Sarah Zribi
email: szribi@linagora.com

Aurélie Montarnal
email: aurelie.montarnal@mines-albi.fr

Frédérick Bénabén
email: frederick.benaben@mines-albi.fr

Matthieu Lauras
email: matthieu.lauras@mines-albi.fr

Jacques Lamothe
email: jacques.lamothe@mines-albi.fr

Michael Bailly
email: mbailly@linagora.com

Jean-Pierre Lorré
email: jplorre@linagora.com

Towards an Enterprise Social Network to Support Inter-organizational Collaborations

Keywords: Enterprise Social Network, Collaborative Platform, Support for Inter-Organizational Collaborations, Inter-enterprises Process Deduction

Since the 2000s, social networks have grown spectacularly until they are now regarded as indispensable and introduced as a daily practice of millions of users. Enterprises have become aware of the need and the importance of these collaborative tools, and the concept of Enterprise Social Network (ESN) has now emerged. As such, OpenPaaS is an innovative ESN that aims at facilitating inter-organizational collaborations. In this sense, this paper describes the new OpenPaaS platform to address current issues of ESNs: (i) the management and exchange of large amount of data during inter-organizational collaborations; (ii) the ability of the system to provide synchronous communications between collaborative partners; and finally, (iii) the establishment of transverse collaborations. This last point is a key feature of OpenPaaS, which goal is to automatically generate new inter-organizational coalitions by deducing collaborative processes in response to an opportunity of collaborations brought by any enterprise of the ESN.

Introduction

Social Networking has emerged with the development of a new technology, "Web 2.0", when it became possible for web users to participate actively in the production and disseminating content. They are shifting the Web to turn it into a participatory platform, in which people not only consume content but also contribute and produce new content [O'reilly, 2007]. Over the past few years, Social Networks (SN) have attracted much attention from the web users and they have grown spectacularly until begin now regarded as indispensable and having deeply penetrated our lives.

Companies have become aware of the need and the importance of SN collaborative tools and the concept of Enterprise Social Networks (ESN) has nowadays emerged. However, social working inside organizations is still a wild place that is looking for the right implementation models. In this context, this paper aims at proposing a new Enterprise Social Network OpenPaaS that is open-source and supports both inter-and intra-organizational collaborations.

The remainder of this paper is organized as follows. Section 2 presents a brief state of the art on the topic of Enterprise Social Networks and existing collaborative platforms. In Section 3, we sketch an overview of the proposed architecture. Sections 4 and 5 describe the main characteristics of OpenPaaS. Thereafter, Section 6 illustrates an implementation of practical use case study. Finally, the last section concludes and gives insights of future works.

Enterprise Social Networks

Enterprise Social Networks allow creating or developing friendly or/and professional ties between people. They don't have a unique or fixed form: they are customized to the needs of the organization. In [START_REF] Li | Making the business case for enterprise social networks[END_REF], Altimeter defines ESN as a set of technologies that creates business value by connecting the members of an organization through profiles, updates, and notifications.

Various ESN solutions are available (more than 80 according to the last census of Hervé Bébin in [START_REF] Bébin | Le marché du RSE en 2012[END_REF], but only 29 are interested in social collaboration). According to authors in [START_REF] Koplowitz | The Forrester Wave™: Enterprise Social Platforms[END_REF], [START_REF] Drakos | Magic quadrant for social software in the workplace[END_REF], [START_REF] Lecko | Réseaux sociaux d'entreprise (tome 4) : urbanisation du SI Social : entre gouvernance, technologie et usage[END_REF], and [START_REF] Portela | Implantation et usages d'un réseau social d'entreprise: l'expérience d'Astral[END_REF], IBM Connections, Jive SocialBS, NewsGator, Telligent, Confluence, Microsoft SharePoint 2010, Yammer, SocialText, Webex Social and Open Text are among the most important existing solutions.

However, all the aforementioned solutions are proprietary and our principal focus is open-source. Among the existing open-source ones, we find Buddypress, Elgg, Lovdbyless, Ning, Statusnet and People Aggregator. Although those solutions consider the main collaborative concepts resulting from Social Networks, the establishment of a transverse collaborative communication was not treated.

Overall Architecture

We illustrate the overall architecture of OpenPaaS in Figure 1. Our approach consists on a PaaS (Platform as a Service) technology dedicated to enterprise collaborative applications deployed on hybrid cloud. It provides an innovative Enterprise Social Networks that innovates both at collaborative level by its capacity to leverage heterogeneous cloud technologies at the IaaS (Infrastructure as a Service). Within OpenPaaS Platform, a set of collaborative services is made available in an IaaS infrastructure. The ESN is itself a service available in SaaS (Software as a Service) and serves as a point of access to applications deployed in the PaaS. Video Conferencing, messaging, calendar management and file sharing services are included in OpenPaaS platform and are presented in the next section. Moreover, our proposed platform provides Profile and Collaboration Editors tools in order to facilitate the definition of collaborative workflows adapted to the enterprise's needs. Furthermore, OpenPaaS platform includes a Roboconf module that allows both applications deployment and auto-adaption of the infrastructure.

OpenPaaS Collaborative Framework

Social Interaction Services

OpenPaaS is a reliable social platform in the cloud. Its main contexts of collaboration are:

• Community, which is comprised of members, has a name, can have an avatar and a description. Its main space is an activity stream (compatible on mobile phones) where members can exchange several kinds of messages. Moreover, it has an intrinsic rule regarding the visibility of information that is shared inside. Four types are considered (open, restricted, private and confidential): an open community allows every one to read and to add content, whether or not users are part of the community; a restricted one allows everyone to see the content but only members can contribute; nonmembers of a private community can only see its name, avatar and description; finally a confidential community is invisible for all users that are not members. Membership to a community depends on its type. For open ones, the user can freely join it. For the other types, a membership request shall be sent by the user and, then, be validated or denied by the community manager (CM), or an invitation is sent by a CM to a user to become a member who decides whether to accept or not.

• Project. While communities result from an organic self-organization of the users, a project is more tied to the activity of the company. As such, a project has a start and end dates. Besides, project's members can be users or/and communities.

• Conference consists on a short-lived collaboration. It includes instant messages and WebRTC (Web Real-Time Communication) videoconference.

• Synchronization with external contacts lists, which allows to import contacts from an existing database in order to invite them to join. Currently, OpenPaaS can be connected to Google Contacts API.

• Moreover, other features are ensured within OpenPaaS, such as calendar management and messaging services (Indeed, thanks to OBM1 integration within OpenPaaS) and Sharing of large files between members (which is ensured by an integration of LinShare2 within OpenPaaS in order to allow user to add and share files with other users).

Automated Creation of New Collaborations

In addition, a collaborative module has been implemented and aims at facilitating new inter-organizational collaborations: it gathers knowledge on collaborative contexts and needs (profiles and objectives of collaboration) through two modelers and exploits it to create new collaborations: (i) the Profile Modeler lets the enterprises describe their business capabilities (e.g. produce cars) and (ii) the Objective Modeler offers a way to propose new collaborative objectives (e.g. buy cars) and answers to them by setting up the corresponding optimal (e.g. on cost, delivery time, quality criteria, etc.) collaboration (i.e. selecting the best partners to answer the objectives, and order their corresponding capabilities into a business process). A last Collaborative Business Process Modeler allows the users to adapt the latter process and to orchestrate it on the later run-time phase. Figure 2 illustrates these three parts of this knowledge-based system.

Profile Modeler Objective Modeler Collaborative Process Modeler

Enterprise Social Network Ontologies (CO + BFO) Fig. 2. Overview of the three modelers.

In [START_REF] Montarnal | Towards Automated Business Process Deduction through a Social and Collaborative Platform[END_REF], authors explain the interaction of these three modelers with two ontologies as structured knwoledge bases: the Collaborative Ontology (CO) provides a decomposition of collaborative objectives into sub-objectives, and for each objective the corresponding capabilities to execute in order to fulfill it; the Business Field Ontology (BFO) has been implemented since the latter objectives of the CO remained very generic (e.g. "Buy" which doesn't make the difference between "Buy cars" or "Buy candies"). The CO has been populated y adapting the MIT Process Handbook OWL version [START_REF]Organizing business knowledge: the MIT process handbook[END_REF], and the BFO results from the decomposition of the international business activities in the ISIC Classification (International Standard Industrial Classification of all Economic Activities) [START_REF]United Nations and Statistical Division, International Standard industrial classification of all economic activities (ISIC)[END_REF].

As a first step, the capabilities, described via the Profile Modeler, are represented by their "intrinsic" name, and their inputs and outputs. The capability itself is linked to a capability of the CO, and the input and the output are linked with business fields of the BFO. Then, the objectives described via the Objective Modeler are represented with a link to an objective of the CO and are linked with a specific domain of the BFO. The third step is executed in back office: it is based on an Ant Colony Optimization algorithm (ACO) that exploits the knowledge included in the ontologies and also gathered by the Profile and Objective Modelers. The overall mechanism of this algorithm can be found in [START_REF] Montarnal | Towards Automated Business Process Deduction through a Social and Collaborative Platform[END_REF]. This ACO allows selecting the optimal set of partners to answer the objectives of the collaboration, and their capabilities. The sequencing of these capabilities into a process is achieved according to a right-to-left process: if one of the outputs of the selected capabilities matches the business field of the objective of the collaboration, it is considered as the final capability of the process. Then, capabilities are linked one to each other by making a correspondence between the input of a capability and the output of the previous capability. The deduced process can be downloaded as a file, which can now be opened, analyzed and potentially adapted by the users in the Collaborative Process Modeler.

For a better understanding of these steps, a use-case is given and detailed in the next section.

Use Case Validation

In order to constitute the fulfillment of the OpenPaaS platform, to illustrate the work, we present hereafter a practical use-case that meets the needs of the company SuperCookie that produces cakes with fruits, and which is actually looking for a new collaboration to supply the fruits.

First of all, we start by creating a collaboration context: a use case participant creates a community inside the ESN and chooses its visibility. Second, he/she invites other people to join. Those who respond by accepting are considered as members and can start sharing messages inside the community's activity stream. They use the most simple type of message, that is basically a text, attachments and, if the permission is granted, geolocalisation. Each message appears on the community activity stream. Any member of the community can answer the root message, thus creating a discussion thread. In the use case, members conclude that they need help to choose some enterprises to work with, and they decide to use a collaboration opportunity modeler.

Profile Modeler

In Figure 3, SuperCookie declares to be able to "place order" and link it to the corresponding capability of the CO. From a business field point of view, the input of this capability refers to the "Combined office administrative services" and the output to "Wholesale of food and tobacco" and "Processing and preserving of fruits and vegetables". Basically, this means that SuperCookie is able to send order for buying high amounts of fruits. For the rest of the illustrative case, it is assumed that many enterprises have already described their capabilities in their own profiles.

Objective Modeler

The Objective Modeler lets the companies of OpenPaaS to propose new opportunities, for which they need to set up a collaboration (select partners, and deduce the corresponding optimal process). The Figure 4 describes such an objective: here, SuperCookie would like to "buy". As this objective is very generic, the users indicate that the purchase refers to the "wholesale of tobacco" since they would like to buy high amounts of food products, and precise it with "processing and preserving of fruits and vegetables".

Collaborative Process Modeler

Finally, the ACO performs the selection of the optimal set of partners and their activities to execute, and order them into a process. This process can be seen in Figure 5. Two companies will take part of the process (SuperCookie and FruitCompany), during the following supply process. A Mediation Information System Pool is directly dedicated to the IT system so that the process can be orchestrated after that the users have adapted this process if needed.

Conclusion

This paper presents an innovative Enterprise Social Network which originality relies on its ability to support and facilitate intra-and inter-organizational collaboration by many ways. First, it provides a complete package of social services that helps coordinating the daily working life of the collaborators by providing easy way to share various types of information. This contribution to the current offers of social and professional networking platforms fits a deep need of the companies today, by providing easy-to-use tools. More than facilitating coordination among collaborators, it also provides a service to create new collaborations to fit current business opportunities of the OpenPaaS' users. The optimal selection of partners (and consequently of their capabilities) can, for example, help the enterprises in their bidding process: it can indeed be performed on a very large scope of candidate partners and thus provides quickly an efficient set of partners. Then, the sequencing of these capabilities into a business process that can be opened in a modeler lets the companies to easily adapt it (according to their specific preferences), and then orchestrate it. Besides, works industrialization should be taken in order to stabilize and improve its usability for a wide number of users. Furthermore, to enrich OpenPaaS's features collaborative real-time services (e.g. editing text documents, spreadsheets, business process modeler) need to be studied.

Fig. 1 .

 1 Fig. 1. OpenPaaS Platform.

Fig. 3 .

 3 Fig. 3. Example of capability description.

Fig. 4 .

 4 Fig. 4. Example of a collaborative objective.

Fig. 5 .

 5 Fig. 5. Example of a deduced collaborative process.

OBM: http://obm.org/

Linshare: http://en.linagora.com/produits/linshare


Samia Gamoura
email: samia.gamoura@gmail.com

Laurent Buzon
email: laurent.buzon@esce.fr

Ridha Derrouiche
email: ridha_derrouiche@esc-saint-etienne.fr

Machine Learning Agents in the Cloud to Support Smart Business Process Management

Keywords: Business Process, Multi Agent System, Virtual Enterprise, modelling, simulation, Cloud Computing, Machine Learning

In Virtual Enterprise, Business Processes Management is regarded as one of the most concerns of managers and academic researchers. Managing flows complexity and actors requirements in terms of high quality in less time, make this management more and more complex and push specialists to explore new promising ways. Like these researchers, we present in this paper, a modelling and simulating software toolkit called BP-EMC² based on a generic framework baptized H-BPM. We propose a solution using machine learning agents operating in an AGR (Agent-Group-Role) organization within the Cloud. Furthermore, this paper includes a real case study of Adecco ® business process deployed into its Cloud solution.

Introduction

Since the beginning of the 90's, inter-enterprises collaboration stills growing and generates new organizations patterns. Today, competition is no more limited in the internal organization but is extended in the whole enterprises network. These new kind of relationships created is called Virtual Enterprises (VE) focused on sharing Business Processes (BP). Here we situate our purpose to address an important issue in Business Processes Management (BPM): 'Collaboration'. The main topic considered in this paper is according to the collaboration strategies and how these strategies could be deployed overall BPM within Virtual Enterprise Network (VEN).

One from the huge number of methods and techniques used as a support for collaboration in VEN is Multi Agents Systems (MAS). As in many other business areas, such as medical, image processing, astronomy, etc. this paradigm of Distributed Artificial Intelligence (DAI) provided an efficient way to propose solutions and simulation of complex issues. Furthermore, we explain a new advanced kind of agents called Machine Learning Agents (MLA), able to use Machine Learning (ML) algorithms efficiently within the Cloud environment in order to extract and predict the best way of providing collaboration to companies.

Business Processes in Virtual Enterprises

VEs can achieve their business objectives only through effective collaboration between the autonomous enterprises that comprise them. A key requirement for theses VEs is called 'Collaborative BP' that explicitly captures and manages the functional and contractual relationships between VE's partners.

Virtual Enterprises Networks

As a formal definition, VEN is a temporary alliance of enterprises that aim to share resources and skills in order to respond better and faster to emerging opportunities in the market, based on a technical infrastructure and information technologies [START_REF] Rosu | Virtual enterprise network general architecture[END_REF].

In Fig. 1. we illustrate the VEN concept with a network of companies created to design and manufacture a new type of stool [START_REF] Buzon | Knowledge exchange in a supply chain context[END_REF].

Tool manufacturer

Seat product Manufacturer (FB) Distributor [C]

End user

Tool trader

Stool product manufacturer (M)

Wood supplier

Tool expertise

Knowledge of industrial application

Market knowledge

Tool expertise

Use constraints

Fashion Knowledge

Technical constraints

Rule and constraint

Best practice

Part constraint

Market evolution Capacity Fig. 1. An example of VEN of a stool Supply chain

The next section deals with the essential elements of BPM to identify concepts and approaches that aim to design an efficient tool to help VEN partners to manage and improve their cooperation.

Business Processes Management Methodologies

As mentioned by the Object Management Group (OMG) in [START_REF]Business Process Model and Notation (BPMN)[END_REF], the primary goal of BPM modelling is to provide a notation that is readily understandable by all business users, from the draft of the initial business analyst, to the technical developers responsible for implementing the technology that will perform those processes, and finally, to the business people who will manage and monitor those processes. The state-of-the-art shows three main modelling methodologies: One-Thing Approach (OTA) [START_REF] Vogel | Software Architecture: A Comprehensive Framework and Guide for Practitioners[END_REF], View-Based Approach (VBA) [START_REF] Hentrich | Patterns for Process-Oriented Integration in Service Oriented Architectures[END_REF] and Holistic Process Methodology (HPM).

The main idea behind the HPM approach is that domain specific process models are required both to capture the contents of a process based application and to present a process model in a user-friendly way. The assumption is that this application is composed of single activities that have to be executed in a certain order [START_REF] Dori | Object-Process Methodology: A Holistic Systems Paradigm[END_REF].

According to our framework, we choose to use this last methodology for several reasons: agility, wide usage and user-friendly feature to insure business people requirements.

Multi Agent Systems and Machine Learning

Systems based on a set of software agents commonly named MAS have been used widely following an exponential trend during recent ten years, and this is mainly due to their potential in understanding various group behaviors such as swarms and flocking. In industry and business applications, in domains as several as manufacturing [START_REF] Liu | Resource management based on multi-agent technology for cloud manufacturing[END_REF], war gaming [START_REF] Tan | Framework of wargame CGF system based on multi-agent[END_REF], satellite clusters [START_REF] Schettera | Multiple agent-based autonomy for satellite constellations[END_REF] and so on. Furthermore, a number of development environments and frameworks are actually available, i.e. SWARM ® [START_REF]SWARM ® Project under GNU Lisence[END_REF], JADE ® [START_REF]JADE ® Framework under LGPL Lisence[END_REF], JACK ® [START_REF]JACK ® Software under AOS Group Lisence[END_REF], etc. appeared. Computer science architects and program designers believe that this paradigm called Agent Oriented Programming (AOP) is the next step forward from Object Oriented Programming (OOP) [START_REF] Jarvis | Multiagent Systems and Applications[END_REF].

In the following section, we begin by positioning MAS in terms of its business uptake. We know that there is a lot of research works, ideas, and projects, but the uptake of the technology is not as rapid or as pervasive as its advocates anticipated [START_REF] Jarvis | Multiagent Systems and Applications[END_REF]. In the configuration MAS-BP, one of the bright works is that one of Fleischermann et al. in [START_REF] Fleischmann | Subject-Oriented Modelling and Execution of Multi-agent Business Processes[END_REF]. According to authors, the emerging paradigm of the subject oriented BPM by MAS is to augment MAS models with a process-centric layer that preserves autonomy and concurrent interactions. Another remarkable work was published by Bonfante et al. in [START_REF] Bonfante | Multi-Agent System for Integration Process Business and Ontologies for the Government Online Strategy[END_REF] inspired by the same principle of the MAS layer above the process layer. The proposed architecture is composed of a layer between BP and Web canals.

Agents and Predictive Machine Learning Algorithms

Research works, publications, books, projects, applications in the area of Machine Learning Agents (MLA) are numerous, especially in recent works concerned by Big Data phenomenon: [START_REF] Rand | Machine learning meets agent-based modelling: when not to go to a bar[END_REF], [START_REF] Kotsiantis | Supervised MachineLearning : A Review of Classification Techniques[END_REF], etc. ML techniques can be classified according on several criteria to several classes. These techniques are to be coupled to learning classes according to the data nature where the learning type could be supervised or unsupervised.

The most widely used technique is the last one; Q-Learning; also called Reinforcement Learning (RL), easy to implement and convergence is guaranteed. This is one of the reasons that push us choosing it to predict our agents' actions.

Cloud Computing in Business Process Management Context

Nowadays, Cloud computing is the fundamental change happening in the field of IT. The special report published by the National Institute of Standards and Technology (NIST) in U.S. [START_REF] Liu | NIST Cloud Computing Reference Architecture[END_REF] provides a clear understanding of Cloud computing. It provides a simple and unambiguous taxonomy of three service models available to Cloud consumers: Cloud Softwares As A Service (SaaS), Cloud Platform As A Service (PaaS) and Cloud Infrastructure As A Service (IaaS).

This paper presents an organized snapshot of the challenges faced by scientists and professionals in designing and deploying BPM within VE in the Cloud. Our background study encompasses both classes of systems: for supporting update dynamic BPM and for ad-hoc analytics and decision support using intelligent tools within SaaS Cloud platforms.

Since 2010, big numeric companies propose industrial software products for BPM in the Cloud, such Oracle Fusion Middleware 11g by Oracle ® [START_REF] Connaughton | Business Process Management and Cloud Computing[END_REF]. A 'Cloudified' BPM allows what is called 'Unified Collaboration' or 'Social BPM' which becomes increasingly more and more important, especially with the IT virtualization phenomenon. Distributed nature of Cloud reinforces the need for process visibility and collaboration, especially as systems and people are distributed. Also, BPM should leverage optimized structure and management of 'Cloudification'.

All these reasons have guided our decision to locate our platform on the Cloud, with services offered in SaaS with appropriate rights management. This particular part of rights management and security will be presented in further publications topics.

Framework Proposal BP-EMC²

In this work, we look at the issue of BPM in VE of nowadays, with new challenge of 'Cloudification'. As we already introduced, we have chosen to automate the dynamic monitoring of changes in processes by AGR machine learning agents (Fig. 2.).

Fig.2. Machine Learning Agents in the Cloud for BP-EMC²

For experimental needs and validation, we worked on an industrial case study of Adecco ® recruitment process shared with its partners; HP ® and Renault ® in a VE context (we call this VE Adecco ® & Co.). In the following sections, we will describe step by step how we design and build our solution by using this case study, without exposing deep details.

Building Smart BPM Model in the Cloud

We regard a process as a collection of activities that consume some inputs in order to produce some outputs based on HPM (as discussed previously in section 2.2) .in the process life management as detailed in the following steps:

Step 1. Managing Process Life Cycle (PMLC) by Holistic Approach (H-BPM):

The BPM life cycle is constituted by a set of activities and the model has to define a clear guideline how a process must be performed. To design our model named H-BPM, our concern was to notice all key concepts in the life cycle model offered in HPM methodology. Thus, we consider some of them: -Item: three types of items; Actor (a reactive or proactive entity which can act and initiate an activity of launch events, such as human task, automatized task, application module, etc.), Object (a passive entity which is handled by actors, such messages, documents, products, etc.) and Event (all events defined in BMPN such as 'timer', 'start and 'end' events). -Configuration: a set of items with related parameters define a configuration. It is the set of all the elements contained in the BMPN relative to a time reference. -Time guide-based: The life cycle is marked by a time stamp. During this cycle, multiple configurations may exist following time.

-Version: each item in the configuration is mentioned by a version, and the configuration itself is versioned. Step 2. Introducing Machine Learning algorithm in H-BPM agents' behavior: As discussed previously, we introduce a Machine Learning algorithm to give ability to our agents to be adaptive and predictive to augur better actions to help human and system. We implement ML based on Q-Learning algorithm where each agent has a history as a sequence of state-action-rewards.

Step 3. Modelling H-BPM components: Our built model is based on autonomous agents, with whom we aim to understand and study the behavior actors withinBPM.

In our proposed platform, agents are necessary to initiate and drive the execution of processes. Based on key concepts described previously, we design our system components based on three main entities: Actors, Events and Objects.

Pools in H-BPM should be designed as 'Roles' entities. And agents indicates 'Actors', Objects are designed by 'Objects' and finally events are defined as 'Events' for agents' input/output flows. Actions performed by actors in H-BPM are implemented in 'Roles' (Fig. 5.). Based on this presented model H-BPM, we baptize a software toolkit BP-EMC² as 'Business Process -Evolutive Management by Collaborative agents in the Cloud'. The remaining part in the next section is devoted to the description of this toolkit.

Experimental Validation of BP-EMC²

The software platform was designed and conducted in JAVA ® . Following the study of both platforms SWARM ® and JADE ® , this last was chosen because of the following advantages: it is a platform FIPA compliant (meaning feature ensures interoperability with protocols and standards); it manages the task achieving parallelism; it allows reusability and all imported libraries are free software.

BP-EMC² Features: Case Study Adecco ® & Co. Recruitment BPM

Our toolkit named BP-EMC² is a generic model of BPM with agents as we conceive it. The framework embeds two modules: 'Modelling module' where we can configure the system and the 'Simulation module' which is a Graphical User Interface (GUI) that uses the parameters defined in the model described in the previous section for illustration, analysis and numerical and graphical monitoring of experimental scenarios.

During our simulations campaigns, our main objective was to provide proofs that agents in BP-EMC² have the ability to improve overall BPM in terms of time execution and targets. Using predictive agents in the Cloud should provide a high target level with short time execution. Thus, we considered described metrics: Time Execution (TE) and TarGet (TG) according to time-line represented by Versions (V).

Discussion

As we see on the both trend curves in figure Fig. 8, both indicators TE and TG tend to stabilize and to optimize values. When, after several iterations we get close values, we speak of stability. At the 11 th iteration, the average execution time of the action Agent_Job_Requester is 2.9 hours with a TG/action indicator of 0.08/10 ~ 80%, and this is satisfactory and maintained for next versions. Then, if we compare this (Fig. 8) with extractions in figures Fig. 9 and Fig. 10, we can notice that the average time per action moy(TE)/action may be slightly more interesting (0.5 to 1 episode) but with a mediocre quality indicator TG of 5.5 / 10 ~ 55% in longer global time execution (30 days vs 17 days). Also, we have not insurance that this will be maintained as there is no system for experience storage and management (no memory). As we see, these values vary and may worsen from an episode to another.

These results are admittedly preliminary but very promising: Learning agents helped refine the convergence to a more optimal BPM model. This convergence is reached after a number of versions obtaining a short execution time with a high quality indicator. These results may be similar to a conventional BPM (without the use of Machine learning agents Results), but can take more time longer and without any insurance of stability.

Conclusion

This paper attempts to address the issue of collaboration in the area of Virtual Enterprises which concerns Business Process Management under Cloud Computing requirements. As technology evolves, flexibility of BPM adapts to new requirements. Processes can be managed at anytime from anywhere and optimization allows to adjust processes to Cloud SaaS context. Our toolkit called BP-EMC² (Business

Fig. 3 .

 3 Fig. 3. Recruitment BPM in Adecco ® & Co. modeled by H-BPM (by IBM-Bonitasoft ® 6.5.1)

Fig. 5 .

 5 Fig.5. Learning with AGR in H-BPM (by StartUML 5.0.3 ® )

Fig. 8 .Fig. 9 .Fig. 10 .

 8910 Fig.8. Training for Agent_Job_Requester in BP-EMC² (50 iterations) (with γ =0.8, Q 0 [0], 11 versions, 17 days)

Process -Evolutive Management by Collaborative agents in the Cloud), tries to provide a complete platform for BPM partners to face new IT challenges. We believe that, our work may be an efficient tool to reduce complexity and provides the flexibility required for any BPM in Virtual Enterprise.


Shadan Gholizadeh-Tayyar
email: shadan.gholizadeh_tayyar@mines-albi.fr

Jacques Lamothe
email: jacques.lamothe@mines-albi.fr

Lionel Dupont
email: lionel.dupont@mines-albi.fr

Integration of Supply Chain Planning with Time and Resource Constrained Project Scheduling Problems for Building's Thermal Renovation Projects

Keywords: Supply chain planning, resource constrained multi project scheduling problem, time constrained multi project scheduling problem, mixed integer programming

CRIBA is a project that aims at industrializing thermal renovation processes of buildings. It consists in designing and configuring make-to-order insulated panels that will be installed on the external facade of the buildings to meet the thermal renovation objectives. Our study provides an optimization model that comprehensively plans supply chain network, which delivers insulated panels to the building's worksites, and schedules renovation activity that should be executed at the worksites under the limited quantity of the resources' availability. In this context, integration of supply chain planning problem with resource constrained multi project scheduling problem and time constrained project scheduling is of interest in realizing the decision making tool.

Introduction

Generally, resource constrained multi project scheduling problem (RCMPSP) is defined as extension of resource constrained project scheduling problem (RCPSP). In RCMPSP the decision makers deal with simultaneous planning of multiple projects that use a common pool of resources for scheduling of their activities whereas in RCPSP one single project is aimed at scheduling while it uses its own dedicated resources. According to [START_REF] Payne | Management of multiple simultaneous projects: a state-of-the-art review[END_REF], nearby 90% of on-going projects in worldwide are executed in a multi-projects environment. In both RCPSP and RCMPSPs two major types of the constraints are distinguishable: (a) precedency constraints and (b) resource satisfaction constraints [START_REF] Badiru | Comprehensive Project Management: Integrating Optimization Models, Management Principles, and Computers[END_REF]. In this context, the activities are forced to use the resources up to the amount that is available on the periods. A modified approach of this hypothesis is considered in Time Constrained Project Scheduling problem, TCPSP, that it supposes additional quantity of the resources has temporarily to be allocated in certain periods, [START_REF] Klein | Schedulung of resource constrained projects[END_REF].

Furthermore, regarding types of the resources used in projects, two main sorts could be stood out: Renewable and non-renewable ones [START_REF] Shirzadeh Chaleshtarti | Branch and Bound Algorithms for Resource Constrained Project Scheduling Problem Subject to Nonrenewable Resources with Prescheduled Procurement[END_REF].

From the viewpoint of renewable resources, we use the approach of TCPSPs. Herein; the availability of the renewable resources such as labor-works, cranes and trucks can increase by renting additional limited quantities on the periods that the demand for these resource types may exceed the available amount by the activities.

From the viewpoint of non-renewable resources, like the basic RCMPSP, consumption of the nonrenewable resources of the model cannot exceed the available quantity. In our case, this quantity is limited by the capacity of supply chain that produces and supplies the resource to the projects' worksites. In this context, our attention is drawn to consider chain of the organizations, which coordinate together, to feed the final required product (the insulated panels in our case) at the projects' worksites and to plan optimally the quantity of materials that should be flowed between the organizations to satisfy projects' worksites on time. Noticeably, such a challenge relates a typical Supply Chain Planning, SCP, problem to the multiple projects scheduling problems.

To the best of our knowledge, integration of supply chain planning problem with resource constrained multi project scheduling problem and time constrained project scheduling is not considered up to now in the literature.

In the rest of this paper, we review the literature. Then, we define use case of the study. The decision making tool and the results are presented in following. Conclusion and future researches will be discussed at the final section.

Literature Review

The literature in resource constrained multi projects scheduling dates back to the 1960s. However, RCMPSP has not studied as expensively as single project scheduling [START_REF] Krüger | A heuristic solution framework for the resource constrained (multi-)project scheduling problem with sequence-dependent transfer times[END_REF]. Dealing with multi project scheduling problems distinguishes two main approaches: 1-Single project approach, wherein all the projects are joined together to make a single super-project. Herein, a single critical path is regarded in the scheduling of the projects. 2-Multi projects approach, in which the parallel separated projects are treated simultaneously while they use the same restricted resources of the management company. Different separated critical paths can be recognized in planning of the projects in multi projects approach.

Considering the multi projects problems with single project approach leads the researchers to the literature of RCPSPs. Different extensions of single project scheduling are defined in the literature. As a variant of RCPSPs, TCPSP would remarkably be applicable on practical project scheduling. Therein, a pre-defined duedate is given for completion of the project but it may be too tight to achieve with the resources that are available initially. TCPSP considers an approach that a given project can get complete on time by adding certain additional amounts of the resources [START_REF] Klein | Schedulung of resource constrained projects[END_REF], [START_REF] Guldemond | Time-constrained project scheduling[END_REF] and [START_REF] Hurink | Time-constrained project scheduling with adjacent resources[END_REF]. In our study, this idea is utilized as well in order to make closer the completion time of the projects' activities to the expected dates that are regarded. In [START_REF] Guldemond | Time-constrained project scheduling[END_REF], the authors develop a decomposition method to deal with a TCPSP problem with adjacent resources. [START_REF] Hurink | Time-constrained project scheduling with adjacent resources[END_REF] provides a two stage heuristic that solves several instances of TCPSPs to optimality.

In order to discover more the other extensions of the single project planning problems, we refer the readers to the reviews [START_REF] Hartmann | A survey of variants and extensions of the resourceconstrained project scheduling problem[END_REF] and [START_REF] Węglarz | Project scheduling with finite or infinite number of activity processing modes -A survey[END_REF] and textbook [START_REF] Klein | Schedulung of resource constrained projects[END_REF].

Besides the variants and extensions, from viewpoint of objective functions, resource constrained project scheduling problems are grouped according to different objectives: (i) Time-based objectives minimizes targets like completion time, earliness, tardiness and lateness [START_REF] Baker | Minimizing earliness and tardiness costs in stochastic scheduling[END_REF]; (ii) Quality-based objectives in which maximization of the projects' quality is regarded [START_REF] Icmeli-Tukel | Ensuring quality in resource constrained project scheduling[END_REF]; (iii) Cost-based objectives where the objective function minimizes the total cost of projects like execution costs, material costs, inventory holding costs, costs related to tardiness or earliness of the project, [START_REF] Ranjbar | An optimal procedure for minimizing total weighted resource tardiness penalty costs in the resource-constrained project scheduling problem[END_REF] and [START_REF] Rodrigues | An exact algorithm for minimizing resource availability costs in project scheduling[END_REF], and the costs of adding supplementary resources in TCPSPs, [START_REF] Klein | Schedulung of resource constrained projects[END_REF]; (iv) Net present value objectives that they are dealt with when certain predefined cash flows happen in the time periods. In fact, net present value maximization of the projects reflexes the time value of money in project scheduling problems, [START_REF] Artigues | Resource-Constrained Project Scheduling: Models, Algorithms, Extensions and Applications[END_REF]; and, (v) multi objective models that investigate two or more of the above-mentioned objectives simultaneously in one model. In [START_REF] Browning | Resource-constrained multi-project scheduling: Priority rule performance revisited[END_REF] criteria such as time, cost, quality and whole robustness are considered to build the multi objective model for scheduling multiple projects. Based on the importance of different objectives, the proposed model is expected to generate scheduling alternatives. For that purpose, a cloud genetic algorithm is proposed.

Multi projects approach little drew the attention of the researchers, [START_REF] Browning | Resource-constrained multi-project scheduling: Priority rule performance revisited[END_REF]. In [START_REF] Browning | Resource-constrained multi-project scheduling: Priority rule performance revisited[END_REF], the authors justify this choice because (1) it is more realistic, (2) it presents great opportunity for improvement and (3) critically. Within their work, they consider a RCMPSP with two lateness objectives, projects' lateness and portfolio lateness. Set of the priority rules for planning the resources of the model are used by the authors. They distinct several situation, in which priority rules perform poorly. In [START_REF] Dumond | An examination of resourcing policies for multi resource problems[END_REF] different resource availability levels are intoduced for the multiple projects. In [START_REF] Bock | A Comparison of Due Date Setting, Resource Assignment, and Job Preemption Heuristics for the Multiproject Scheduling Problem[END_REF], the preemption of the resources is considered for the multiprojects. [START_REF] Navi-Isakow | Managing multiple project environments through constant work-in-process[END_REF] uses queuing theory for multi project planning.

Dealing with the multi projects planning in both single project approach, and multi projects approach, engages the researchers with NP-hard problems. In term of computation time of the models, treating with small size of these problems is reasonable by the commercial softwares. In the large size of the problems, more than 50 activities for scheduling [START_REF] Fatemi Ghomi | A simulation model for multi-project resource allocation[END_REF], application of the heuristics and meta-heuristics reduce considerably the computational time.

From the viewpoint of mathematical modeling, generally two types of the formulation are regarded: discrete time formulation and continuous time formulation. In discrete models the start time of the activities takes integer values whereas in continuous it can take a non-integer value as well. [START_REF] Kopanos | New continuous-time and discretetime mathematical formulations for resource-constrained project scheduling problems[END_REF] presents two different types of models for each of the mentioned formulations. The authors compare the proposed models with six literature models in 3240 benchmark instances. They define three criteria of good, optimal and feasible to study and rank the proposed models in each of the types. Our model is built based on the discrete time formulation. For the other formulation and developments, we refer the readers to [START_REF] Hait | On electrical load tracking scheduling for a stel plant[END_REF].

The last part of the literature relates to the supply chain planning topic, which is considered in our study to plan the procurement of the nonrenewable resources of the problem. The decisions in supply chain planning are made in three levels of operational, tactical and strategic. In operational planning, decision makers try to provide a decisional framework that corresponds to very short periods of time, [START_REF] Schütz | The impact of flexibility on operational supply chain planning[END_REF]. Control and procurement planning of necessary materials and short-term transport policy decisions correspond to this level of decision making. The tactical level in supply chain aims to consider the decision that associate with medium terms of planning. They can be considered in the decision making for planning the procurement of required materials, controlling the inventories, planning for production and distribution of the products, [START_REF] Chen | A 0-1 goal programming model for scheduling multiple maintenance projects at a copper mine[END_REF]. Major and fundamental decisions of network such as locating new facilities among the existing ones, selection of new technologies and selection between potential suppliers are taken into account in strategic level of decision making, [START_REF] Chai | Application of decision-making techniques in supplier selection: A systematic review of literature[END_REF].

Problem Definition and Formulation

Use Case

This work is a part of a research project, called CRIBA, (Construction et Rénovation Industrialisé Bois Acier). The project is defined in building sector in France to industrialize thermal renovation activities of the buildings. The business is determined to accomplish by designing and configuring make-to-order panels that will be installed on external facades of the buildings to insulate them and to reduce their energy consumption. The main composing elements of the panels are wooden frames, insulation material types, external coating product types and high-insulated carpentries. The carpentries are mailnly made from aluminum, PVC and wood. Each composing element of the panels are procured by corresponding suppliers/ manufacturers. The ready-to-use panels are shipped from the panels' manufacturing unit to different buildings' worksites. Several renewable resources such as laborworks, trucks and cranes should be present at the worksites to make progress on installing the panels. After installation, the former carpentries should be removed from the buildings. In order to respect the sustainability rules regarded in the environmental engagements, the wastes of the worksites are shipped to a recycling center. It is worthwhile to mention that the stocking the panels is not allowded at the thermal renovation worksites, Fig 1.

Problem Definition

Our study attemps to present a mid-term comprehensive decision making tool for CRIBA project that is provided by considering the decisions engaged in planning and scheduling of the projects' activities (project planning ) as well as the decisions faced on procuring the projects' required non renewable resources (supply chain planning) Following points represent our attributers for each of the approaches :

From the viewpoint of project planning : the model encompasses a set of w projects which run at different buildings' worksites. Every project has its own specified activities, I ୵ . For each activity i, a processing time Du ୧ , earliest start time e ୧ , latest start time l ୧ , latest finish time Lf ୧ and due-date DD ୧ are attributed which are estimated by project managers. If the due date is not met, a penalty cost Penc ୧ will be imposed to the system. The predecessor relationship between two activities i and j is denoted by Pre ୨ . In addition, each activity uses certain amount of renewable resources, Dr ୧୰ , and non-renewable resources, Dp ୧୮ . The nonrenewable resources are supplied to the worksites with a limited capacity of its manufacturer over the different time periods. Meanwhile, Ar ୰ units of renewable resource r are available to share at the worksites. An additional quantity of renewable resource type r can be rent with cost Rc ୰ . Relation set φ ଵ୵ is defined to model a per period cost ܲܿ ௪ between the beginning and ending activity of the worksite w.

From the viewpoint of supply chain planning: A network of organizations cooperate together to ultimately satisfy the demand of the worksites for the panels. One single organization is responsible to procure each type of the materials at the supply chain network. The set of the organizations N includes the carpentries' raw material suppliers ݏ , the panels' raw material suppliers ݏ , the manufacturing units of different carpentry ݊ , the panels manufacturing unit ݊ , worksites ݓ and wastes recycling center re, (N=൛ݏ , ݏ , ݊ , ݊ , ,ݓ ݁ݎൟ). In the model,  ᇱ ሺ݊ሻ indicates the articles that are consumed at the organization n, i.e. set of raw materials of the panels rp and set of raw materials of the carpentries ܿݎ . Besides, ሺ݊ሻ denotes the articles that are produced at the corresponding organization n. It can be panels  or carpentries ܿ. ܰሺሻ is the destination units where a produced article o can be used. In the supply chain network, in order to smooth the flow of products, each carpentry's and panel's manufacturing unit assigns a limited capacity to stock the required raw materials and the finished products, ݏܽܥ ௧ . Beside of stocking the raw materials and ready-to-use panels, the panels' manufacturing unit stocks some limited quantity of the carpentries as well. ܵܫ ᇲ ሺሻ, and ܵܫ ሺሻ, regard the initial stocks. Furthermore; ݎܽܥ ௧ and ݑݏܽܥ ᇲ ሺሻ,௧ are defined to consider production capacity of the manufacturing centers and supply capacity of the organizations. Notation ݐܲ ሺሻ presents the workload of the production for producing the panels and carpentries at the corresponding manufacturing centers. In order to deal with the delays of the supply chain network, transportation lead-time ݈ܶ ሺሻ, / ݈ܶ ᇲ ሺሻ, and production lead-time ݐܲ ሺሻ are defined. Notation ܤ , ᇲ is generally used to define the bill of material of the product o'.

Three different type of the costs including transportation costs ܥܳ ᇲ ሺሻ, ܥܳ/ ሺሻ, production cost ܥܲ ሺሻ and stock costs ܥܵ ᇲ ሺሻ ܥܵ/ ሺሻ are attended to calculate the total cost of the network.

Mathematical Formulation

Objective function: the objective of the model is to minimize total cost of the system execution. It includes different types of the costs:

-Project planning costs which includes total periodic cost of running the projects till their completion time, (ii) total penalty cost for lateness in completion of the jobs and (iii) total cost of renting the additional renewable resources.

-Supply chain planning cost including (v) the total transportation cost for shipping the raw materials and products at the network, (vi) production cost of the panels and carpentry types and (vi) the stock costs, which includes the stocking cost the raw materials and finished products at the carpentries' and panels' manufacturing units. Min Z=

ቂ ∑ ∑ ሺܵ ݆ + ሺ݅,݆ሻє ߮ ݓ1 ݑܦ ݆ -ܵ ݅ ሻܲܿ ௪ + ∑ ݏ݊ݐܮ ܲ݁݊ܿ + ∑ ∑ ܴ ௧ ܴܿ ௧ ቃ + ቂ∑ ∑ ∑ ܳ ᇲ ሺሻ,,௧ ௧ ᇲ ሺሻ ܥܳ ᇲ ሺሻ, + ∑ ∑ ∑ ܳ ሺሻ,ேሺሺሻሻ,௧ ௧ ሺሻ ܥܳ ሺሻ, ቃ + ቂ∑ ∑ ∑ ܲܳ ሺሻ,,௧ ௧ ሺሻ ܥܲ ሺሻ є൛ , ൟ ቃ + ቂ∑ ∑ ∑ ܵ ᇲ ሺሻ,,௧ ܥܵ ᇲ ሺሻ ௧ ᇲ ሺሻ є൛ , ൟ + ∑ ∑ ∑ ܵ ሺሻ,,௧ ௧ ሺሻ ܥܵ ሺሻ є൛ , ൟ ቃ (1)

Constraints:

Supply chain design constraints Constraints ( 2) to ( 4) concern the capacity constraints. Constraints ( 2), ( 3) and ( 4) respectively deal with the production capacity, supply capacity and stock capacity of the organizations.

∑ ݐܲ ሺሻ, ܲܳ ሺሻ,,௧ ሺሻ ≤ ݎܽܥ ,௧ ∀ n є൛݊ , ݊ ൟ, t єܶ (2) ܳ ᇲ ,,௧ ≤ ݑݏܽܥ ᇲ ,௧ ∀n є൛݊ , ݊ ൟ,  ᇱ єܱ ᇱ ሺ݊ሻ, t єܶ (3) ∑ ܵ ᇲ ሺሻ,,௧ ᇲ ሺሻ + ∑ ܵ ሺሻ,,௧ ሺሻ ≤ ݏܽܥ ,௧ ∀ n є൛݊ , ݊ ൟ,  ᇱ є ܱ ᇱ ሺ݊ሻ ∪ ,ܥt єܶ (4)
Constraints ( 5)-( 8) represent the balance of the flows. Equation ( 5) and ( 6) respectively consider the balance for stocked quantity of the finished products and the raw materials at their manufacturing centers considering their consumption, production and transportation. Equation ( 7) and ( 8) deal with the initial stocks.

ܵ ,,௧ିଵ + ܲܳ ,,௧ି = ∑ ܳ ,ேሺሻ,௧ ேሺሻ + ܵ ,,௧ ∀ n є݊ ∪ ݊ , є ܱሺ݊ሻ, t єܶ (5) ܵ ᇲ ,,௧ିଵ + ܳ ᇲ ,,௧ି் ᇲ , = ∑ ܲܳ ,,௧ ܤ ᇲ , + ܵ ᇲ ,,௧ ∀  ᇱ є ܱ ᇱ ሺ݊ሻ ∪ ,ܥ n є݊ ∪ ݊ , t єܶ (6) ܵ ᇲ ,,௧ ܵܫ= ᇲ ,, ∀n є݊ ∪ ݊ ,  ᇱ є ܱ ᇱ ሺ݊ሻ, t = 0 (7) ܵ ሺሻ,௧ ܵܫ= ሺሻ, ∀n є݊ ∪ ݊ , є ܱሺ݊ሻ, t = 0 (8)
Equation ( 9) presents the reverse logistic constraints. It guarantees that all the waste produced at the worksites will be shipped to the recycling center.

ܳ ᇲ ሺሻ,௧ = ݎܲ ܳ ᇲ ሺ௪ሻ,௪,௧ି் ሺሻ ∀ ݐє ܶ (9)

Project planning constraints

In this context, constraints ( 10)-( 15) present the activities' scheduling constraints. Constraint [START_REF] Baker | Minimizing earliness and tardiness costs in stochastic scheduling[END_REF] guarantees that all the activities of the projects should be executed in a time interval between their earliest start and latest start time. Equation [START_REF] Icmeli-Tukel | Ensuring quality in resource constrained project scheduling[END_REF] represents that the sum of the activity's execution periods should be equal with its processing time. Constraint ( 12) and ( 13) deal with the start time of the activities. Constraint [START_REF] Ranjbar | An optimal procedure for minimizing total weighted resource tardiness penalty costs in the resource-constrained project scheduling problem[END_REF] uses the activities' precedency relations for defining the start times. Equation ( 13) calculates the start time of the activities. Relying on the start times and activity's processing time, constraint [START_REF] Browning | Resource-constrained multi-project scheduling: Priority rule performance revisited[END_REF] relates two decision variables ܼ ௧ and ܷ ௧ . Constraint [START_REF] Browning | Resource-constrained multi-project scheduling: Priority rule performance revisited[END_REF] deals with the lateness may occur in executing the activities. It is considered by the difference between the due date, which is forecasted for completion of activity i, and the real completion time of activity i.

∑ ܼ ௧ ௧ୀ = 1 ∀ ݅ єܫ (10) ∑ ܷ ௧ ி ିଵ ௧ୀ = ݑܦ ∀ ݅ єܫ (11)
ܵ ≥ ܵ + ݑܦ ∀ ݆є ݁ݎܲ (12) ܵ = ∑ ݐ ܼ ௧ ௧ୀ ∀ ݅ єܫ (13) ∑ ܷ ௧ିଵା௨ ୀ௧ ≥ ݑܦ ܼ ௧ ∀ ݅ є I, ݐє {݁ , …, ݈ } (14) ݏ݊ݐܮ ≥ ܵ + ݑܦ -ܦܦ ∀݅ є I (15)
Constraints ( 16) and ( 17) deal with the resources availability constraints. Constraint [START_REF] Browning | Resource-constrained multi-project scheduling: Priority rule performance revisited[END_REF] deals with the requirement of the activities for renewable resources. It guarantees that the demand for renewable resource types of the activities that are executing at a certain time period will be satisfied by the available quantities of these resources and the quantities that probably will be rented. Since panels cannot be stocked on the projects 'worksite, equation [START_REF] Bock | A Comparison of Due Date Setting, Resource Assignment, and Job Preemption Heuristics for the Multiproject Scheduling Problem[END_REF] guarantees that the total quantity of the panels that are transported to the worksites over a time period t will satisfy the demand for the panels of activities that are progressing at time period t.

∑ ݎܦ є ூ ܷ ௧ ≤ ݎܣ + ܴ ௧ ∀ rє R, n є{}ݓ , t єT (16) ∑ ܼ ௧ є ூ ܦ , ᇲ ሺሻ =ܳ ᇲ ሺሻ,,௧ ∀ n є{}ݓ ,  ᇱ ሺݓሻє{ܲ},t єܶ (17)
Constraints ( 21), ( 22) and ( 23) represent the variable types that are used at modeling of the problem.

ܷ ௧ , ܼ ௧ є {0 ; 1} ∀ iє I, tєT (18) ܴ ௧ , ݏ݊ݐܮ , ܳ ሺሻ,,௧ , ܲܳ ሺሻ,௧ , ܵ ሺሻ,௧ , ܵ є ܼ ା ∀ ሺ݊ሻ є ܱሺ݊ሻ, ݎє ܴ, ݅є ,ܫ n є N,t єT(19) ܳ ᇲ ሺሻ,,௧ , ܵ ᇲ ሺሻ,௧ ≥ 0 ∀  ᇱ ሺ݊ሻ, єܱ ᇱ ሺ݊ሻ, n є ܰ,t єT (20)

Numerical Results

Parameter setting presented in Table 1 is applied on the model. The problem is solved by using CPLEX algorithm on a notebook with Core i7 CPU, 2.7 GHz processor, 64-bit and 4 GB of memory. Fig. 2.A depicts the planning events that are engaged with each of the activitis, ( i .e. events related to start of the activies and also related to the procurement of the demanded consumable resources) Fig. 2.B presents the total stock and production quantity of all the panel and carpentry types. Fig. 2.C shows the graphs, which stand out the total quantity of the transported raw materials and products to the destination of use over the different time periods.

For the presented model, a failure in progressing of the thermal renovation activities over the time interval that are forecasted (execution of the activities between ݁ and ݈ ) originates from two kinds of reasons : one can be taken place by the failure of the supply chain network in supplying the resources and the other can be orginated from the worksites during the execution of the activities. In this study to deal with the effects of the failure in starting of the activities on the total cost of the system, we carry out sensitivity analyisis. For this purpose, we suppose that the earliest start time of the activities be postoponed for one unit of time. The results of the sensitivity analysis are presented inTable 2.

Conclusion and Future work

In this study a multi project scheduling problem is regarded. Two types of the resources including renewable and nonrenewable resources are demanded by activities to do progress. A common pool of renewable resources with limited availability quantity is shared among the projects. In our model, we consider the possibility of renting additional quantity of the renewable resources, which lets the model to make closer the completion time of the activities, as much as possible, to the expected due dates (Integration of the time constrained project scheduling problems with multiple project scheduling problems). The non-renewable resources of the project are supplied at the worksites by their corresponding manufacturers. Procurement planning of these resources relates the model to the supply chain planning problem. The proposed optimization tool is built based on a case study that is defined by ADEME in context of CRIBA project. The results of solving the model for a small dimension of the problem are obtained by using CPLEX algorithm. A sensitivity analysis is carried out to study the effect of the failure in starting of the activities on different costs of the system. For the future studies of this research, the authors aim at developing the model by applying the uncertainty modeling approaches such as robust optimization. Using the meta-heuristics to deal with large scale of the problem is also of interest.

Acknowledgement

The authors gratefully acknowledge the Agence d'Envirronnement et Maîtrise de l'Enegrie (ADEME) and SYRTHEA enterprise for founding of this research study.

Fig. 1 .

 1 Fig. 1. Thermal renovation projects' framework.

Fig. 2 .

 2 Fig.2. A :Start time of activities, B :total stock/ production quantities and C :total transported quantities of products and raw materials.

Table 1 .

 1 Dimension of the indices of the model.

	: activities: 1,…,10 : panel types: 1,2,3 : worksites: 1, 2 : renewable resource	Indices : raw materials of the panels, including: insulating materials:
	types: 1,2,3 : time periods: 1,…,10 : Product families of the carpentries, including: PVC:1,2,3	1,2,3 Coating-materials:1,2,3 Wood materials:1,2,3 : raw materials of the carpentries, 1,…,4,
	Wooden:1,2,3		including:
	Aluminum: 1,2,3		PVC, Aluminum,
			wood and glass.

Table 2 .

 2 Results of the sensitivity analysis.

	Cost(%)	Total Running	Total Penalty	Total Resource-
	Activity	Cost in	Cost, (ii)	add Cost, (iii)
		Completion
		Time,(i)
	1(in worksite1)	0%	3%	0.23%
	2(in worksite1)	50%	1%	0.23%
	3(in worksite1)	50%	1%	0.23%
	4(in worksite1)	0%	-1%	0.23%
	5(in worksite1)	50%	1%	0.23%
	6(in worksite2)	0%	3%	0.23%
	7(in worksite2)	50%	1%	0.23%
	8(in worksite2)	50%	1%	0.23%
	9(in worksite2)	0%	-1%	0.23%
	10(in worksite2)	50%	1%	0.23%


Leila Sakli
email: leila.sakli@lsis.org

Jean-Claude Hennet
email: jean-claude.hennet@lsis.org

Jean-Marc Mercantini
email: jean-marc.mercantini@lsis.org

Impact of Changes in Quality of Deliveries on the Vulnerability of Supply Chains

Keywords: Risk, supply chain, vulnerability, resilience, quality

The main objectives of the study are to present the vulnerability of the supply chain related to the change in the quality of the products supplied, and propose solutions to mitigate its disturbance. We use ARMA (Auto Regressive Moving Average) time series to model a supply chain with one supplier and one retailer. We then analyze how changes in the quality of products delivered by the supplier may affect the system variables, taking into account the system constraints and the uncertain demand from customers. A quality predictor can then be introduced in the model to improve the resilience of the chain.

Introduction

New technologies and globalization increase the complexity of supply chains and therefore expose them to risks of different types. Faced with uncertainty, supply chains appear more sensitive in the context of competitive pressure, unpredictable and volatile global market demand. In particular, supply chains are sensitive to local disturbances and uncertainties related to demand [START_REF] Lee | Information distorsion in a supply chain: The bullwhip effect[END_REF] supplies [START_REF] So | Impact of supplier's lead time and forecast demand updating on retailer's order quantity variability in a two-level supply chain[END_REF] or information [START_REF] Huang | The impacts of sharing production information on supply chain dynamics : a review of the literature[END_REF], [START_REF] Babai | Forecasting and inventory performance in a two-stage supply chain with ARIMA(0,1,1) demand: Theory and empirical analysis[END_REF]. Several studies have been conducted to analyze the topic of risk especially in the context of the supply chain [START_REF] Sakli | An Analysis of Risks and Vulnerabilities in Supply Networks[END_REF] [START_REF] Manuj | Global supply chain risk management[END_REF]. In general, risk is a combination of a probability of occurrence of an adverse event and a measure of the severity of the consequences of this event in terms of damage or injury (ISO / CEI73) [7]. The concept of risk is significant only in the presence of targets vulnerable to the effects of hazards induced by accidents [START_REF] Hennet | Toward an integration of risk analysis in supply chain assessment[END_REF].

Vulnerability is an intrinsic property of a system. It measures its sensitivity to adverse events. We distinguish endogenous vulnerabilities, which are properties of the companies that make up the supply chain, and vulnerabilities external to the company, at the level of interconnections between companies or flows [START_REF] Wagner | An Empirical Investigation into Supply Chain Vulnerability[END_REF].

In the field of the supply chain, Ou Tang and Nurmaya Musa [START_REF] Tang | Identifying risk issues and research advancements in supply chain risk management[END_REF] argue the lack of a difference between uncertainty and risk in the literature. However, as [START_REF] Manuj | Global supply chain risk management[END_REF] we distinguish between these two concepts. Indeed according to ISO / 2009, the risk is defined as the effect of uncertainty on objectives [11]. This definition highlights both the difference and the relationship between the concepts of risk and of uncertainty. Under the effect of uncertainty, a deviation can be positive or negative. In practice, one is interested in the negative effect [START_REF] Manuj | Global supply chain risk management[END_REF]. In this context Wagner and Bode [START_REF] Wagner | An Empirical Investigation into Supply Chain Vulnerability[END_REF] define risk as "the negative deviation from the expected value of a certain performance measure, resulting in negative consequences for the focal firm" [START_REF] Wagner | An Empirical Investigation into Supply Chain Vulnerability[END_REF].

Due to the complex structures of today supply chains, a risk in a company may have consequences for other companies upstream or downstream. It thus threatens the entire chain. The resilient supply chain has the ability to adapt whatever the events to which the chain is subjected. Resilience is "the system's ability to return to a new stable situation after an accidental event" [START_REF] Asbjørnslet | Assessing the Vulnerability of Supply chain[END_REF]. Taking into account that it is a multidimensional concept, Serhiy Y et al. [START_REF] Ponomarov | Understanding the concept of supply chain resilience The Int[END_REF] define resilience as "the adaptive capability of the supply chain to prepare for unexpected events, respond to disruptions, and recover from them by maintaining continuity of operations at the desired level of connectedness and control over structure and function" [START_REF] Ponomarov | Understanding the concept of supply chain resilience The Int[END_REF]. To preserve the resilience of supply chains, the areas of risk analysis and risk management are currently acquiring great interest, both from the theoretical and applicative standpoints. It is necessary to have indicators of vulnerabilities in the chain to determine the sensitivity of the chain to adverse events and to characterize the system's lack of resilience.

To form a resilient supply chain, the company must select the most reliable suppliers. Product quality is among the key factors in determining the reliability of a supplier, and the quality of a product may critically depend on risks in production, delivery or storage. In this research, we focus on uncertainties about the quality of supplied components and the demand, and try to analyze the vulnerability of the supply chain due to the variation in the quality of the product supplied. In a previous work [START_REF] Sakli | An Analysis of Risks and Vulnerabilities in Supply Networks[END_REF], we have proposed a model based on ARMA time series to study supply chain vulnerabilities under demand uncertainty. The choice of ARMA time series can be argued by the fact that such model takes into account both the random nature of the system and its history.

As shown in the next section, starting from the works of Box and Jenkins [START_REF] Gilbert | An ARIMA supply chain model[END_REF] for ARMA series and Gilbert [START_REF] Gilbert | An ARIMA supply chain model[END_REF] for their applications to modeling supply chain dynamics, we have introduced in the model constraints on inventory and supplier capacity. From this non-linear model, we can infer indicators of system vulnerability. After that, we add to this model a quality index. First, the product quality model is supposed ARMA and can be estimated based on the history of deliveries from the same supplier. Next, the product quality model is supposed determinist with random time. In section 3, and to simplify the study, we consider a basic two-stage supply chain consisting of a company and its supplier receiving random demands from customers. The dynamics of the system are studied by simulation, to measure the influence of quality uncertainty and compare the cases when quality variations are anticipated and when they are not, and also to compare between the different models of quality index.

Model Development

In this section we start by modeling the supply chain with ARMA. In many cases, supply chains "can be viewed as virtual systems subject to dynamic reconfigurations, through arrival or departure of partner enterprises. » [START_REF] Hennet | Toward an integration of risk analysis in supply chain assessment[END_REF]. The formulation of the model is as follows.

Model of the Supply Chain

The modeling of the chain is given by the representation of the demand, the level of stock of each company and the quantity of products or components to be ordered. When a prime contractor places orders to his supplier, it also transmits information about customer demand. This demand is often of random nature. A mathematical formulation of the demand t D can be constructed by the method of Box and Jenkins [15] as an ARIMA (p, d, q) (Auto Regressive Integrated Moving Average). The main purpose of this model is to predict the future values of the random demand, taking into account its previous values observed. ( )

1 p q t k t k t l t l k l D D a a µ ϕ µ θ - - = = + -+ + ∑ ∑ . ( 1
)
Based on this representation, Gilbert [START_REF] Gilbert | An ARIMA supply chain model[END_REF] proposed a linear model of the supply chain by introducing the stock level t I , and the order quantity t O at the end of period t according to the forecast demand

k t D + ˆ. k t D + ˆ
is calculated by using a forgetting factor α. Starting from a series of stationary demand, Gilbert demonstrated that the stock and order are also ARMA [START_REF] Gilbert | An ARIMA supply chain model[END_REF]. The ARMA model is a special case of the ARIMA model mentioned above. It treats the stationary series. If the series is not stationary, its variable is integrated until stationarity, hence the letter I in the model name. In the model below, we assume that the order policy is the classical "Order up to policy".

I S O + - - - - - + + + - = (3)
By definition, S is the level of safety stock required to limit stock-outs. A study that generalizes this order policy was also proposed by Gilbert et al. [START_REF] Gilbert | An ARIMA supply chain model with a generalized ordering policy[END_REF]. The ARMA model also allows the chain to represent a widely known vulnerability in the field of supply chain, known as the bullwhip effect [START_REF] Sakli | An Analysis of Risks and Vulnerabilities in Supply Networks[END_REF] [16] [START_REF] Lee | Information distorsion in a supply chain: The bullwhip effect[END_REF]. It represents the amplification phenomenon of demand variability in the stages upstream in the supply chain. The proposed model allows evaluation of the bullwhip effect on the stock and on the order. Note that another phenomenon is also studied in the literature regarding the reverse bullwhip effect. It aims to evaluate the amplification of disturbances in the prices of raw materials on the downward stages and determine its effect on the product's final cost [START_REF] Rong | Bullwhip and Reverse Bullwhip Effects under the Rationing Game[END_REF].

The Constrained Model

The model of the supply chain presented above does not take into account the constraints of the companies. In real cases, the company has a limited storage capacity and cannot order more than a maximal amount of products from the supplier. At the other end of the feasibility intervals, the level of the stock and the quantity delivered cannot have negative values. To take these constraints into account, Sakli et al. [START_REF] Sakli | An Analysis of Risks and Vulnerabilities in Supply Networks[END_REF] present a saturated ARMA model, in which the dynamic equations ( 2), (3) are replaced by the following non-linear equations.

Inventory equations. Due to the limits on the storage capacity, the current inventory level is computed by: 1 1 min( , ) . max( ,0)

t t t L t t t t L t I I O D I I I O D - - - -  = + -  = + -  (4)
Order equations. Due to the limits on the quantity ordered, the current order is computed by:

S I D D L O O O O S I D D L O O - -+ - -+  = -+ + + - --  = -+ + + - --  (5)

Representation of the Quality Problem

When a requested quantity is produced or delivered, this amount may not have the desired quality or be delivered within the scheduled time. The variation of product quality can be caused by the production process, but also by the delivery, because of the handling or transport of the goods or by storage. The amount of products that do not meet the desired quality can either be returned to the supplier, be accepted by the company at a lower price, or considered as waste and therefore discarded. This depends on the nature of the goods and the severity of the defect. Let t z be an index of the quality of supply in period t. The quality of goods is supposed variable in time. Two cases are analyzed in this study: either t z is random with variations around a mean value or t O takes two values: 0 and 1 with deterministic jumps occurring at random times.

Case of random variations. An example of random variations is when t z is supposed ARIMA (0, 1, 1). In fact, this model of quality must be truncated as follows, to avoid quality values under 0 or above 1.

t t t t t N ( 0 ,s ig m a ) 0 1 . 1 1 0 0 t t t t t e h e z if z if z if ζ ζ ζ ζ ζ   = +  = ≤ ≤  = >  = <   (6)
Case of deterministic values with random jumps. A typical example of this case is given by formula (7).

z if t T O r if T t T O r if T t T t z if T t T O r if T t T t = ≤ < ≤ < ≤ ≤   = ≤ < ≤ <  (7)
T1, T2, T3 and T4 are random dates that may be obtained in simulation from uniform laws in given intervals. 1

= t z
is the case when the quantity ordered respects the desired quality. The opposite case, t z = 0 represents the case when the supplier cannot deliver the requested products with the required quality. Such a case may be due to interruption of production (machines' breakdown, strikes, etc.), or transportation problems.

Whatever the law of evolution of z, the dynamic equation of evolution of the stock is constrained by saturation values in the following form:

   - + = - + = - - - - ) 0 , * max( ) , * min( 1 1 t t L t t t t t L t t t D z O I I I D z O I I . ( 8
)
It can be noted that the unconstrained model is bilinear. Moreover, integration of constraints as in section 2.2 introduces other nonlinearities. To compensate for the lack of reliability of the supplier, it is possible to adjust the value of the quantity to order based on the predicted quality of delivery. For this, we propose to build a quality predictor, taking value t z ˆ at time t. Under this assumption and after introduction of constraints saturation, the equation for the order is:

O S I D D L O O O z O S I D D L O O z - -+ - -+  = -+ + + - --     = -+ + + - --   (9)
For example, a predictor t z ˆcan be calculated recursively with a forgetting factor f as follows:

. * * ) 1 ( ˆ1 1 - -+ - = t t t z f z f z (10)
In the previous expression, , which has just been received at time t-1. Equations ( 9) tend to increase the order from the supplier up to its maximal capacity. This increase corresponds to the collaboration mechanism between the supplier and the producer to better satisfy customers.

Detecting the saturation of the system further allows the construction of indices that keep in memory the information on the occurrence of saturation. Saturation index of the inventory:

1 if 0 0 if 0 . 1 if II I t t II I I t t II I I t t  = - =  = < <   = =  (11)
Saturation index of the order:

1 if 0 0 if 0 . 1 if OI O t t OI O O t t OI O O t t  = - =  = < <   = =  (12)

A Case Study

The case study concerns a basic two-stage supply chain with a company (producer) and its supplier. The company receives random orders from customers. The demand is supposed ARMA (0, 1, 1) with a fixed delivery lead time L, and is written as follows.

Here t ε denotes as the white noise, representing an additive system disturbance.

.

t t ε + = D D (13)
A demand predictor is constructed by recursive forecast with forgetting factor α :

1 1 ˆ(1 ) * * . t t t D D D α α - - = - + (14)
In numerical examples, the selected value of the forgetting factor is α = 0.15. The curves of demand t D and predicted demand t D )

are shown in Fig. 1. To validate the analytical results, we represent the influence of changes in quality in the two cases previously presented. For both cases, the system is simulated with and without a quality predictor given by [START_REF] Tang | Identifying risk issues and research advancements in supply chain risk management[END_REF] with forgetting factor f=0.55, to evaluate the accuracy and effectiveness of this predictor to improve the system resilience.

Simulation under the Multiplicative Quality Disturbance

Firstly, we simulate the system dynamics with a random quality index t z . The mean value of quality is supposed to be 0.8. Of course, this value is not supposed to be known by the producer, who computes the order value by formula [START_REF] Wagner | An Empirical Investigation into Supply Chain Vulnerability[END_REF]. Simulation without quality disturbance prediction. The quality index t z is simulated by formula [START_REF] Manuj | Global supply chain risk management[END_REF]. Fig. 3 describes the evolutions of the inventory t I computed by [START_REF] Hennet | Toward an integration of risk analysis in supply chain assessment[END_REF] and the order t O computed by [START_REF] Wagner | An Empirical Investigation into Supply Chain Vulnerability[END_REF] with t z ˆ=1. In this simulation, the quality defects are unknown and there is no prediction of the quality index ( t z ˆ=1). This figure provides some insights on the system behavior. In particular, it can be noted that the inventory level is often zero and the inventory index (11) takes value -1. It represents the case when demand t D is greater than the quantity available in stock t I . Due to the high frequency of stock-outs, it seems necessary to take into account the quality perturbation in the order process. Simulation with quality disturbance prediction. Under the quality index predicted by formula [START_REF] Tang | Identifying risk issues and research advancements in supply chain risk management[END_REF], the system has a less vulnerable behavior. It can be observed on Fig. 3 that the mean value of inventory seems stationary. However, the order values computed by ( 9) are frequently hitting the maximal delivery level.

Simulation with Quality Jumps at Random Times

The system is now simulated under random jumps of the quality percentage between 0 and 1 at random times. Again, the system is first simulated without any quality disturbance predictor ( t z ˆ= 1) and with the same predictor as in the previous example ( t z ˆgiven by ( 10)).

In this numerical example, the dates T1 = 177, T2 = 227, T3 = 395 and T4 = 431 have been chosen at random by uniform laws in given intervals of dates. As shown in Fig. 4, the quality index is 1 between the dates (0: 177), (228: 395) and (432: 500). In these intervals, quality is perfect and there is no defective products discarded. On the contrary, the quality index is zero between dates (178: 227) and (396: 431). Simulation with quality disturbance prediction. To predict the quality index, we use formula (10) again, with forgetting factor f = 0.55. The curve of the estimated index is very close to the quality index of Fig. 4. However, it can be observed on Fig. 6 that the order and inventory evolutions are still strongly disturbed around the dates of the states changes.

Fig. 6. Order and inventory evolutions

It is clear that the system gets out of stock throughout the supplier interruption period. On the other hand, the order level commonly reaches the maximum threshold value 330 of the supplier's capacity. However, such a systematic increase of the order level during supplier breakdown periods has limited effect on the inventory curve since deliveries are zero regardless of the amount of the order.

Conclusion

This paper presented concepts related to risks in a supply chain, namely uncertainty, vulnerability and resilience. We proposed a nonlinear model based on time series ARMA for representing a supply chain, taking into account the constraints of the real system. Then, we simulated the system subject to random disturbances on demand and supply, under positivity and capacity constraints on the quantity ordered and available stock. Two types of quality disturbances from the supplier were simulated. In both cases, it is clear that without taking into account the quality index, the system often is often out of stock and gets into strong disturbance that propagate upward and downward the supply chain. To mitigate that problem, we have proposed to construct a quality predictor, and we have introduced it into the formula for calculating the order quantity. If out of stock, the company orders a larger quantity often equal to the maximum capacity of the supplier. This corrective policy appears to be efficient in the case of random fluctuations of the quality. But its impact is rather limited in the allor-nothing supply quality case.

  .

  t

Fig. 1 .

 1 Fig. 1. Curve of demand and predicted demand

Fig. 2 .

 2 Fig. 2. Order and inventory evolutions with t z ) = 1

Fig. 3 .

 3 Fig. 3. Order and inventory evolutions

Fig. 4 ..

 4 Fig.4. A curve of quality index evolution with randomly generated commutations Simulation without quality disturbance prediction. We have first simulated the system with t z ˆ = 1 [ ]0 500 t ∀ ∈. Fig.5illustrates the order and inventory evolutions without any prediction of the quality index.

Fig. 5 .

 5 Fig. 5. Order and inventory evolutions

  To represent the model of the supply chain, we use the following notation:

	t D : Random demand at period t
	a	t	1 -	,	e	t	,	ε	t	: White noises
	µ : mean demand

t I : Inventory level at the end of period t t O : Order placed at the end of period t t D ˆ: Estimated value of demand at period t I : Maximal storage capacity t II : Inventory index at period t O : Maximal quantity ordered from the supplier in one period t OI : Order index at period t t z : Quality index at period t t z ˆ: Estimated quality index at period t S : Safety stock level