João Bastos

Américo Azevedo

Paulo Ávila

A Lean Set-Based Design Approach for Development of Customizable Products in Collaborative Networks

Keywords: Product Development, Collaborative Networks, Product Customization, Set-Based Design, Lean

In nowadays competing market, companies are constantly challenged to reduce the lead time for new products design process by diminishing the time response that goes from the arise of the market opportunity to the satisfaction of the customer need. Simultaneously, companies and networked organizations face a growing number of product configurations, lower product volumes, a continuously growing appetence for personalized products, pressing the decision makers into adopting more efficient product development processes. The present paper addresses the main collaborative product development issues by proposing a responsive and efficient use of knowledge on networked environments through a lean-based framework for collaborative networks. In particular, this work describes the main lean concepts and tools that are enhancers of an efficient and distributed customizable product development process in networked environment.

Introduction

Manufacturers and sellers of a multitude of products from simple t-shirts to luxury woman purses and even more general consumer packaged products are finding out the value of letting customers creating and customizing their own unique products. Retailers use intensively market analysis tools to understand and cope with the market trends and be prepared to present a personalized set of "one-of-a-kind" products to their customers. Fast fashion retailers such as Zara have dramatically reshaped their business processes on designing, manufacturing and distribution to respond to current and emerging market trends by adapting their product collections as quickly and effectively as possible. Similarly, a driving force behind Amazon's success has been the company's customer experience pillar based on providing the "earth's biggest selection" with its biggest focus on product personalization.

In reality, an increasing number of brands are now taking personalization and customization in their offer a step further by resorting to a new paradigm, such as codesign approach aligned to mass customization practices, a production strategy focused on the broad provision of personalized products. These companies are discovering that they can raise customer interest, commitment and loyalty in the nowadays volatile global markets.

Several web-based manufacturers have used product customization practices to boost sales on their own websites and gain share on retailer's sites. For example: bivolino.com provides on its site custom tailored man shirts and woman blouses with several thousand of possible product combinations selectable by the customers; in jawbone.com customers can configure their own Jambox speakers, and Brooks Brothers (brooksbrothers.com) allows men to custom their own shirts and suits.

However, despite the obvious advantages of manufacturers offering customized products, its acceptance by the majority of companies has been very limited. Past examples have shown that in order to a company embrace the customization game it is necessary to enhance their capabilities in three areas: product development capabilities; efficient processes design practices and supply chain integration.

The research performed in the recent years have shown that the customization transformation of a company's offer is achieved through modularized product/service design, flexible and efficient processes, and integration & collaboration between supply chain members [START_REF] Piller | New directions for mass customization[END_REF][START_REF] Fogliatto | The mass customization decade: An updated review of the literature[END_REF][START_REF] Tseng | Mass customization[END_REF].

In parallel to the customization game, companies area facing in their quest for innovation an increase in the complexity of their products, designing processes and manufacturing activities. Coupled with the complexity increase, managers are constantly challenged to reduce the lead time for new products technical design, diminishing the time interval that goes from the arise of the market opportunity and the satisfaction of the customer need with full-rate production of marketable products.

In overall, the current trend is forcing companies to be faster, more flexible and increasingly efficient in the design approach of new products and simultaneously taking into consideration the customer aspirations of more personalized products. The growing number of product configurations, lower product volumes, a continuously diminishing response time in designing and delivering new products have a significant impact on the company operations management strategy and is changing the landscape of collaborative networking.

This paper addresses the multidisciplinary complexity of personalized product development processes in customer-driven value chains, in particular, by tackling the main collaborative business processes on the operational level, namely on its competencies, resources and processes dimensions tailored for responsiveness and efficient use of knowledge on customized manufacturing environments through a lean-based framework proposal.

The proposed approach transposes the lean basic concepts and practices, historically implemented in in-doors manufacturing operations, to a networked and extended environment of Collaborative Networks (CNs) through a set of tools and methods aimed to support the design, modeling and implementation of the necessary development processes for customizable products.

The remaining of this paper is organized as follows: first the existing related literature and research questions are presented, followed by the description of the lean set-based principles in collaborative networks. Afterwards, the concepts, methods and tools of the framework are presented. Finally, conclusions and future developments are detailed concerning the framework instantiation and further improvement.

Background and Research Topics

The last decades have shaped the context on manufacturing consumer goods with a tendency to an increase in the number of product variants, a dramatic reduction of products life-cycle and a shorten in the expected response time from market requests. Furthermore, paradigms such as mass customization and personalization are changing the traditional relationship with the customer from "made-to-stock" to "made-toorder" [START_REF] Tseng | Mass customization[END_REF]. The shift from mass production to a more complex and highly demanding "high-variety-low-volume" production is defying the traditional product development processes and supply chain management policies forcing companies to increase their flexibility in order to produce small batches -till one-of-a-kind product -in order to satisfy customer demand [START_REF] Zangiacomi | Reference Model Framework for Production of Small Series of Innovative and Fashionable Goods in Manufacturing Networks[END_REF].

Design for Personalization

In order to support the new paradigm resulting from the personalization process, the company should rethink the whole value chain from the front-end to the back-end in order to consider four factors: efficiency, time-to-market, variety, and economy of scale.

All these issues pose a challenge for manufacturing companies: how they can cope with the consumers demand for personalized value-added products and simultaneously assure high quality, innovative functionalities and responsiveness?

In fact, in order to the manufacturing value chains be able to address this new challenging kind of market demand with efficient development processes, they need to resort to new collaborative methods and tools. These new forms of networked organizations fitted with efficient product development processes present a promising approach to deal with the need to customer driven focus, reduced time to market of new products and cost effective manufacturing in a cooperative and collaborative environment [START_REF] Carneiro | Reference model for collaborative manufacturing of customised products: applications in the fashion industry[END_REF].

The development value stream produces operational value streams which run from suppliers through factories, into product features and out into the customers. Design for product customization is to consider economy of scale at the early stage of product development process, seeking efficiency in all the stages of this value stream [START_REF] Kennedy | Ready, Set, Dominate: Implement Toyota's Set-based Learning For Developing Products And Nobody Can Catch You Author[END_REF].

From a traditional approach, product development processes, including the case of customized products, usually follow a "waterfall" approach or "V" methodology. With this approach, after the business opportunity identified, it is created a concept specification, which in turn is translated into a system design. This overall system design, which in the case of customizable products is modular, in reality freezes the interfaces between the different modules or subsystems, allowing the next phase of independent and in many cases parallel design of the subsystems. This hierarchical design process follows a top-down approach during the design phase and bottom-up approach during testing and prototyping [START_REF] Bastos | Towards a Customer-Driven Value Chain Framework-A Set-Based Oriented Approach[END_REF].

Due to its independent subsystem designs in autonomous modules, this "waterfall" approach is widely used in collaborative networks. Even though abundantly used, this traditional approach, has significant drawbacks. By following a modular and top down approach, this means that critical systems decisions about module or subsystems interfaces are made on the basis of early insufficient data and wishful thinking of the designers of what the final product will be. As several studies point out, this distributed product development process is performed mostly from draft designs of products, processes and network configurations. Hence, these drafts designs are usually vague, leading to inconsistent final solutions, resulting in problems that are discovered late or in advanced phases of the design process. Another reported drawback of this traditional approach is the low levels of reutilization of parts, manufacturing systems or reconfiguration of networks [START_REF] Ward | Toyota, concurrent engineering, and set-based design[END_REF][START_REF] Liker | Involving suppliers in product development in the United States and Japan: Evidence for set-based concurrent engineering[END_REF][START_REF] Inoue | Collaborative engineering among designers with different preferences: Application of the preference set-based design to the design problem of an automotive front-side frame[END_REF]. These problems observed in advanced phases of the product development process force design loopbacks and network reconfigurations (see Fig. 1) which often consumes 50 to 75% of engineering resources [START_REF] Kennedy | Ready, Set, Dominate: Implement Toyota's Set-based Learning For Developing Products And Nobody Can Catch You Author[END_REF]. Therefore with the traditional "waterfall" approach it is observed the following disadvantages [START_REF] Bastos | Towards a Customer-Driven Value Chain Framework-A Set-Based Oriented Approach[END_REF]:

• inefficient resource usage -due to the late discovery of design problems which require loopbacks and rework;

• discard of knowledge -due to the early commitment to rigid product design specifications, the knowledge acquisition is restricted and the network partners involvement and knowledge generation is suppressed;

• poor and unreliable solutions -since every new product development project only aims in attaining a single feasible solution in terms of products specs and network configurations, usually there is insufficient domain knowledge that results in a good or optimal solution.

In summary, the traditional networked product development approach, presents efficiency, knowledge acquisition and responsiveness shortcomings that demand for an overall rethinking of the product development process in collaborative networks.

Lean Principles and Tools for Product Development

Womack and Jones in "Lean Thinking" stated that "lean companies figure out what value is (what customers actually want) and concentrate on 'value streams', the connected activities that create value" [START_REF] Womack | Lean Thinking: Banish Waste and Create Wealth in Your Corporation[END_REF]. These authors argue that conventional companies often get so engaged with their internal way of doing business that lose sight of what is actually creating value and instead produce waste. On the other hand, lean companies are focused on ways to add value by eliminating non-value creating activities. Lean is defined as an efficient and systematic approach to maximize value by minimizing waste, and by pull flowing the products through the resources at the customer demand pace. In order to achieve this goal, it is useful to outline the characteristics of a lean approach in manufacturing systems. Lean enterprises are always looking for ways to cut the use of any of these resources anywhere in the company [START_REF] Bruun | Lean production and the Internet[END_REF].

Despite the lean started from the improvement of physical production processes, since the beginning, the lean pioneers accepted the challenge of extending the lean philosophy to the product development process. The effort for creating an efficient product development process struggled with the high variability and mostly immaterialized flow of activities present in any product development process.

A major obstacle in using the lean approach for product development processes arises from the fact that the core element in the development process is the peoplethe knowledge workers -which fear the blocking of their creativity by the standardization of work practices. Nevertheless, the practice have shown that a significant part of the product development effort comprises the discovery of the information required, the identification of the information sources, and what to do with this information since it is collected. These are all activities that can be simplified and standardized using lean practices. Afterwards, once these processes have been simplified and all the data collected, often the development team finds out that they have more time for actually creative and innovative activities [START_REF] Locher | Value stream mapping for lean development: a how-to guide for streamlining time to market[END_REF][START_REF] Radeka | The mastery of innovation: a field guide to lean product development[END_REF] Although the novelty of this research area, there are very few examples of published works that studied and documented the use of lean principles in product development. The most significant was published by J. Morgan and J. Liker in 2006. In this book, the authors identify 13 principles that distinguish the lean product development process in three categories: the process; the skilled people; and tools and technology [START_REF] Morgan | The Toyota product development system. Integrating people, process, and technology[END_REF]. The lean principles identified by the authors show that the challenge in product development is to reduce variability while conserving the creativity that is necessary to the product design process.

From the analysis of selected manufacturing success cases, it was possible to identify in addition to the main principles which are the methods and tools that support the lean product development system. In Table 1 it is summarized the most significant tools used by lean companies in their product development process.

Although in recent years it was observed a disclosure of lean practices, methods and tools to support the product development process, yet very few companies followed the lean approach in this critical process for competiveness. This is especially true for Collaborative Networked organizations that need to undergo in a series of alliances as part of their strategy to obtain new technologies, enter new markets and, in general, increase responsiveness to customers by enhancing their flexibility and efficiency.

The question is, what is still missing? How can networked organizations, often with poorly defined existing development processes, redesign it in order to achieve higher efficiency and get their arms around the lean thinking? The SBCE tool take into consideration several possible designs and technical solutions at the beginning, and as the process progress, the workable solutions are narrowed as more information from development, testing, the customer, and across the organization is obtained in order to obtain the most efficient solution.

VSM (Value Stream

Mapping)

Through mapping of the development value stream, it is analysed the set of all actions required to develop a specific product or service through the critical management tasks in order to eliminate the waste.

QFD (Quality Function

Deployment)

Methodology used to capture the customer perspective and translate the customer needs into design requirements and specifications. QFD consists of a series of interlocking matrices that transform the customer needs into product and process characteristics.

Pugh Matrix (Criteria Based

Matrix)

It is a matrix used to compare several different design concepts under consideration allowing the developer team to compare the different concepts, create strong alternative concepts from weaker concepts and arrive to an "optimal" concept, which may be a combination the best aspects of other designs.

DOE (Design of Experiments)

DOE is statistical technique to increase the effective use of the information generated through experimentation. It can help the designing team understand the dependency or relationships between different critical variables.

To start, Collaborative Network managers need a reference model or a step-by-step methodology that they can apply, in a practical way, to their own networked development processes. This is especially true, because despite the abundant information on the appliance of lean method in indoors product development, there is still missing from the literature practical guides and references that assist collaborative networks practitioners into the goal of becoming efficient product development networked organizations.

Set-Based Design in Networked Product Development

The extension of the lean principles from a mostly in-house scenario to a network environment, especially in the case of Collaborative Networks, poses some challenges. In reality, it is necessary to adapt some of the lean basic principles and include some new methods and tools to support the redefinition of the basic concepts.

Let's take the example of waste. Ohno and Shingo defined the seven principal manufacturing wastes as: overproduction; waiting; transporting; over-processing; excessive inventory; excessive motion; rework and defects [START_REF] Womack | Lean Thinking: Banish Waste and Create Wealth in Your Corporation[END_REF].

Since in the case of the CNs product development processes, most of the activities are dematerialized, the equivalent examples of waste need to be identified from the customer perspective of the net added-value of the activity. Therefore, based on the assumption that the customer is only willing to pay for an activity in the development process if it sees its value, it was possible to characterize waste in a networked product developing process in its different forms according to Table 2. Another adaptation successfully implemented of extending the lean principles to a collaborative network environment, was the concept of lean set based thinking. This concept resulted in the adaptation of the principles behind the lean tool called SBCE (Set-Based Concurrent Engineering) [START_REF] Bastos | Towards a Customer-Driven Value Chain Framework-A Set-Based Oriented Approach[END_REF][START_REF] Ward | Toyota, concurrent engineering, and set-based design[END_REF].

The concept derives from the Toyota's product development practices. This automobile manufacturer is the industry leader and presents the most reduced lead time for new product launches and product development. In order to achieve this performance, Toyota values the knowledge it can collect from the different actors involved in the development process.

Similarly, in the case of collaborative networks, due to its dynamical nature, the effort to collect and reuse knowledge during the product development process is a critical factor to the success of the business opportunity. This assertion is especially true when it is considered the case of innovative and customized products with an increased emphasis in the time constraints and the usual complexity of the task.

The knowledge focus in the development of new products in CNs starts immediately at the customer request early definition. Traditionally, when using the "waterfall" approach, the customer requirements are frozen at the beginning, followed by a more detailed design system with a fixed interface specification of the subsystems. This in turn allows the independent development phase of the subsystems between the different members of the collaborative network.

This traditional approach in many cases results in inconsistent final solutions, due to problems that are discovered late or in advanced phases of the design process. It has also the drawback of low levels of reutilization of knowledge and a suboptimal regarding the network configuration.

In contrast, with the set-based approach, the development process begin with a set of possibilities that comply with the customer requirements, then through a series of tests and experimentation, an intensive acquisition and combination of knowledge occurs, which results in the elimination of the unfeasible solutions narrowing the set of solutions until arriving at an unique solution supported in a final network configuration (see Fig. 2).

Fig. 2. Set-based development life-cycle in Collaborative Networks

This set-based development process occurs simultaneously with a collaborative planning construction and is oriented to address the demand planning and demand fulfillment activities for new personalized and innovative products. This integrated tool allows each partner of the collaborative network to contribute to the value-added knowledge acquisition process. After the detailed design approvable and the selection of the final network participants, the tool also allows each partner to collaboratively negotiate the collaborative production plan by directly proposing delivery dates, production lead times and costs, via a web-based planning graphical tool which is available and shared by all supply network partners [START_REF] Fornasiero | Collaborative Services for Customized Production in Networked Companies[END_REF].

Ultimately, through negotiations undertaken between all the core partners and potential partners of the collaborative network it is reached a feasible and efficient manufacturing plan for the supply network, where all the necessary operations are defined in terms of lead times, time overlaps, minimum cost, and other relevant negotiation indicators defined at the beginning of the negotiation.

In summary, a set-based development approach offers remarkable opportunities for efficient learning and knowledge acquisition before decision making. By allowing delayed decision-making, till the moment where enough knowledge is available, enables intelligent decisions and minimizes mistakes. Another advantage derived from this approach is the support for collaborative decision-making, facilitating robust product designs that take into consideration the best solutions in terms of products configurability as well as the need for fast response to market requests.

A third adaptation of extending the lean principles to a collaborative network environment, is the value stream mapping. Value stream mapping (VSM) is an effective and confirmed tool to analyze existing business processes and to help redesigning them based on lean concepts.

The VSM uses lean concepts to analyze the current state of a process, in this case the development process, and seeks to improve its performance, which means to develop the "future state" (the to-be), and creates a plan for implementing the new efficient process. When using the VSM on the customizable product development processes in CNs, the key is to focus the analysis on the work flow and on the waste in its different forms as presented in Table 2. The practitioner when analyzing a specific development project has to focus is eyes on the different forms of waste, seeing specific activities for what they truly are -waste or nonvalue-added activities.

For the current case of establishing a more efficient product development process in collaborative networks, the VSM tool prototype developed inside the framework offers a way to assess the overall efficiency of a development project, based in lean principles (see Fig. 3). The approach is proving to be a very powerful tool towards an easy and intuitive interpretation of the relevant indicators of the aggregated efficiency in the management of customizable product development processes. The VSM collaborative analysis tool is also very helpful to handle the common trade-offs that arise in development projects so that the managers can see the consequences of a decision that has multi-criteria impacts. In order to test and validate the lean concepts addressed in the proposed set-based framework, it was developed the two prototype tools described previously: a setbased collaborative development tool and a value stream mapping collaborative designing analysis tool. These two tools were included in a previously developed Collaborative Portal aimed to support the formation and the operation of collaborative networks for production of innovative and personalized products.

The Collaborative Portal is an ongoing research project that includes industrial manufacturing companies and it is aimed to help managers in face of business opportunities to form and configure collaborative networks. Figure 4 The Collaborative Portal is intended to provide a comprehensive set of tools aimed to cover the full life-cycle of collaborative networked organizations from the arise of the business opportunity to the execution and the delivery of the product. With the set-based product development module latest inclusion it was possible to tackle more clearly issues such as the knowledge acquisition and efficient development of personalized products in networked environments.

Conclusions and Future Developments

The present work proposes a lean set-based design approach for development of customizable products in Collaborative Networks. This approach intended to support the creation of efficient collaborative environments that enable manufacturing companies to produce customizable high value-added products. The main concept that mobilized this approach was the effort to address the "time to market" issue or responsiveness for innovative and personalized products inside collaborative networks. This critical factor of responsiveness is assuredly associated with the efficient use of resources and the preservation of the knowledge inside the companies. Therefore in order to guarantee full compliance with these objectives it was selected a lean inspired knowledge-based engineering approach.

In particular, the approach represents a translation of the lean manufacturing principles, tools and methods. Using this approach, the objective is to provide companies with the necessary means to develop and manufacture collaboratively customizable products with increased efficiency. Despite the immediate obstacle in using the traditional lean approach for product development due to the inexistence of material flows and the main element involved in the development process correspond to the human element, nevertheless the implementation of standard work practices and other lean concepts bring to this knowledge intensive activity great benefits.

The proposed approach aims to facilitate collaborative networks managers in achieving more efficient and faster responses to customer request of personalized products through: the use of lean principles such as waste reduction; the support of a innovative knowledge engineering design of new products through a lean inspired setbased approach; and through the assessment of the overall efficiency of the development projects by using the value stream mapping analysis tool.

The conceptual model of the approach, developed from previous and ongoing R&D international and national projects with industrial partners has been translated into prototypes applied to the real cases of textile and clothing industry.

The proposed approach of a lean set-based design approach for development of customizable products in Collaborative Networks represents a contribution towards the definition of adequate business models addressing responsiveness and efficient use of knowledge on customized manufacturing and collaborative environments.

As future developments, it is planned for the research team to continuing testing the current prototype Portal through the contributions of the industrial users. Simultaneously seeking to add to the current set of tools other lean methods and tools that contribute to the ongoing effort to deliver a more efficient and reliable knowledge-based framework designed to assist companies in operating in collaborative networked environments.

Fig. 1 .

 1 Fig. 1. Waterfall approach for collaborative networks product development process

Fig. 3 .

 3 Fig. 3. Value Stream Mapping in Collaborative Designing Analysis

  represents the business process definition of the Collaborative Portal which now includes the setbased product development toolset.

Fig. 4 .

 4 Fig. 4. Business Process of Set-based Development Process in CNs By using web-based technology, the current prototype implementation of the Collaborative Portal allows the network managers in CNs to interact dynamically and in real-time in order to deal with the complexity of addressing the demand of innovative and personalized products in a efficient and responsive way.The Collaborative Portal is intended to provide a comprehensive set of tools aimed to cover the full life-cycle of collaborative networked organizations from the arise of the business opportunity to the execution and the delivery of the product. With the set-based product development module latest inclusion it was possible to tackle more clearly issues such as the knowledge acquisition and efficient development of personalized products in networked environments.

Table 1 .

 1 Lean Tools used in Product Development Process

	Lean Tool	Use in the Product Development Process
	SBCE
	(Set-Based
	Concurrent
	Engineering)

Table 2 .

 2 Waste examples in a networked product development process

	Type of Waste	Examples
		-Over-engineering;
		-Over-complex solutions from poor designs
	Overproduction	-Completing design elements that are not needed before time; -Develop features that the customer does not see as a value;
		-Dividing the developing tasks and letting each network partner
		duplicate what others are doing.
		-Unnecessary approvals from other partners in the network;
		-Waits for other partners to process their tasks;
	Waiting	-Queuing to use an overloaded partner facility; -Waiting from customers inputs;
		-Waiting for partner responses;
		-Waiting for completion of other design elements.
		-E-mailing information to other partners;
	Transportation	-Multiple hand-offs between partners; -Circulating paperwork for signatures;
		-Reports distribution among network.
		-Preparing reports or paperwork that aren't used;
	Overprocessing	-Creating features the customer doesn't want;
	(Nonvalue-Added	-Re-entering data for each partner;
	Processing)	-Re-designing products or components that already have been designed;
		-Most network engineering support services
		-Poorly organized projects that take too long to complete;
	Excess Inventory	-Working on projects that are not commercially viable; -Batch processing transactions among partners;
		-"Large" design releases.
		-Searching for information that has not been, often across partners;
	Excess Motion	-Going to meetings;
		-Travel.
		-Design errors;
	Rework and	-Data service failures or data missing;
	Defects	-Engineering change orders due to design errors;
		-Missing or not understanding customer needs;
		-Missing or incomplete information.
	Underutilized People	-Limited authority and responsibility for basic tasks inside the network; -Not sufficiently sharing knowledge; -Not involving partners early in the development process.

Acknowledgments. Project "TEC4Growth -Pervasive Intelligence, Enhancers and Proofs of Concept with Industrial Impact/NORTE-01-0145-FEDER-000020" is financed by the North Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, and through the European Regional Development Fund (ERDF).


Oliviu Matei
email: oliviu.matei@holisun.com

Giovanni Di Orio

Javad Jassbi
email: j.jassbi@uninova.pt

José Barata

Claudio Cenedese

Claudio Cenedes
email: claudio.cenedes@electrolux.it

Collaborative Data Mining for Intelligent Home Appliances

Keywords: Collaborative Data mining, Intelligent Home Appliance, Collaborative Network

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

Introduction

Intelligent products are pushing more and more the Collaborative Networks (CN) discipline to a new level where the product itself is acting as an active and autonomous agent within an environment where people, processes, data, and things are connected together for designing/creating new products and services, while product manufacturers to more securely manage the risk and to extend the global reach by allowing higher collaboration from anywhere and at any time. In this scenario, the data continuously produced by intelligent productsif properly gathered and analyzedcan provide fundamental feedback information to product manufacturers about the products performance as well as products usage. This information can be used by the manufacturers for accelerating the product innovation process and increasing their competitiveness in market sharing. For these reasons, products have become an indispensable part of New Generation of Collaborative networks ( [START_REF] Picard | Resilient and Robust Human-Agent Collectives: A Network Perspective[END_REF]). According to Sanou [START_REF] Sanou | ITC Facts and Figures 2013[END_REF], the access to the Internet has grown from an estimated 10 million people in 1993, to almost 40 million in 1995, to 670 million in 2002, and to 2.7 billion in 2013. As the connectivity and Internet of Things penetrate the daily life, a reasonable concern of the producers is to monitor and understand the behavior of the users along with the usage patterns of their devices and appliances. This would bring up invaluable knowledge as a basis for further technical and marketing developments, both in industrial and business environment, as well as in home context.

Therefore, much research has been invested in determine these usage patterns, such as the ones reported in [START_REF] Di Orio | A Platform to Support the Product Servitization[END_REF] and [START_REF] Matei | PRELIMINARY RESULTS OF THE ANALYSIS OF FIELD DATA FROM OVENS[END_REF]. Both use data mining to fulfil this objective. The aim is to determine an expected behavior of the device or user based on some known sensors outputs.

Human Agent collectives (HACs), are interesting investment for companies. Home appliance market leaders are keen to build smart houses (including smart kitchens) with the collaboration of both humans and intelligent products. This means HACs are the heart of smart collaborative networks while Intelligent Products are playing crucial role and the advantage is the stream of available data through sensors in the products. To manage this data/ Information in a productive way, different types of algorithm need to be employed. Collaborative Data Mining is a successful example of emerging algorithms to deal with "big data" collected from Collaborative Networks.

The term of collaborative data mining has been used several times, by Appleman in [START_REF] Appleman | Collaborative internet data mining systems[END_REF], Maimon in [START_REF] Maimon | Data mining and knowledge discovery handbook[END_REF] and Moyle in [START_REF] Moyle | Collaborative data mining[END_REF]. But the term is not defined in a comprehensive manner that allows one to have a view of what are the advantages of such an approach compared to classical data mining, what are the benefits of such an approach, what are the underlying principles of such an approach and how this approach may be different compared to other approaches. Later on, in 2008, Zhan et al. [START_REF] Zhan | Privacy-preserving collaborative data mining[END_REF] used the term collaborative as referring to using more data sources for mining.

As the connectivity is present in our daily lives [START_REF] Haythornthwaite | Social networks and Internet connectivity effects[END_REF], the quantity of available data is ever increasing and companies have real interest in understanding the behaviour of their customers [START_REF] Heierman | Improving home automation by discovering regularly occurring device usage patterns[END_REF], a trend is to collaborate all these data source for more accurate analysis [START_REF] Hajibandeh | Resemblance measurement of electricity market behavior based on a data distribution model[END_REF]. The research questions are:

• What is the influence of using the data from two sources to predict the behavior of one source? • Is there any relationship between the accuracy of such predictions and the correlation between the two sources?

Collaborative Data Mining

As stated in [START_REF] Moyle | Collaborative Data Mining[END_REF], collaborative data mining is a setting where the data mining effort and/or process is distributed among multiple collaborative agents that are autonomously executing actions in the environment. Collaborative data mining is based on the main assumption that collaborative data mining processes can better tackle the considered data mining process with respect to a data mining process built on the top of individual and non-collaborative agents. Data mining is the process of extracting information or better knowledge from large quantity of data. Collaboration is the act of a variety of entities to share information, resources and responsibilities to jointly plan, implement, and evaluate a program of activities to achieve a common goal [START_REF] Camarinha-Matos | Collaboration forms[END_REF]. As stated in [START_REF] Camarinha-Matos | Collaboration forms[END_REF], collaboration is a difficult process and typically its success depends on several requirements, namely: i) the main purpose for collaboration; ii) the initial baseline for collaboration; iii) the collaborative process (a set of generic steps); iv) the creation of a space for collaboration; v) and finally the definition of resources, rewards, commitment and responsibilities. Despite these difficulties the main motivating point is that by using collaborative processes it is possible to reach results that cannot be reached by parties/entities/agents working alone. With this in mind, the proposed research is based on the assumption that there are similarities between usage patterns of the same devices or more in general agents [START_REF] Sanou | ITC Facts and Figures 2013[END_REF]. In such a way, we propose a data mining model which takes into account also the behavior of other similar devices/agents in the region when doing patterns recognition. This extends the individual data mining with the input set of other devices/agents, while meaning that the size of the input set doubles with the data from the sensors of corresponding devices as shown in Table 1 In the Table 1, the first 5 columns are the data from the devices/agents to be analyzed, namely the timestamp, from which the date of the week ("DW"), the date and the hour of the day ("Hr") are derived. The column "Door_close" shows the event of opening or closing the door, not whether or not the door is opened. That is why two successive records always have a true and a false value for "Door_close". The same data (shown in the main column "Similar device") is available for another device. While the classical data mining tries to predict the outcome as a Boolean value (column "Door_close") only based on the data from the same device/agent (main column "Analyzed Device"), the collaborative data mining take into account all available data, in this case both columns "Analyzed Device" and "Similar device".

Thus, in the context of this paper collaborative data mining is intended as the application of data mining techniques on multiple data sources (autonomous agents) to better understand the behavior of one of them as well as the correlation -if it exists -between them. The rapid progress on computer networks and the pervasive computing -supported by new computing paradigms and technologies such as IoT, CPS, web services (WS), cloud computing, Service Oriented Computing (SOC), etc -is offering the technical infrastructure and foundation for new forms of collaboration in several context of application [START_REF] Camarinha-Matos | Motivation for a theoretical foundation for collaborative networks[END_REF], [START_REF] Orio | A Cloud-Based Infrastructure to Support Manufacturing Resources Composition[END_REF], and where the proposed model can be easily deployed. In particular, for this research we have decided to use the technology and the infrastructure provided under the scope of EU-FP7 ProSEco1 project, where intelligent products (intelligent autonomous agents) are providing data during their operation. This data is then used for applying the proposed collaborative data mining process i.e. as input to the data mining process. More specifically, we aim to combine the results generated by data mining processes -applied on isolated agents (i.e. devices) -in a collaborative manner, or better, the usage of the obtained results in order to refine and improve the outcome of the data mining process on a selected agent (see Fig. 1).

Methodology

We aim to compare the collaborative data mining with standalone data mining, hence we use the same research methodology as reported in [START_REF] Di Orio | A Platform to Support the Product Servitization[END_REF]. The training data records are structured like in Table 1.

For collaboration, three devices have been selected randomly, along with the one used in [START_REF] Matei | Applying data mining in the context of Industrial Internet[END_REF] and [START_REF] Di Orio | A Platform to Support the Product Servitization[END_REF]. The appliances are real ones, deployed by Electrolux to real customer in the United States, for tests. The monitored period is 13th of November 2013 -25th of December 2013, with 1170 data records.

The objective is to determine the number of door openings per day. This process aims to determine how many times the device will be opened based on the number of openings in the previous days. This would be a good statistical indicator about the usage of the device and could help to manage internal functions (such as "Defrosting" procedure of refrigerators) in an efficient way. As the records are event-based, the data is aggregated over the day. The number of openings is a count of all records for which the value of "Door_close" is T (true).

The experiments have been done for the following benchmarks: 1. oven 1, 13, respectively oven 14 alone; 2. oven 13 using the previous data for oven [START_REF] Camarinha-Matos | Collaboration forms[END_REF], respectively oven 14 using the previous data for oven [START_REF] Moyle | Collaborative Data Mining[END_REF]. The two ovens have been chosen because there is a high correlation between them. The mathematical foundations of the correlation are explained in section 3.1. 3. oven 13 using the previous data for oven [START_REF] Heierman | Improving home automation by discovering regularly occurring device usage patterns[END_REF], respectively oven 1 using the previous data for oven 13. Between oven 1 and oven 13 there is a very low correlation (0.01). The first set of benchmarks would provide a standard for comparing the results of the benchmark sets 2 and 3.

The methodology refers to the correlations between some ovens. The definition and the computations of the correlations are shown in the next section.

Correlations between the Benchmark Appliances

Correlation between some benchmark appliances means correlation between some time series consisting of the usage patterns of the devices over the time [START_REF] Wei | Time series analysis[END_REF]. The main challenge here is that the two series do not have the same time samples, although the tick is the same, e.g. one can be sampled at 15.

, = ∑ [ x i -mx y i -d -my ] ∑ x i -mx ∑ y i -my (1)
where mx and my are the means of the corresponding series. Out of the 143 assets monitored by Electrolux, for which data is collected, only the ovens Kenmore Elite 97102 (counting up to 14 pieces) have the "Door_close" event, which is used in this research. Therefore we cannot talk about other correlations expect between the usage of these. Fig. 2 displays graphically the collaborative network of the ovens over a period when most of the ovens were used, namely December 2013. The nodes represent the ovens, denoted as numbers for a better comprehension. Their size is proportional with the total correlation for that respective oven, computed as:

= r i, j (2)
The oven number "2" misses because that oven starts being used only in April 2014.

The vertices are inverse proportional with the correlation of usage of the respective ovens. The closer the nodes, the more cross-correlated the ovens. The cross-correlation factor is in absolute values, as the negative values represent a negative relationship (yet existent). Ovens "9" and "14" have a very similar behavior, which is why they overlap. On opposite, the farther the nodes (or the longer the vertex), the lower correlation between the usages of the respective ovens. If there is no vertex between two nodes, it means that the correlation between the nodes is almost zero and was not displayed in the network.

Fig. 2. Collaboration network based on the correlation between the usages patterns of the ovens

Fig. 3 shows the correlations between usage patterns of the ovens over the whole period (November 2013 -April 2014) as a bubble chart. The larger the diameter of the bubbles, the higher the correlation. The smaller the bubbles, the lower the correlation. Please not that the positive and negative correlations are represented having the same diameters. The chart is symmetric as the correlation is symmetric. A missing bubble, like for the pairs (2, 4), [START_REF] Sanou | ITC Facts and Figures 2013[END_REF][START_REF] Matei | PRELIMINARY RESULTS OF THE ANALYSIS OF FIELD DATA FROM OVENS[END_REF], [START_REF] Sanou | ITC Facts and Figures 2013[END_REF][START_REF] Appleman | Collaborative internet data mining systems[END_REF] and so on, means that the correlation is between the usage of the respective ovens is zero. It is the case of the oven 2 because it was used for a short period of time.

Fig. 3. The correlation between usage patterns over the whole period

The experimental results are summarized in the next section.

Experimental Results

Three sets of benchmarks have been experimented, as shown in section 3:

-For three ovens (1, 13 and 14) independently; -For oven 13, respectively 14, using the data from both 13 and 14, as the usages of the two ovens are correlated; -For oven 1, respectively oven 13, collaboratively, as the usages of the two are not correlated. The data mining tool is Rapid Miner because it provides also the libraries with which it can be embedded in any Java software. Therefore it can be used also in real field applications, as this research is meant to be a first step for introducing intelligent features such as predictive maintenance in electronic appliances.

Several algorithms have been used: LPR (local polynomial regression), SVM (support vector machine), NN (neural network) and k-NN (k-nearest neighbour). The results are summarized in Table 2. For avoiding overtraining, 20% of the data was set aside for cross-validation.

The results are summarized in Table 2 for ovens 13 and 14, respectively in Table 3 for ovens 1 and 13. The first column displays the algorithm used, as the ones reported in [START_REF] Matei | Applying data mining in the context of Industrial Internet[END_REF]. The next two columns present the accuracy for each oven in the case of individual data mining. The last two columns present the accuracies for predicting the number of openings for each oven when applying collaborative data mining.

When the usage patterns of the ovens are correlated (see ovens 13 and 14, summarized in Table 2), the collaborative data mining got the best results (highest accuracies). In one case, the stand-alone and collaborative approaches had the same accuracy for oven 13 (in the case of SVM). For oven 14, in two cases the results were not improved by collaborative data mining (algorithms SVM and NN). However, the average accuracies for collaborative data mining are better. The second researched case is of collaborative data mining when there is a very low correlation between two ovens, in this case, ovens 1 and 13, with the correlation factor of 0.01. The experimental conditions are similar with the previous benchmark. In this case, the collaborative accuracies are lower than stand-alone ones with 8.91% for the oven 1, respectively 1.4% for oven 13 (see Table 3). The improvements in accuracy of collaborative data mining has proven reasonable, but including context information, such as outside temperature and number of users could increase the accuracy even more. However, this kind of data is not available for now.

5

Conclusions and Discussions

We have shown that collaborative data mining means the use of data from two different data sources for determining the output of one source (in this case home appliances, but the specific embodiment of the source has no significance). We have proven that if the two sources are correlated, the accuracy of the data mining or machine learning process increases, whereas if the two sources are not correlated, the accuracy decreases. Eventually this could lead to predicting the output of a source using only the data from another, correlated source when the data from the former one is not available.

The main challenge of this work is dealing with information collecting from distributed system which would be recognized as Collaborative network. This information provided by real business cases from Electrolux using intelligent products. We have proven that there are varying similarities between usage patterns of the 143 electric appliances (refrigerators and ovens) in the field, studied in our research. Of course, those similarities influence the impact on the data mining results. This is why the average values displayed in Table 2 are quasi-equal, but the best values are significantly better in the case of collaborative data mining. Of course, those values are obtained when the data mining process takes into account devices with similar usage patterns.

This concept of "collaborative data mining", can be applied in any case when there are more devices with similar behavior which could be ideal tool dealing with huge amount of information in intelligent Products Ecosystem. Therefore, before using it, a correlation analysis must be performed. Such approach fits very well in the context of Industrial Internet (see also [START_REF] Di Orio | A Platform to Support the Product Servitization[END_REF]), where the number of machines are relatively low, but with similar behavior. This could help to analyze distributed information from intelligent collaborative products.

Further Developments and Extensions

It is beyond the scope of this paper to research what is the (mathematical) relationship between the accuracies in the collaborative data mining and the series correlations described in Section 5.

Further research needs to be carried out on collaborative data mining with at least three devices, with various correlations. Another topic is how a series alone influences another series, relatively to the correlation factor. And yet, how can be handled the common case when the two series are not aligned temporarily.

As principle, collaborative data mining can be applied in any field, with any data arguments. However, the heuristics are obviously specific for each case, as well as the tuning of the parameters of the machine learning algorithm. Also extending the proposed methodology for analyzing the behavior of HACs could be interesting direction for future researches. Finally, from a more technical point of view further research is needed on identify a common representation for the data coming from the collaborative agents. As a matter of fact, as the number of collaborative agents are increasing more and more it is necessary to find a common way to represent the data in order to allow the data mining process to analyze get the data always in the same way, i.e. with the same syntax and semantic. It is a necessary issue that need to be considered and handled whenever new type of agents are considered and new context of application are studied.

Fig. 1 .

 1 Fig. 1. Proposed collaborative data mining model flowchart

Table 1 .

 1 Some samples of the data set in the case of collaborative data mining

		Analyzed Device				Similar device		Out-come
	Time-stamp	DW	Date	Hr	Door_ Close	Time-stamp	DW	Date	Hr	Door_ Close
	15.11.2013 00:28	6	15.11.2013	0	T	15.11.2013 00:49	6	15.11.2013	0	T
	15.11.2013 00:28	6	15.11.2013	0	F	15.11.2013 00:49	6	15.11.2013	0	F
	15.11.2013 01:11	6	15.11.2013	1	T	15.11.2013 02:15	6	15.11.2013	2	T
	15.11.2013 01:11	6	15.11.2013	1	F	15.11.2013 02:15	6	15.11.2013	2	F
	15.11.2013 01:40	6	15.11.2013	1	T	15.11.2013 02:45	6	15.11.2013	2	T
	15.11.2013 01:41	6	15.11.2013	1	F	15.11.2013 02:45	6	15.11.2013	2	F
	15.11.2013 01:44	6	15.11.2013	1	T	15.11.2013 03:18	6	15.11.2013	3	T

Table 2 .

 2 The accuracies for stand-alone, respectively collaborative data mining of ovens 13 and 14 (highly correlated in terms of usage patterns)

	Algorithm	Window	Oven 13	Oven 14	Oven 13 collabo-	Oven 14 collabo-
		size	alone	alone	rative	rative
	LPR	3	81.5%	91.3%	80.0%	92.0%
	SVM	5	91.3%	95.7%	91.3%	95.7%
	NN	1	46.2%	51.9%	48.1%	51.9%
	k-NN	3	80.4%	96.0%	92.6%	96.2%
	Average		74.85%	83.73%	78%	83.95%
	Improvement				4.21%	0.27%

Table 3 .

 3 The accuracies for stand-alone, respectively collaborative data mining of ovens 1 and 13 (loosely correlated in terms of usage patterns)

	Algorithm	Window	Oven 1	Oven 13	Oven 1 collabora-	Oven 13 collabora-
		size	alone	alone	tive	tive
	LPR	3	48.1%	81.5%	32.0%	70.6%
	SVM	5	81.5%	91.3%	91.3%	91.3%
	NN	1	18.5%	46.2%	14.8%	48.1%
	k-NN	3	36.0%	80.4%	29.6%	85.2%
	Average		46.03%	74.85%	41.93%	78%
	Improvement				-8.91%	-1.4%

https://www.proseco-project.eu

Acknowledgments. This work is partly supported by the ProSEco project of EU's 7th FP, under the grant agreement no. NMP-2013 609143.


Hanzel Grillo
email: grillo7@gmail.com

M M E Alemany

A Ortiz

Modelling Pricing Policy based on Shelf-life of Non Homogeneous Available-To-Promise in Fruit Supply Chains

Keywords: Order-promising process, Available-To-Promise, Lack of Homogeneity in the Product, fruit supply chain, perishability

Fruit Supply Chains (SCs) are influenced by uncontrollable natural factors causing heterogeneity in their products, as regards certain attributes that are relevant to customers and vary over time because of the shelf-life. As a consequence customers should be served not only with the required quantity and due date as usual, but also with the quality, freshness and homogeneity specified in their orders. The order promising process (OPP) is based on the uncommitted availability of homogeneous product quantities in planned lots (ATP) that are uncertain. Therefore, there is a risk of not being reliable in the commitments because of discrepancies between the real and planned homogeneous quantities. Furthermore, due to the shelflife (SL), serving customers with the freshest product introduce the risk of increasing waste because of the aging process. To efficiently manage these risks, this work proposes a mathematical model for handling the heterogeneous ATP in fruit SCs and a pricing policy based on the product SL in the moment of delivery. In order to illustrate the application of the modelling approach, a short numerical example is introduced. The example evidences a conflictive situation when optimizing the assignation of homogeneous ATP between serving orders with fresh and more valuable product, what could lead to increase the risk of having waste because of expiration, and consequently, more costs and less profit.

Introduction

The order promising process (OPP) presents especial features and more complexity in fruit supply chains (SCs), where uncontrollable natural factors like weather, land, water drought, etc. are present. That kind of factors can confer heterogeneity to units of the same product as regards certain attributes relevant to customers. Additionally, due to the perishability, products are not just affected by the non homogeneity but also for the aging process. The order proposals of these SCs require homogeneity in units of the same product, and normally, customers expect to be served with the freshest product, with the quality required, but with a reasonable price. For this reason, the pricing policy can be directly based on the status of the product at the time of delivery. These aspects become a problem when customer orders are promised based on future planned homogeneous quantities; because final characteristics are not known certainly until the product is harvested, classified, packed and transported to the customer. Then, fruit supply chains has inherent uncertainty in the handling of the available to promise (ATP) quantities, due to not just the homogeneity in the product, but also to the shelf life (SL). One of the main challenges when modelling the OPP in fruit SCs, is firstly to estimate the homogeneous ATP quantities derived from the master plan in advanced to be produced and classified. Secondly, due to perishability, those homogeneous ATP quantities deteriorate over time being necessary to provide traceability. Thirdly, the harvesting time and SL, become critically important in terms of the freshness of the product in the moment of delivery. Consequently, it also affects earns obtained, in case the pricing policy is directly linked with the product freshness. Therefore, the main contribution of this paper is to include these challenges combined into the OPP for fruit SCs. To properly handle them, a mathematical programming model for supporting the OPP has been formulated that takes into account the homogeneity required in the ATP, the dynamism conferred to it by the SL and a proper pricing policy linked to the perishability of the product.

The rest of the paper is organized as follows: Section 2 presents a short summary of the related work founded. Section 3 and 4 describes the proposed way to model the ATP in fruit SCs and the modelling of the SL, respectively. Section 5 presents the link assumed between the remaining SL and the pricing policy for the ATP. Section 6 presents a numerical example to show the conflict when freshness and benefit are both them combined for being optimized. Finally, Section 6 presents the main conclusions and future research lines.

Related Work

This work aims to introduce less investigated characteristics in the OPP, such as the homogeneous ATP quantities and their perishability in fruit SCs. The homogeneous ATP concept is included in the so called lack of homogeneity in the product (LHP). LHP is defined as the absence of uniformity among units of the same product, that can originate from the incorporation of raw materials directly derived from nature, and/or production processes features that confer heterogeneity to it [START_REF] Alarcon | The lack of homogeneity in the product (LHP) in the ceramic tile industry and its impact on the reallocation of inventories[END_REF][START_REF] Alemany | Available-To-Promise modeling for multi-plant manufacturing characterized by lack of homogeneity in the product: An illustration of a ceramic case[END_REF], 2015), [START_REF] Mundi | Fuzzy sets to model master production effectively in Make to Stock companies with Lack of Homogeneity in the Product[END_REF] and [START_REF] Grillo | A review of mathematical models for supporting the order promising process under Lack of Homogeneity in Product and other sources of uncertainty[END_REF]. Improper management of non-homogeneous units of the same product and its inherent uncertainty can impact very negative on customer service level. It is established that, due to inherent LHP uncertainty, the planned size of homogeneous sublots and the real ones can differ once produced and classified into subtypes. A variety of other studies, like [START_REF] Lin | A model for batch available-to-promise in order fulfillment processes for TFT-LCD production chains[END_REF], have dealt with some characteristics related with the LHP without explicitly mention it. In the specific case of fruit SCs, the lack of literature is even more evident, being [START_REF] Kilic | Order acceptance in food processing systems with random raw material requirements[END_REF] the closest case validated in the food processing sector. In this paper, the main LHP characteristic appear randomly in raw materials with a strong effect over the finished product. The perishability (SL consuming) is identified as one of LHP types [START_REF] Grillo | A review of mathematical models for supporting the order promising process under Lack of Homogeneity in Product and other sources of uncertainty[END_REF], and as a cause of conflictive decisions in order to either maximise the incomes by sells of the product, or minimise the cost as a consequence of avoiding waste. Since customers require homogeneous and fresh products, they hope the price is directly linked on its quality, homogeneity and its freshness (that can be measured as a fraction of consumption of its maximum SL). This is also a lacking area of research because of only a few models have dealt with pricing of perishables (see for example [START_REF] Maihami | Optimizing the pricing and replenishment policy for noninstantaneous deteriorating items with stochastic demand and promotional efforts[END_REF] and [START_REF] Tsao | Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments[END_REF]). Furthermore no one makes it under LHP conditions. The findings from the literature, that serve as a basis for the main contribution of this work could be summarised as follows: (i) when dealing with perishables, there is a lack of literature dealing with OPP in LHP contexts that consider the splitting of ATP into homogeneous quantities; (ii) since customers of fruit SCs specify the subtypes required in their orders, it is necessary to estimate not only the homogeneous ATP quantities, but also the subtype obtained to accomplish with customer requirements; (iii) existing OPP models for fruit SCs do not calculate the remaining SL of homogeneous ATP quantities, in a way that the selling price could be linked to it. The above issues confer specific characteristics to the OPP that in case of not being correctly managed could originate: a) dissatisfaction of customers due to the failure in the freshness desired, and b) even more, high stocks and waste that produces SC inefficacy and loss of profit.

In the next sections the proposed way to characterise homogeneous ATP in fruit SCs is presented, followed by the proposed calculation of the SL. Finally, the combination of both is made to properly model the pricing policy for the homogeneous ATP, based on the SL of the product.

Modelling the Homogeneous Available-To-Promise for Fruit Supply Chains

With the aim of serving customers in the homogeneity terms required in their orders, fruit supply chains are forced to include different classification steps along the productive process [START_REF] Blanco | Operations management of a packaging plant in the fruit industry[END_REF]. Therefore, fruit is sorted into homogeneous sublots based on the following characteristics and/or attributes: (i)Variety: it represents the types of the same fruit; (ii) Quality: the product can be classified into quality categories, according to the status it brings from the fields; (iii) Calibre: this criteria refers to the size and volume of the product; (iv) Packaging type: it refers to the different boxing classes that the product can be commercialized and (v) Harvesting time: it represents the time period at which the fruit is collected from fields. Since each of this characteristic can have different values, the specific combination of each attribute can define what is known as a "subtype". Since these attributes can vary with the specific type of fruit, it will be always possible to define the different subtypes as a combination of them. In order to model the homogeneous Available-To-Promise in this kind of SCs, let us define the following nomenclature: If a multi-plant production stage should serve different customers with the subtype specified in their orders on a required due date, and where the supply stage is taking into account the inclusion of the product's harvesting time, the first step to be done is ensuring a reliable calculation of homogeneous ATP quantities of each subtype. Since ATP quantities are derived from the subdivision of the master plan, through the fraction corresponding to each homogeneous subtype, and subtracting the requested quantity in the proposals that might be committed beforehand and the quantity promised to the incoming order proposals; this can be represented through Eq. ( 1):

b i, t, h, p, Y rq acq β mps = atp ophtr ib o r o ib pht ib pt ib pht i pht ib ∀ ∑ ∑ - - (1)
In order to ensure that that the ATP defined in Eq. ( 1) can be served just from the specific subtype required by the customer, and that different subtypes cannot be mixed the Eq.(2) must be considered:

i r, t, h, p, o, , = Y b ophtr ib ∀ 1 ∑ (2)
As it can be seen in Eqs. ( 1)-( 2), the variable ophtr ib Y depends on the price range inside the order proposal might be served. As a novel approach, we are connecting the price range of the served orders with the product SL at delivery time. In sections 4 and 5 we will introduce the concepts and explain how to model this approach.

Modelling the Shelf-life

One strategic issue on modelling the ATP for fruit supply chains is the perishability. This factor makes ATP characteristics of each subtype defined in Eq. ( 1) to change over time while the SL is consuming. If we assume that the SL is pre-defined for each subtype, the freshness of products committed with customers will depend on the remaining SL in the moment of delivery to customer. To maintain a traceability of the remaining SL is necessary in fruit SC for different reasons: 1) customer satisfaction is strongly influenced by the freshness of the product, 2) in case the freshness will be lower than expected, a discount in the price can restore a proper level of customer satisfaction, and finally, 3) because of the perishability, product waste should occur if its SL is exhausted and it has not been assigned to any customer order. Therefore, to mathematically describe the relationship of homogeneous ATP with its selling price, it is necessary to first calculate the SL. When reserving homogeneous ATP in a specific time period, to be delivered in the customer's place on a due date ( o dd ), the SC must take into account the time required for transporting the product from the harvesting point to the packing plants where the classifications and packing operations take place, as well as the transporting time since the product is shipped from the plant until it is delivered to the customer. This is necessary to deliver the product with the minimum portion of its SL ( ib sl ) already consumed. In terms of calculation, we can define the fraction of already lost SL ( o LSL ), of the ATP in the moment of the delivery to the customer as follows:

( ) o , sl Y h dd = LSL r t, h, p, b i, ib ophtr ib o o ∀ ∑ ∑         - (3)
Where o dd is the due date expected for the order proposal o. Consequently, the remaining shelf life ( o RSL ) as:

o , LSL = RSL o o ∀ 1- (4)
Figure 1 shows a short example about the way of calculate Eqs.( 3) and (4).

Shelf life handling

t = 1 t = 3 t = 6 t = 9
Reserving date (assigning some ATP to the order o)

Shipment date (sd).

The product is sent to the customer.

Delivery date (dd).

The product is finally delivered to the customer.

Harvesting time (h) of the ATP Maximum shelf life (sl) of the ATP.

t = 15

Already lost shelf life (LSL) % Remaining shelf life (RSL)

LSL= (dd-h ) sl = (9-1) 15 = 53.3% RSL = 1-LSL= 1-0.533 = 46.7%
Fig. 1 Example of shelf life calculation

Shelf Life-based Pricing Policy

It is usual in fruit SCs that products maintain their initial classification over time once classified and packed. This means that no quality level changes are considered. Instead, the selling price of the product is adjusted according to the aging process until the delivery date. This adjustment is made on a discrete basis, where prices are set based on predefined remaining SL intervals. 2), where there are three price ranges of the ATP based on three predefined limits of the already lost shelf life (ms), and a fourth limit where the product is considered waste. Then, if the product has not overpass the first limit of the price range 1 (ms1), the selling price applied will be the highest one.

With time passing the product gradually loses part of its SL until reaching the second limit. When overpassing this second limit, the selling price applied should be the second one and so on, until the product becomes waste. Therefore, the SL-based pricing policy for the assignation of homogeneous ATP should include as minimum, the following components: (  )

o , sl Y h dd = LSL r t, h, p, b i, ib ophtr ib o o ∀ ∑ ∑           - (6) r o, , Y ms LSL b i, t, h, p, ophtr ib r o ∀ 1 ∑ - ≤ - (7) nr < r o, , Y LSL ms + r = r b, i, t, h, p, ophtr ib o r ∀ 1 1 ∑ - ≤ - (8) nr = r o, , LSL ms o r ∀ ≥ (9)
In the above model, Eq. ( 5) aims to maximise the total sells of the product. Eqs. ( 1) and ( 2) specify the computation of the available to promise, while Eq. ( 6) calculates the remaining SL for the product used to fulfill each specific incoming order. Eqs. ( 7) and ( 8) oblige the binary variable to set just one price range for the subtype of product used to fulfil each specific order. Finally, Eq. ( 9) establishes that product used to fulfil orders cannot exceed the last price range, otherwise it becomes waste.

Numerical Example

The objective of the numerical example presented in this section is twofold. On one hand, it is shown the utility of the above equations for computing the incomes in case the product price depends on the product's freshness. On the other hand, it is shown that only maximizing incomes through serving customers with the most fresh product at the best price, presents the risk of increasing the waste. This could make impossible to serve future incoming orders. Let us assume the case of one packing plant that has to process four production lots of just one fruit (master plan) during the planning horizon composed by eight periods of time. Each lot is classified into 3 subtypes (b1, b2, b3) according to the pt ib β parameter (Table 1). At the beginning of the OPP, we assume that no order has been already committed. Suppose a maximum shelf life of 5 periods for all subtype, a pricing policy with 3 ranges (Table 2) and cost of 5€ per unit of product expired. Based on the harvesting time, the SL, the last price range, and Eq. ( 4), it is possible to compute the period at which each lot becomes waste (Table 1). This means that the ATP quantities derived from each lot may only be used to serve orders with a due date before the period at which it expires. Furthermore, due to customer homogeneity requirements, it is not possible to accumulate discrete ATP to serve the same order (Eqs. ( 1)-( 2)). Suppose the sequential arrival of five customer order proposals requesting certain quantities of subtype b1 for different due dates. It is our aim to analyse the results of committing these orders on-line under two different policies: a) to serve orders with the freshest product (Table 3), that is equivalent to sell the product at the highest price range and b) to serve orders with the less fresh product (Table 4). To implement the first policy, it is necessary to reserve the product from the ATP quantity as near as possible from the due date of the order. The column "Lot" in tables 3 and 4, show the value of the lot in which the corresponding variable ophtr ib Y should have a value of 1. The huge issue in fruit supply chains is that the effect of the non homogeneous product combined with the perishability, brings out an enormous risk of having waste (since the remains of the ATP cannot be mixed in order to have more quantity to fulfill new orders). As it can be seen in Table 3, the first policy maximizes the incomes per order but at the same time presents two important drawbacks. First, it is not possible to serve the last order because there is not enough unexpired homogeneous product. Second, if we assume that no more orders arrive during the planning horizon, the remaining ATP of periods 1 and 4 will expire in periods 5 and 7, respectively. Consequently, this first policy originates a negligible waste of 300 units with a total cost of €1.500. On the contrary, in order to implement the second policy it is necessary to reserve product from the ATP as far as possible from the due date, but without being expired (Table 4). Through this second policy, it is possible to serve all customer order proposals. Although the incomes per sales are lower as compared with the first policy, the total profit is higher for the second policy because the waste is considerably reduced (only 20 units for a total cost of €100). Then, there is a conflictive situation when deciding on the best balance between being careful in sell out the product as it is near to the maximum shelf life, knowing that it implies to lose a portion of profit, and achieving higher incomes by selling more fresh product but with the risk of not being able to serve some future orders and having more waste. This conflictive decision (due to the LHP, the perishability, and the expected selling prices linked with the shelf life), and the uncertainty involved in its solution, are important issues during the OPP optimization in fruit supply chains.

Conclusion

To better analyse fruit supply chains and the corresponding order promising process, it is needed to consider the non homogeneity in the product as an inherent characteristic from nature. Subdivision of the ATP into homogeneous sublots has to be performed. Another factor is the perishability that makes even more complicated the analysis because of the risk of having wasted product. Since the customer normally need fresher product, then the pricing policy can be adjusted to the shelf life. This paper describes an approach for modelling the splitting of the ATP into homogeneous sublots can be done, how to calculate the shelf life of the product at the moment of delivery, and based on that, an expected selling price. A numerical example shows a strong conflictive situation when the OPP must decide between the prioritization between profit (as a balance of sells income and waste cost) and the customer service (as a requirement of always have fresh and homogeneous product).

To better analyse this conflictive situation, uncertainty methods could be used in future research work.

  pt ib β Homogeneity coefficients that represent the fraction of each lot of product i of subtype b. Their sum should equal to 1 (

  pht ib atp Planned homogeneous available-to-promise quantity of subtype b of product i, harvested during time h that becomes available during period t. o ib rq Requested quantity of finished subtype b, of product i, in order proposal o. pht ib acq Already committed quantity from each homogeneous sublot at the beginning of the horizon. Variables ophtr ib Y Binary variable with a value of 1 if requested quantity oz ib rq is completely served by the pht ib atp within price range r, and a value of 0 otherwise. pht ib UATP The updated homogeneous pht ib atp after taking into account the customer order proposals committed.

Fig. 2

 2 Fig.2 Pricing policy schema Let us consider the example in Figure (2), where there are three price ranges of the ATP based on three predefined limits of the already lost shelf life (ms), and a fourth limit where the product is considered waste. Then, if the product has not overpass the first limit of the price range 1 (ms1), the selling price applied will be the highest one. With time passing the product gradually loses part of its SL until reaching the second limit. When overpassing this second limit, the selling price applied should be the second one and so on, until the product becomes waste. Therefore, the SL-based pricing policy for the assignation of homogeneous ATP should include as minimum, the following components:

  price range level r. These percentages are defined when the price of ATP lowers from lower ranges to higher ones. r ib sp Selling price of product i, belonging to the subtype b, according to price range r.

  Production plant. t Time buckets. h Harvesting time of the product available to promise. i The product. b Subtypes, defined as the combination of quality, calibre and packaging type. o Customer order proposals waiting to be promised. r Price range defined based on the shelf life.Master plan schedule of plant p, harvested in h, and available in period t.

	Parameters
	pht i mps

Indices p

Table 1 .

 1 Input data

						Period (t)
			1	2	3	4	5	6	7	8
	Master plan (	) pht mps i	350			500		400	200
	β ib pt	b1 b2	0,5 0,3			0,6 0,3		0,4 0,3	0,7 0,2
		b3	0,2			0,1		0,3	0,1
	atp ib pht	b1 b2 b3	175 105 70			300 150 50		160 120 120	140 40 20
	Harvesting time (h)	1			3		5	8
	Period of becoming waste	5			7		9	12

Table 2 .

 2 Selling price based on price ranges.

	Price Range	Subtype	ms r	€/unit sp ib r
	r1	b1	0,3	10 €
	r2	b1	0,6	8 €
	r3	b1	0,8	5 €

Table 3 .

 3 Serving orders from the freshest product (highest price range/Last-In-First-Out)

									UATP ib pht
	Order	Subtype Quantity Due date Lot(	Y ib ophtr	) Lost Shelf Life (	) Price range LSL o	1	4	6	8	Selling income
	1	b1	100	8	8	0,0%	r1	175 300 160 40	1.000 €
	2	b1	125	5	4	40,0%	r2	175 175 160 40	1.000 €
	3	b1	150	6	6	20,0%	r1	175 175 10 40	1.500 €		Waste
	4 5	b1 b1	50 130	4 7	4	20,0%	r1	175 125 10 40 175 125 10 40	500 €	5 175	7 125	Total 300	Total Profit
				Total			175 125 10 40	4.000 €	875 € 625 € 1.500 €	2.500 €

Table 4 .

 4 Serving order from the less fresh product (lowest price range/First-In-First-Out)

									UATP ib pht
	Order	Subtype Quantity Due date Lot(	Y ib ophtr	) Lost Shelf Life (	) Price range LSL o	1	4	6	8	Selling income
	1	b1	100	8	6	60,0%	r2	175 300 60 140	800 €
	2	b1	125	5	1	80,0%	r3	50 300 60 140	625 €
	3	b1	150	6	4	60,0%	r2	50 150 60 140	1.200 €		Waste
	4 5	b1 b1	50 130	4 7	1 4	60,0% 80,0%	r2 r3	0 150 60 140 0 20 60 140	400 € 650 €	5 0	7 20	Total 20	Total Profit
				Total			0	20 60 140	3.675 €	0 €	100 € 100 €	3.575 €

Acknowledgement

This research has been supported by the Ministry of Science, Technology and Telecommunications, government of Costa Rica (MICITT), through the program of innovation and human capital for competitiveness (PINN)( PED-019-2015-1).


Ivan Popov
email: ipopov@rmr.tu-darmstadt.de

Alexander Krylatov
email: a.krylatov@spbu.ru

Victor Zakharov
email: v.zaharov@spbu.ru

Integrated Smart Energy System Based on Production-Oriented Consumption

Keywords: demand side management, multi-agent systems, power grids, congestion, load flow. 36 26 15 14 27

Modern power grids are facing a number of challenges, such as everincreasing consumption, development of alternative energy generators, and decentralization of energy markets. Renewable energy sources are strongly weather-dependent and, therefore, cannot provide reliable production profiles. This leads us to the concept of demand side management, where energy users modify their consumption patterns due to the availability of generation capacities. Additionally, power flow distribution should be carefully studied in order to avoid overloads in the grid. In this work, we describe a multi-supplier multiconsumer grid model and formulate a problem of an optimal energy contract assignment with respect to power flow constraints. Though generally energy consumers are selfish, we assume their readiness for collaboration within a smart energy system. We offer a cooperative solution for this problem on the assumption of appropriate coordination between agents. Finally, we provide an example illustrating the applicability of our methods.

Introduction

The structure of power supply has been changing significantly in last two decades. A new vision of power grid structures has appeared due to set of reasons, firstly, such as ever-growing energy consumption and development of alternative energy sources. New requirements for power grid structures with generators of renewable energy exacerbate such a crucial problem in power grid management as imbalance between energy demand and supply. Hence, the power system should turn to the production-oriented consumption that leads us to the idea of demand side management (DSM).

Much work has been done in the field of demand side management and, more specifically, demand response. Basic pricing mechanisms for systems with single supplier and multiple consumers are studied by [START_REF] Mohsenian-Rad | Autonomous demand-side management based on game-theoretic energy consumption scheduling for the future smart grid. Smart Grid[END_REF], [START_REF] Veit | Multiagent coordination for energy consumption scheduling in consumer cooperatives[END_REF]. Distributed generation and storage are considered in [START_REF] Atzeni | Demand-side management via distributed energy generation and storage optimization. Smart Grid[END_REF], [START_REF] Atzeni | Noncooperative and cooperative optimization of distributed energy generation and storage in the demand-side of the smart grid[END_REF]. Coalition formation for local networks is examined in various scenarios in [START_REF] Alam | Cooperative energy exchange for the efficient use of energy and resources in remote communities[END_REF], [START_REF] Mihailescu | Dynamic coalition adaptation for efficient agent-based virtual power plants[END_REF] with use of methods of cooperative game theory. However, the questions of power grid's topology and congestion in transmission lines are not taken into account in these works. In present paper we fill this gap since transmission network is a significant element of any power grid system.

Actually, the question of collaboration in energy market has long been irrelevant, and, in contrast to smart grid consumer collaboration, competitive market forces of power generation, consumption, and transmission have been deeply investigated [START_REF] Chao | A market mechanism for electric power transmission[END_REF], [START_REF] O'neill | A joint energy and transmission rights auction: proposal and properties[END_REF], [START_REF] Dolmatova | Optimal nodal capacity procurement[END_REF]. Nowadays, the newly established circumstances force us to investigate collaborative mechanisms in power consumption. Due to modern technologies, generators and consumers are now able to be integrated spatially in a smart local (nodal) power system. Smart grid power system could guarantee the conditions of optimal nodal demand-side consumption by virtue of the agreement between consumers to collaborate in energy consumption.

In this paper we formulate a model of cooperating consumers in a power network. We show that an integrated smart energy system could reduce overall costs in congested networks with multiple producers. An example of a network with tree structure is considered in order to show the applicability of this idea.

Model Description

In this section, we formulate the power grid model with multiple generators and consumers. Each generator has a production cost function, and it depends on the total amount of energy this generator is assigned to produce. Consumers are price-taking agents with energy demand that they need to meet. Both production and transmission costs are covered by consumers. We now discuss all elements of this model in detail.

Network Structure

Consider a directed connected graph ( )

A , V G =
, where V is a set of nodes and A is a set of arcs. Since energy current in a power grid can flow in either direction of any link, we assume that for any arc ( ) A l , k ∈ there is also an arc ( ) A k , l ∈ . We also claim that only one of these two arcs can be used at the same time (i.e., energy current cannot proceed in both directions of a link simultaneously).

We enumerate nodes in V a specific way, so that set V consists of three subsets: a set of m consumer nodes

{ } m , , V Q K 1 = , a set of n producer nodes { } n m , , m V P + + = K 1
, and a set of all other nodes

{ } V , , n m V O K 1 + + =
. Consumers make bilateral energy contracts with multiple producers in order to meet their energy demands. By 0

≥ ij e
we denote a contract between a consumer

Q V i ∈ and a producer P V j ∈ , and 0
≤ i d is an energy demand of consumer Q V i ∈ . Let us also define { } P ij i V j , e e ∈ =
, consumer i 's contract profile, and

{ } P Q ij V j , V i , e e ∈ ∈ =
, a contract profile of all consumers. Therefore, demand constraints take the following form:

0 1 = + ∑ + + = n m m j ij i e d , Q V i ∈ . ( 1
)
For all other nodes

O P V V k ∪ ∈
, we also define k d :

∑ = = m i ik k e d 1 , P V k ∈ , 0 = k d , O V k ∈ . (2)
Let us call k d an energy input in a node V k ∈ . It is positive in producer nodes, negative in consumer nodes, and equal zero otherwise.

For each producer

P V j ∈
we define a unit production cost

( ) 0 ≥ j j d
α , a function of an energy input j d , the total sum of contracts assigned to this producer. Consumers share production costs proportionally to their contracts, and for a given contract profile e consumer

Q V i ∈ pays to producer P V j ∈
the following price: (

( ) ( )         ⋅ = ⋅ = ∑ = m i ij j ij j j ij ij
Therefore, we can determine the overall production cost of each consumer

Q V i ∈ for a
given contract profile e :

( ) ( ) ∑ ∑ ∑ ∈ = ∈         ⋅ = = P P V j m i ij j ij V j ij i e e e c e c 1 α . ( 4
)

Load Flow

Transmission costs are the second type of expenses covered by consumers. These costs depend on the load flow in a network, and we require to make several further definitions. By power flow 0 ≥ kl f in arc ( ) A l , k ∈ we denote a non-negative value of current flowing in this arc. According to our assumption, kl f and lk f cannot be both positive. A flow profile

( ) { } A l , k , f f kl ∈ =
is a set of flows in all arcs. We assume that each arc ( ) A l , k ∈ charges a transmission fee ( ) kl kl f β that must be shared between consumers using this arc.

In order to determine the transmission cost of consumer i similarly to (4), we need to answer two questions: how does flow profile f depend on contract profile e ? And how should the transmission costs be shared between consumers?

The first question can be answered by applying Kirchhoff's laws to this power grid. Let us denote all neighbours of node k by

( ) { } A l , k | V l W k ∈ ∈ =
. Then the first Kirchhoff's law takes the following form: andk π is a potential in node V k ∈ , we can formulate the second Kirchhoff's law for our model:

k W l lk W l kl d f f k k = -∑ ∑ ∈ ∈ , V k ∈ ∀ . ( 5
) If ( ) kl kl f Θ is a voltage change function for an arc ( ) A l , k ∈ ,
( ) kl kl l k f Θ = -π π , ( ) A l , k ∈ ∀ . ( 6
)
It is well-known that the flow profile can be found as a solution of a non-linear optimization problem (cf. Ch. 2.6 in [START_REF] Patriksson | The traffic assignment problem: models and methods[END_REF]):

( )

( ) ∑ ∫ ∈ Θ A l , k f kl f kl ds s 0 min , (7)
subject to k W l lk W l kl d f f k k = -∑ ∑ ∈ ∈ , V k ∈ ∀ , (8) 0
≥ lk f , ( ) A l , k ∈ ∀ , (9)
where contract profile e defines coefficients { } k d in (8).

By ( )

e f
we denote the solution of problem ( 7)-( 9) for a given e . Mathematical programming formulation of the problem of finding equilibrium currents and voltages in electrical networks is an electrical network analogy of traffic equilibrium problem [START_REF] Patriksson | The traffic assignment problem: models and methods[END_REF], [START_REF] Zakharov | Competitive routing of traffic flows by navigation providers[END_REF], [START_REF] Zakharov | OD-matrix estimation based on plate scanning[END_REF].

The second question is more complicated, since electricity is a homogeneous product, and unlike transportation problems it is not possible to track what portion of energy belongs to which consumer-producer contract. There are different methods used to determine transmission cost pricing, e.g. [START_REF] Bohn | Optimal pricing in electrical networks over space and time[END_REF]. In general case, we define a set of functions ( ) { } e kl i δ that impose the cost sharing rule:

( ) 1 = ∑ ∈ Q V i kl i e δ , ( ) A l , k ∈ ∀ , ( ) 0 ≥ e kl i δ , ( ) A l , k ∈ ∀ , Q V i ∈ ∀ . (10)
According to this rule, one can find transmission cost of consumer

Q V i ∈ charged by arc ( ) A l , k ∈ as follows: ( ) ( ) ( ) ( ) e f e e t kl kl kl i kl i β δ ⋅ = . (11)
Thus, total transmission cost paid by consumer i is

( ) ( ) ( ) ( ) ( ) ( ) ( ) ∑ ∑ ∈ ∈ ⋅ = = A l , k kl kl kl i A l , k kl i i e f e e t e t β δ (12)
We are ready to formulate a network optimization problem for a system of cooperative consumers.

Integrated Smart Energy System

Usually, the participants of energy market are assumed to be selfish and independent, that leads us to a system formulated in terms of competitive games. However, if energy resources are scarce and/or uncontrollable (such as renewable energy generation) it may be more profitable for consumers to cooperate. This section formulates a total cost minimization problem for a power grid with multiple suppliers.

Total Cost Minimization Problem

In order to reduce total costs for energy production and transmission, we need to solve a total cost minimization problem. Let us consider the total cost of all consumers, according to (4), ( 12):

( ) ( ) ( ) ( )= + = ∑ ∈ Q V i i i e t e c e C ( ) ( ) ( ) ( ) = ⋅ +         ⋅ ∑ ∑ ∑ ∑ ∑ ∈ ∈ ∈ ∈ = Q Q P V i A l , k kl kl kl i V i V j m i ij j ij e f e e e β δ α 1 ( ) ( ) ( ) ( ) ( ) ( ) ∑ ∑ ∈ ∈ + ⋅ A l , k kl kl V j j j j e f e d e d P β α . ( 13
)
The minimization problem can be formulated in the following form: subject to (1), ( 2),

( ) ( ) ( ) ( ) ( ) ( ) ∑ ∑ ∈ ∈ + ⋅ A l , k kl kl V j j j
where flow profile ( )

e f
is found as a solution of optimization problem ( 7)-( 9). Note that the solution of constrained optimization problem ( 14), (15) does exist. However, it is not a trivial task to define the uniqueness of the solution in general case. Nevertheless, the properties of a solution could be established via differentiating Lagrangian with respect to ij e and using Kuhn-Tucker conditions. The only thing to be state is that Kuhn-Tucker conditions are necessary and sufficient when product

Consumer Cooperation

There are different ways of fair cost sharing among consumers. Ideas of the cooperative game theory may be applied, such as the concept of Shapley value for a coalition of consumers (see, e.g., [START_REF] Roth | The Shapley value: essays in honor of Lloyd S. Shapley[END_REF]). Another simplified policy to encourage the cooperation between consumers is to share the total cost proportionally to the demand of each consumer:

( ) ( ) e C d e C i i ⋅ = , Q V i ∈ ∀ . (16)
In this case each consumer i minimizes the same function (up to a constant coefficient { } i d .

In the following example we do not consider any specific rule of cost sharing, but rather the possible total cost reduction in the network without cycles.

Example and Simulation Results

This section shows how our methods can be applied to a specific example of a network with tree structure.

Example

Consider a network with 7 nodes that is depicted in Figure 1. There are 3 consumers (red nodes), 3 producers (green nodes) and one intermediate node. Therefore, { } All nodes are located in the same local area except for node 4 that depicts a conventional energy generator, e.g. a power plant. Hence, arc (4, 2) is longer than all other arcs, and transmission costs are higher for this arc.

Since there are no cycles in the network, we only need to check the first Kirchhoff's law [START_REF] Alam | Cooperative energy exchange for the efficient use of energy and resources in remote communities[END_REF]. A flow on each arc is a linear combination of { } ( )

j j j x x µ λ α ε + ⋅ = + 1 , P V j ∈ ∀ , ( ) ζ λ β + ⋅ = 1 x x kl kl , ( ) A l , k ∈ ∀ , (17)
where all coefficients are non-negative. We now solve the problem ( 14), [START_REF] Roth | The Shapley value: essays in honor of Lloyd S. Shapley[END_REF] with specific values of demands { }

Q i V i , d ∈
and coefficients in (17), and evaluate the total cost reduction.

Simulation

Let us assume that consumers have similar demand values, and that the transmission cost in arc (4, 2) is higher due to longer distance, while other five arcs have identical coefficients of transmission function (i.e., ≠ ∀ > a , a λ λ 42 [START_REF] Atzeni | Noncooperative and cooperative optimization of distributed energy generation and storage in the demand-side of the smart grid[END_REF][START_REF] Veit | Multiagent coordination for energy consumption scheduling in consumer cooperatives[END_REF]). We also assign = = ζ ε 0.2. We compute and compare minimal total costs of consumers in two different cases: sin C if each consumer buys energy from a single supplier, and opt C for a case, when consumers distribute their contracts between several producers. 2) (0.001, 0.12) (0.005, 0.1) 15.81 17.21 8.1% -10 -12 -9 0.005 0.001 (0.002, 0.2) (0.001, 0.12) (0.005, 0.1) 5.43 5.5 1.2% -10 -12 -9 0.005 0.001 (0.002, 0.2) (0, 0.12) (0.01, 0) 3.98 4.33 7.9%

It is clear that the cooperative contract distribution reduces the total cost significantly (up to 8 %). However, this reduction strongly depends on the demand values of consumers and cost functions of producers.

Conclusion and Future Work

In this work, we described and studied a collaborative model of local area energy consumption in the presence of multiple producers. We showed that the distribution of power flow can be determined by solving an optimization problem based on Kirchhoff's laws, and we formulated the total cost minimization problem considering the congestion in the network arcs. We also considered an example of a network without cycles and presented promising simulation results. There are several possible

  functions. Generally, one could use most appropriate powerful numerical method for constrained nonlinear optimization[START_REF] Bertsekas | Nonlinear Programming: 2nd Edition[END_REF].

Fig. 1 .

 1 Fig. 1. 7-node network with no cycles

  flow in arcs[START_REF] Veit | Multiagent coordination for energy consumption scheduling in consumer cooperatives[END_REF][START_REF] Alam | Cooperative energy exchange for the efficient use of energy and resources in remote communities[END_REF] and (2, 7) may differ depending on the values { }

  22 -23 0.005 0.001 (0.002, 0.

Table 1 .

 1 Some of simulation results are given.

extensions of this model. First of all, it is crucial to consider a dynamic setting over several periods of time (e.g., 24 hours of a day). Second direction is the investigation of cost sharing techniques.