufacturing sector are encouraged to consider the environmental aspect of its production process. This condition is caused by the shrinking life cycle of electronic and electrical equipments (EEEs) henceforth increases the amount of waste electrical and electronics equipments (WEEEs). The main reasons are government's mandates to extend the responsability of manufacturer (mainly in EU, USA, Australia, Japan and South Korea), consumers' consciousness [START_REF] Sasikumar | Issues in Reverse Supply Chains, Part I: End-of-Life Product Recovery and Inventory Management-an Overview[END_REF][START_REF] Yang | The Optimization of the Closed-Loop Supply Chain Network[END_REF][START_REF] Ilgin | Performance Improvement Potential of Sensor Embedded Products in Environmental Supply Chains[END_REF] and the potential worthwhile of EOL products.

The disassembly process is considered to deal with this condition. It is a set of activity for disassembling the EOL product in order to release its precious and hazardous parts. Since it is expensive and time consuming acitivity, optimization is required for attaining the profitable state. Our research focuses on a field of disassembly process known as disassembly line balancing problem (DLBP).

DLBP is the assignment of disassembly tasks into a sequence of stations such that the returned product is disassembled based on the desired level of disassembly respecting the disassembly precedence relations and some measure of effectiveness [START_REF] Altekin | Profit-oriented Disassembly Line Balancing[END_REF]. Researches have been conducted in several related factors such as demanded and hazardous part prioritation, task failure, profit orientation etc.

However, the studies on DLBP are usually not connected with other decisions in reverse supply chain. Since the studies on forward supply chain show that the decisions integration permits the cost reduction [START_REF] Boudia | Integrated Optimization of Production and Distribution for Several Products[END_REF][START_REF] Boudia | A Reactive GRASP and Path Relinking for a Combined Production-Distribution Problem[END_REF][START_REF] Boudia | A Memetic Algorithm with Dynamic Population Management for an Integrated Production-Distribution Problem[END_REF][START_REF] Bard | A Branch-and-Price a Algorithm for an Integrated Production and Inventory Routing Problem[END_REF], the same idea should be investigated in the reverse supply chain.

For this purpose, this work is intended to deal with the collection and the disassembly process of EOL products. This research proposes an integrated model for Capacitated Vehicle Routing Problem based waste collection (w-VRP) and DLBP called integrated procurement-disassembly problem. The model minimizes the total cost corresponding to EOL products collection and disassembly process related to w-VRP and DLBP, respectively. During products collection process, we assume only one available vehicle and several suppliers who have EOL product to be collected. The model admits partial disassembly since it aims to release the demanded parts only. To the best of our knowledge, it is the first work proposes the integration between collection process and disassembly balancing problem.

The next sections are organized as follows. Section 2 gives an overview of related literature. Section 3 describes our mixed integer linear programming formulation. Section 4 provides computational results. The last section gives a conclusion and some prospects for future work.

Literature Review

DLBP has been investigated by researchers in many cases. Such as assembly line balancing problem (ALBP), one of the objectives is to minimize the number of workstations required to reach a given cycle time [START_REF] Dolgui | Supply Chain Engineering: Useful Methods and Techniques[END_REF]. Altekin et al. [START_REF] Altekin | Profit-oriented Disassembly Line Balancing[END_REF] proposed a profit-oriented partial DLBP model to maximize the earned profits of released part while taking into consideration the cost of performing disassembly task as well as fixed cost caused by opening workstations. Partial disassembly is represented by associating the disassembly task with its incurred cost. Bentaha et al. [START_REF] Bentaha | A Decomposition Method for Stochastic Partial Disassembly Line Balancing with Profit Maximization[END_REF][START_REF] Bentaha | A Sample Average Approximation Method for Disassembly Line Balancing Problem under Uncertainty[END_REF][START_REF] Bentaha | L-Shaped Algorithm for Stochastic Disassembly Line Balancing Problem[END_REF][START_REF] Bentaha | A Stochastic Formulation of The Disassembly Line Balancing Problem[END_REF][START_REF] Bentaha | Chance Constrained Programming Model for Stochastic Profit-Oriented Disassembly Line Balancing in the Presence of Hazardous Parts[END_REF][START_REF] Bentaha | Dealing with Uncertainty in Disassembly Line Design[END_REF] offered novel models of profit-oriented partial DLBP based on transformed AND/OR graph of [START_REF] Koc | Two Exact Formulations for Disassembly Line Balancing Problems with Task Precedence Diagram Construction using An AND/OR Graph[END_REF] under stochastic condition. The objective of [START_REF] Bentaha | A Sample Average Approximation Method for Disassembly Line Balancing Problem under Uncertainty[END_REF][START_REF] Bentaha | L-Shaped Algorithm for Stochastic Disassembly Line Balancing Problem[END_REF][START_REF] Bentaha | A Stochastic Formulation of The Disassembly Line Balancing Problem[END_REF] was to minimize the total fixed cost of opening workstations and recourse cost caused by task failure. The revenue of released products was considered in [START_REF] Bentaha | A Decomposition Method for Stochastic Partial Disassembly Line Balancing with Profit Maximization[END_REF][START_REF] Bentaha | Dealing with Uncertainty in Disassembly Line Design[END_REF]. The cost of handling hazardous parts was taken into account [START_REF] Bentaha | Chance Constrained Programming Model for Stochastic Profit-Oriented Disassembly Line Balancing in the Presence of Hazardous Parts[END_REF].

New issues combining several decisions related DLBP are emerged. Özceylan et al. [START_REF] Özceylan | Modeling and Optimizing the Integrated Problem of Closed-Loop Supply Chain Network Design and Disassembly Line Balancing[END_REF] dealed with closed-loop supply chain (CLSC) and DLBP. The proposed model aims to determine the material distribution in forward and reverse flows as well as to balance disassembly line through tasks assignment. Özceylan et al. [START_REF] Özceylan | Interactive fuzzy programming approaches to the strategic and tactical planning of a closed-loop supply chain under uncertainty[END_REF] proposed a model under undeterministic condition concerning task cost, inventory level, demand and reverse rates.

The decisions integration was principally studied for forward supply chain. Boudia et al. [START_REF] Boudia | Integrated Optimization of Production and Distribution for Several Products[END_REF][START_REF] Boudia | A Reactive GRASP and Path Relinking for a Combined Production-Distribution Problem[END_REF] and Boudia and Prins [START_REF] Boudia | A Memetic Algorithm with Dynamic Population Management for an Integrated Production-Distribution Problem[END_REF] worked on IPDP by minimizing the routing and production cost. Bard and Nananukul [START_REF] Bard | A Branch-and-Price a Algorithm for an Integrated Production and Inventory Routing Problem[END_REF] considered time windows into IPDP. Shiguemoto and Armentano [START_REF] Shiguemoto | A Tabu Search Procedure for Coordinating Production, Inventory and Distribution Routing Problems[END_REF] considered the cost of production and inventory at the production facility as well as consumers. Varthanan et al. [START_REF] Varthanan | A Simulation Based Heuristic Discrete Particle Swarm Algorithm for Generating Integrated Production-Distribution Plan[END_REF] proposed IPDP model under stochastic demand. Gharehyakeh and Tavakkoli-Moghaddam [START_REF] Gharehyakheh | A Fuzzy Solution Approach for A Multi-objective Integrated Production-Distribution Model with Multi Products and Multi Periods Under Uncertainty[END_REF] took into consideration the uncertainty of demand, machine and labor level with time windows. However, no study proposes a model integrating procurement -disassembly problem although these problems are interdependent due to their sequencial decisions.

Problem Description

Before being disassembled, the EOL products are collected from suppliers to disassembly plant. Subsequently, the products are stored at the inventory and will be disassembled in order to release the demanded parts. A single vehicle and a product type are considered. The data concerning product collection and disassembly process are known and deterministic.

In this section, a mixed integer linear programming (MILP) model of integrated procurement-disassembly problem is presented. The problem is defined on weighted and undirected graph network G = (N, E, D). N is the set of node denoting the considered suppliers and the inventory of facility plant. This inventory is denoted as node 1. E is the set of edges and D ab is the distance between node a and node b where D ab = D ba , a ∈ N , b ∈ N . The plant disassemblies a single product type during planning horizon T . A single vehicle with capacity C and unit running cost RC is used for collecting EOL products from suppliers. A supplier a has certain amount of EOL products at period t denoted as S at . A single vehicle visits each supplier at most once for each period. The collected products are stored at the inventory with unlimited capacity where the inventory level at the end of period t is denoted as I t , t ∈ T .

At the beginning of period t, the disassembly process begins based on the required demand of part l denoted by d lt , l ∈ L, t ∈ T . Our model requires binary variable d b lt , l ∈ L, t ∈ T which is equal to 1 if d lt is greater than 0. Since it is assumed that each product consists of exactly one part of type l, the minimum amount of products stored at inventory d max t , t ∈ T , before performing disassembly process at the beginning of period is the biggest amount for all required part at period t.

Our model adopts the AND/OR graph (AOG) in [START_REF] Koc | Two Exact Formulations for Disassembly Line Balancing Problems with Task Precedence Diagram Construction using An AND/OR Graph[END_REF] where auxiliary node A k , k ∈ K represents subassembly and basic node B i , i ∈ I denotes disassembly task. The relations between subassemblies and disassembly tasks are presented in AOG. The dummy task s is introduced to indicate that disassembly process at period t is finished due to the consideration of partial disassembly. P k is the set of tasks which preceedes subassembly A k , k ∈ K. S k , k ∈ K, denotes the set of tasks which succeeds A k , k ∈ K. Our model requires the set of tasks which permits to release part l, l ∈ L, denoted as P l .

Disassembly task times time i are known where the time of dummy task s, time s is 0. At period t, each required disassembly is assigned to a workstation. Workstation time is less than the given cycle time CT . F C denotes the fixed cost of opening a workstation. In our model, the decision variables are:

-I t inventory level at the end of period t; -Y at cumulative load of vehicle after visiting node a at period t; -X abt = 1 if the vehicle visits node a just before node b at period t; 0 otherwise.

x ijt = 1 if disassembly task i is assigned to workstation j at period t; 0 otherwise.

-

z jt = CT if x sjt = 1 ; 0 otherwise. Minimize Z = RC t∈T b∈N a∈N D ab • X abt + F C t∈T j∈J j • z jt (1)
Subject to:

I t = I t-1 + b∈N a∈N \{1} X abt • S at -d max t ∀t ∈ T, a = b; (2) a∈N
X abt ≤ 1 ∀b ∈ N \ {1} , ∀t ∈ T, a = b; (3) a∈N
X act = b∈N X cbt ∀c ∈ N, ∀t ∈ T, c = a, c = b; (4)
a∈S b∈S

X abt ≤ |S| -1 ∀t ∈ T, ∀S ⊆ N \ {1} : |S| ≥ 2;
(5)

Y bt -S bt -Y at ≥ - l∈L d lt • (1 -X abt ) ∀a ∈ N, ∀b ∈ N \ {1} , ∀t ∈ T, a = b; (6)
Y bt -S bt -Y at ≤ l∈L d lt • (1 -X abt ) ∀a ∈ N, ∀b ∈ N \ {1} , ∀t ∈ T, a = b; (7)
Y at ≤ C ∀a ∈ N, ∀t ∈ T ; (8)
Y 1t = 0 ∀t ∈ T ; ( 9
)
j∈J i∈P l x ijt ≥ d b lt ∀l ∈ L, t ∈ T ; ( 10
) j∈J i∈S0 x ijt = 1 ∀t ∈ T ; ( 11
) j∈J x ijt ≤ 1 ∀i ∈ I, ∀t ∈ T ; (12) i∈S k x ivt ≤ i∈P k v j=1 x ijt ∀k ∈ K \ {0} , ∀v ∈ J, ∀t ∈ T ; ( 13
)
i∈S k j∈J x ijt ≤ i∈P k j∈J x ijt ∀k ∈ K \ {0} , ∀t ∈ T ; ( 14
) j∈J x sjt = 1 ∀t ∈ T ; ( 15
) j∈J j • x ijt ≤ j∈J j • x sjt ∀i ∈ I, ∀t ∈ T ; (16)
z jt = CT • x sjt ∀j ∈ J, ∀t ∈ T ; ( 17
) i∈I x ijt • time i ≤ CT ∀j ∈ J, ∀t ∈ T ; ( 18
)
I t ≥ 0 ∀t ∈ T ; (19)
X abt ∈ {0, 1} ∀a ∈ N, ∀b ∈ N, ∀t ∈ T, a = b; (20)
Y at ≥ 0 ∀a ∈ N, ∀t ∈ T ; (21) x sjt , x ijt , ∈ {0, 1} ∀i ∈ I, ∀j ∈ J, ∀t ∈ T ; (22)
z jt ∈ {0, CT } ∀j ∈ J, ∀t ∈ T ; (23)
The objective function (1) aims to minimize the total cost consisting total procurement cost and total cost of opening workstations for entire planning horizon. Constraint set (2) balances the plant inventory at each period. At each period, constraint set (3) imposes that each supplier is visited at most once. Constraint set (4) guarantees that the vehicle leaves a node after visiting it. Constraint set [START_REF] Boudia | Integrated Optimization of Production and Distribution for Several Products[END_REF] eliminates the subtour occurrence. Constraint sets (6-7) update the vehicle load after visiting a node at each period. Constraint set (8) limits the vehicle load during its trips. After leaving the plant as depot of the trip, constraint set (9) resets the vehicle load as zero. Constraints sets [START_REF] Bentaha | A Decomposition Method for Stochastic Partial Disassembly Line Balancing with Profit Maximization[END_REF] describe the relation between part demand and its predecessors. Constraint sets [START_REF] Bentaha | A Sample Average Approximation Method for Disassembly Line Balancing Problem under Uncertainty[END_REF][START_REF] Bentaha | L-Shaped Algorithm for Stochastic Disassembly Line Balancing Problem[END_REF][START_REF] Bentaha | A Stochastic Formulation of The Disassembly Line Balancing Problem[END_REF][START_REF] Bentaha | Chance Constrained Programming Model for Stochastic Profit-Oriented Disassembly Line Balancing in the Presence of Hazardous Parts[END_REF][START_REF] Bentaha | Dealing with Uncertainty in Disassembly Line Design[END_REF][START_REF] Koc | Two Exact Formulations for Disassembly Line Balancing Problems with Task Precedence Diagram Construction using An AND/OR Graph[END_REF][START_REF] Özceylan | Modeling and Optimizing the Integrated Problem of Closed-Loop Supply Chain Network Design and Disassembly Line Balancing[END_REF][START_REF] Özceylan | Interactive fuzzy programming approaches to the strategic and tactical planning of a closed-loop supply chain under uncertainty[END_REF] are simplification of the model in [START_REF] Bentaha | L-Shaped Algorithm for Stochastic Disassembly Line Balancing Problem[END_REF]. Constraint set [START_REF] Bentaha | A Sample Average Approximation Method for Disassembly Line Balancing Problem under Uncertainty[END_REF] selects the first tasks succeeding EOL product. Constraint set [START_REF] Bentaha | L-Shaped Algorithm for Stochastic Disassembly Line Balancing Problem[END_REF] assigns the disassembly task into at most a workstation. The precedence relations between disassembly tasks and subassemblies are described by contraint set [START_REF] Bentaha | A Stochastic Formulation of The Disassembly Line Balancing Problem[END_REF]. Constraint set [START_REF] Bentaha | Chance Constrained Programming Model for Stochastic Profit-Oriented Disassembly Line Balancing in the Presence of Hazardous Parts[END_REF] selects only one OR successor. Constraint set [START_REF] Bentaha | Dealing with Uncertainty in Disassembly Line Design[END_REF] assigns sink node into a workstation. Constraint set [START_REF] Koc | Two Exact Formulations for Disassembly Line Balancing Problems with Task Precedence Diagram Construction using An AND/OR Graph[END_REF] guarantees that each disassembly task is assigned into a workstation with lower or equal index of sink node's workstation. The value of z jt is determined by constraints set [START_REF] Özceylan | Modeling and Optimizing the Integrated Problem of Closed-Loop Supply Chain Network Design and Disassembly Line Balancing[END_REF]. Constraint set (18) denotes the limitation of workstation time. Contraint sets [START_REF] Shiguemoto | A Tabu Search Procedure for Coordinating Production, Inventory and Distribution Routing Problems[END_REF][START_REF] Varthanan | A Simulation Based Heuristic Discrete Particle Swarm Algorithm for Generating Integrated Production-Distribution Plan[END_REF][START_REF] Gharehyakheh | A Fuzzy Solution Approach for A Multi-objective Integrated Production-Distribution Model with Multi Products and Multi Periods Under Uncertainty[END_REF](22)(23) describe the nature of decision variables. with zero load. Its capacity forces the vehicle to return back into the inventory for disposing its load. If the invetory level of EOL products is sufficient, the disassembly process begins releasing the demanded parts. The proposed model considers partial DLBP under deterministic condition with single product type. The objective function minimizes the total cost of product colletion and disassembly process through vehicle routing determination and disassembly task assignment. The model takes into account the constraints of DLBP, w-VRP and the balancing constraints coordinating these problems.

Some prospects concerning the proposed model are derived in order to approach the reality. For the next step, the model should be extended to the case of multiple products and multiple vehicles. Then, it should be tested on the industrial data. Moreover, since the uncertainty is major in disassembly process as well as EOL products collection, this factor has to be taken into account.

Table 3 .

 3 Vehicle Trip

			Period
	Vehicle Trip	1	2	3	4
	First trip	1, 4, 2, 1	1, 3, 1	1, 2, 1	1, 2, 1
	Second trip	1, 3, 1	-	1, 4, 1	-

Table 4 .

 4 Task Assignment

			Period
	Workstation	1	2	3	4
	1	2,6	1	1	2,6
	2	9	4,9	4,9	9

Acknowledgement

This work has been supported by Région Rhône-Alpes, France.

Computational Results

Since no benchmark instance exists for our problem, we considered the following example based on [START_REF] Bentaha | A Stochastic Formulation of The Disassembly Line Balancing Problem[END_REF]. A compass consisting seven parts is studied. Ten tasks permits to release one or some parts. At first period, the plant has 20 products available in the inventory. The cycle time is 0.61 second. The opening cost of workstation is 7 euros/second. A vehicle with 5000 capacity is used with running cost as 5 euro/km. Table 1 and 2 present the data of demand, part and supplier. The model was implemented in Java 7 using GNU Linear Programming Kit (GLPK) 4.9 on a PC with processor Intel R Core TM i7 CPU 2.9 GHz and 4 Go RAM under Windows 7 Professional. The optimal solution is obtained in 85.25 seconds with the total cost 1232.83 euros. Only 2 workstations are opened during four periods considered. The vehicle's trips and disassembly tasks assignment are presented in table 3 and 4, respectively.

Conclusion

This work addresses integrated procurement-disassembly problem. It combines w-VRP and DLBP for collecting and disassembling the EOL product. A capacitated vehicle collects EOL product from suppliers. The vehicle begins its trip


Albéric Cornière

Virginie Fortineau

Thomas Paviot

Samir Lamouri

Jean-Louis Goblet

Audrey Platon

Cécile Dutertre

Modelling requirements in service to PLM for long lived products in the nuclear field

Keywords: Requirements Engineering, PLM, Ontology, Long Life-Cycle, Large-Scale, System Engineering

Requirements engineering in usually considered a first step before design that is to evolve with each generation or version in a product line. Nuclear plants however, are subject to modifications during their lifetime, in their design and implementation as well as in the requirements they have to satisfy. Economic, technical and safety reasons lead to extending the requirements engineering process through the whole life-cycle of the nuclear plants. This article presents an ontology-based approach to integrating the requirements engineering into a PLM approach for such long-lived, large-scale products.

Introduction

Requirements engineering in usually considered a first step before design that is to evolve with each generation or version in a product line. Nuclear plants however, are subject to modifications during their lifetime, in their design and implementation as well as in the requirements they are to satisfy. Economic, technical and safety reasons lead to extending the requirements engineering process through the whole life-cycle of the nuclear plants. This article will present the requirements engineering with the goal of setting a frame to the problem, then it presents the different approaches that are used, mainly in the field of computer sciences. In section 4 several particularities in the context of nuclear plants are given, leading in section 5 to a proposition of modelling with the intent to answer the industrial problem.

Definitions and uses of requirements

Requirements engineering is commonly mentioned in scientific publications, especially in the field of computer sciences. However, there is seldom a definition given for this process, and comparatively few of the articles available treat of requirements engineering itself. Jureta [START_REF] Jureta | A core ontology for requirements[END_REF] notices "To say that requirements are engineered is currently more of an ideal than the actual state of affairs". We will retain the definition given by [START_REF] Garion | Apports de la logique mathématique en ingénierie des exigences[END_REF] : "Requirements engineering is the process producing a coherent set of specifications on a yet-to-be-designed object"

As for requirements, the definition is still heterogeneous depending on the context in which the notion thereof is used : in most situations, the starting point with requirements engineering is the expression of what the product is to accomplish, that is to say the expression of the needs of the stakeholders. The SysML specifications [15] refer to requirements in the fields of computer sciences as thus : "A requirement specifies a capability or condition that must (or should) be satisfied. A requirement may specify a function that a system must perform or a performance condition a system must achieve", while many other consider them as high level specifications of what the product is to accomplish [START_REF] Cheng | Research directions in requirements engineering[END_REF]. We were unable to find in the scientific literature a situation presented in which requirements are considered outside the beginning of life of a product, or in which they may change during the product life-cycle.

For the purpose of this article we will consider a requirement as "one or several properties or behaviours of a system that must be satisfied" [15] 3 Requirements modelling today Recent works using requirements engineering are mostly from the field of computer sciences ; about 90% to 95% of the search results on a scientific repository such as Springer link for "requirements engineering" are identified as computer science works. In those works, two main tendencies can be identified : on one hand, works that focus on defining the requirements so as to waive ambiguities, in order to allow design to be based on a reliable transcription of the stakeholders needs; and on the other hand works that focus on analysis of the requirements sets, in order to ensure the requirements set is coherent and satisfiable.

Eliciting the requirements

The first goal of requirements engineering is to define what needs the stakeholders express : several studies focus on this task [START_REF] Greenspan | On formal requirements modeling languages: Rml revisited[END_REF][START_REF] Zave | Four dark corners of requirements engineering[END_REF][START_REF] Helming | Towards a unified requirements modeling language[END_REF]. Goal-driven requirements engineering addresses this question by defining goals to be attained during design, and prioritising them considering which stakeholder expressed it, what importance it has to the main goals, and several other criteria.

The elicitation problem is crucial : even in the nuclear context and considering safety rules and regulations that are not to be interpreted, the requirement still have to be translated into expressions in a model for a computer to manipulate them. The elicitation of requirements is therefore needed to ensure a proper correspondence between expressed requirements and their expression in the model. [START_REF] Jureta | A core ontology for requirements[END_REF] presents a possible use of the DOLCE ontology (from [START_REF] Masolo | Wonderweb deliverable d17. the wonderweb library of foundational ontologies and the dolce ontology[END_REF]) for requirements elicitation.

Analysing the requirements

As most, if not all requirements define an obligation (or an interdiction) for the system, it has been shown by [START_REF] Cholvy | Checking regulation consistency by using sol-resolution[END_REF][START_REF] Garion | Apports de la logique mathématique en ingénierie des exigences[END_REF][START_REF] Garion | A modal logic for reasoning on consistency and completeness of regulations[END_REF][START_REF] Jureta | Revisiting the core ontology and problem in requirements engineering[END_REF][START_REF] Jureta | A core ontology for requirements[END_REF]] that a modal logic can be defined that allows to treat requirements as logic expressions expressed in first-order deontic logic. From there on, the whole set of requirements can be analysed through formal logic, manipulated and corrected to render the requirements set consistent if needed.

Modelling requirements with ontologies

Ontologies, especially using OWL2, allow for reasoning in direct logic: an ontology designed for requirements analysis is presented in [START_REF] Jureta | A core ontology for requirements[END_REF]. This model based on goal-driven requirements engineering is thorough and reliable, although it is thought primarily for the design phase of a product's life-cycle.

In the life-cycle of a product family, this presents little problem, as the evolution in requirements are addressed through different versions of the product; the requirements engineering process may then be repeated for each version of the product.

For the context of the nuclear industry, [START_REF] Fortineau | Improving the interoperability of industrial information systems with description logic-based models -the state of the art[END_REF] shows the benefits of ontologies in modelling products and uses rule-based models to express business rules, which in the model are similar to requirements.

Specificities of a PLM context in the nuclear industry

Modelling requirements for a nuclear plant in a PLM context presents specificities, among which some regarding the scale and complexity of the system, the length of the life-cycle, and the type of requirements considered.

The life-cycle of a nuclear plant, from the beginning of the requirements engineering phase to the end of dismantlement may well exceed a century. During this time-span, advances in the technology as well as experience in the field makes the requirements evolve, as well as the technical solutions available to satisfy them. While works exist regarding the evolution of requirements, they mostly focus on requirements that apply to software systems [START_REF] Ernst | An overview of requirements evolution[END_REF].

A nuclear plant is of large scale : the specifications elaborated through the requirements engineering process apply on billions of parts and systems. All those elements of the product are potentially interacting with each other in nontrivial ways. This makes the system too complex for manually going through the requirement engineering again. One of the characteristic examples is thermodynamic evolution of the reactor : the temperature and pressure inside the reactor can vary slowly in comparison to the speed at which a computer program is usually running.

The requirements on a nuclear plant include safety regulations that specify situations in which the plant has to return to a controlled, stable state when an accidental situation is to arise. This kind of requirements must be satisfied in any configuration, regardless of the evolutions the requirements and of the maintenance on the plant, and through the evolutions of the plant itself. These requirements typically specify the time acceptable to return in a controlled state. As described above, the behaviour of the plant is not trivial, and complex behaviour and business rules may apply to the requirement to lead to the specifications.

To respond to the above-mentioned points, there is a need for a model allowing not only to define a coherent set of requirements, but also reference the specifications inside an as-complete-as-possible model of the plant, including what elements said plant the specifications apply to. This model also must allow the engineers to make requirements evolve. This evolution can be in the form of new requirements being added over time, as well as changes to existing requirements.

5 Proposal of modelling approach

Generic modelling of requirements

Models based on ontologies have the expected benefits of completeness of information, due to the language expressivity, and of embedded intelligence thanks to the reasoning abilities associated with it [START_REF] Fortineau | Improving the interoperability of industrial information systems with description logic-based models -the state of the art[END_REF]. There is also a need to model links between a requirement itself and several other elements of the requirements engineering process, namely the logical statements composing it, both premises and conclusions; the reference phrasing of the requirement, be it a legal document or a rule known by experience; the deontic nature of the requirement, whether an obligation or an interdiction1 ;the specifications they contribute to and information on their validity. These links can be modelled in the form of object properties, to allow for a diversity of relations between the elements, rather than using classes.

To allow for this, it is necessary that requirements, logical statements, deontic functions, business rules, specifications, etc. are modeled as individuals in several classes2 . Those classes are not necessarily all disjoint (for example a business rule can also be a requirement), thus making use of the non-canonic representation of data in ontologies.

An example of such a model is given in Fig. 1 : A requirement is modeled as an individual. Its nature is defined by the link it has (is a) with a member of SDL function, in this case the interdiction function of FOSDL [START_REF] Garion | Apports de la logique mathématique en ingénierie des exigences[END_REF]. Its predicate are also identified with object properties (has premise and has conclusion in this example) and are FOSDL object expressed in RIF [START_REF]W3C: Rif core dialect[END_REF]. It should contain a data property representing the origin and a verbatim of the reference document it is translated from, for verification. The links from a Specification to a Value can, propagate the constraint to the characteristic because of the inferences the ontology-based model is capable of. Examples given in Fig. 1 are inspired by goal driven requirements engineering and represent soft or strict constraints corresponding to soft or functional goals. The Requirement is also mapped to the specifications it infers (through the design phase), in the same way a business rule is mapped to another specification (and may also pair with a requirement, or be composed of statements in the same fashion, links that are not represented on the Fig. 1 for clarity). Lastly, the characteristic can be mapped itself to a measured value, completing the path from the formal requirements model, and the physical implementation of the system.

Case of a safety requirement : physical separation of electrical networks

For the safety of the plant, it is needed that the control system remain functional is case of an incident. This is achievable through a wide array of means, ranging from the protection of the plant's organs to the liability of elements under circumstantial stress. In this part we will present a possible way to model part of the requirement network associated with the physical separation of redundant electrical networks. Let us consider the requirement : "In case of an incident, the plant remains functional".

As stated above, we will represent this requirement as an individual Req 1 in the Requirement class. The premise for this requirement is "in case of an incident" : this premise is modelled as another individual Statement 1 in the SDL statement class. Statement 1 contains in its data properties the mention of the source sentence: "In case of an incident" and its translation as a RIF expression, namely occurs(inc,ctxt),Incident(inc),Context(ctxt) with Incident a class to which all incidents belong, and Context the class of contexts for simulation or domain-restricted requirements.

A link (in the form of an object property) is established from Req 1 to Statement 1 so that has premise(Req 1,Statement 1).

In the same fashion, a Statement 2 individual is created in SDL statement. It represents "the plant remains functional" in the above-mentioned requirement, with a RIF rule in the form Context(c),Functional(sys),inContext(sys,c). This rule needs Context to be a class of contexts4 ; Functional is a unitary function (a class defined by axioms) qualifying the functional state of the system; finally inContext is an object property for evaluation or simulation set-up, describing whether a context applies to a physical individual. An object property is set so that has conclusion(Req 1,Statement 2). As it is mandatory, Req 1 is also connected with an object property is a to SDL Obligation, in class SDL Function.

Next step is to describe business rules derived from this requirement. For instance consider the business rule "Redundant electric systems are to be separated physically". It is a business rule for it is a consequence of a requirement in a certain domain: it applies only to redundant electrical networks.

This business rule will be modelled as an individual BusRule 1, itself connected with object properties to SDL statement individuals, that represent it premise (Electric(A),Electric(B),redundantWith(A,B), translating "Redundant electric systems") and conclusion (physically separated(A,B), translating "be separated physically"). BusRule 1 is also linked with SDL Obligation by a is a property.

As the network is added to the model, more individuals are created : in this case exploring the physically separated object property make apparent the need to define criteria to set or not this property between two objects. This approach being individual-oriented, we chose to define the object property through a set of rules, one of them given below.

Location(place1),Location(place2), is in(A,place1),is in(B,place2), DifferentIndividuals(A,B),physically separated(place1,place2) → physically separated(A,B)

This rule only states that "distinct elements located in physically separated places are physically separated themselves". Such rules reflect the experience and knowledge of the modellers, they are the interface from the requirements engineering to the knowledge management. Another rule can reflect the notion that "elements sufficiently far apart are considered physically separated"5 , with a rule in the form :

Element(A),Element(B),DifferentIndividuals(A,B) distance(A,B)>FarApart → physically separated(A,B)
At the time being however, there is no direct way we know of to quantify a binary function (an object property), that is associate a value to a relation between individuals. It is not possible to directly use the expression distance(A,B)>FarApart. This is prevented only by the current implementations of the model, that do not yet implement ternary functions; and as this can be worked around modelling the relation, it is not established yet if this solution is acceptable on large-scale models.

Conclusions and perspectives

Using SDL and RIF definition for rules and requirements allows to model them as individuals in an ontology, and to leverage the reasoning abilities associated with the existing models. The simple pegging of requirements to specifications is not sufficient to check for the consistency of a set or requirements, or to verify and infer which requirements constrain each specification, and for which reasons. Doing so requires to introduce into the model more information, reflecting the business experience.

While the modelling of requirements into ontological models still need to be studied, it is a reasonable assumption that the ontological model would need to interact with a knowledge model, as well as a business rule model and a model of the physical system, for consistency check, and to allow for a sufficient mapping between informations that are all used in system engineering. Future works will have to investigate the interfaces between the different models.

Although the global work-flow comes from the requirements and leads to the specifications, a complex system and/or a vaguely formulated requirements imply using knowledge that belongs primarily to the designer : for a model to check or validate on a design selection, the knowledge used to make this choice must be incorporated to this model, in a form that allows for the users to incorporate it themselves, thus effectively making an ontological model the explicit representation of a shared conceptualization [START_REF] Gruber | Towards principles for the design of ontologies used for knowledge sharing[END_REF].

Fig. 1 .

 1 Fig. 1. Schematic representation of the object properties network around a requirement individual : individuals are represented by diamond-shaped symbols, classes by ellipseshaped regions in the figure

According to[START_REF] Jureta | Revisiting the core ontology and problem in requirements engineering[END_REF] and[START_REF] Garion | A modal logic for reasoning on consistency and completeness of regulations[END_REF] a requirement might also be any function built from obligation (O), interdiction (F ), necessity ( ), possibility (♦) and negation (¬)

[START_REF] Cholvy | Checking regulation consistency by using sol-resolution[END_REF] The reader should remain aware a class in ontologies is representative of a concept, an open set of individuals, rather than a generator thereof[START_REF] Corniere | A concept-based approach to modelling shared ontology-based models for industrial applications[END_REF]

that is to say, they share the same identity, as 200mm and 20cm

In the scope of this work, a context is a subset of the worlds defined by some known circumstances[START_REF] Corniere | A concept-based approach to modelling shared ontology-based models for industrial applications[END_REF][START_REF] Garion | A modal logic for reasoning on consistency and completeness of regulations[END_REF]

Any reader familiar with the field of nuclear security may object this rule does not exist. We are well aware of this, and this made-up rule merely serves as an illustration of the limits that may occur because of an ontological modelling. Similar rules do however exist regarding minimal distance between electrical cables, for instance.