Antônio Marcos Oliveira Morais

Sérgio Brejão

Pedro Oliveira

Costa Neto

Marcos De Oliveira Morais

Antonio Sérgio Brejão¹

Pedro Luiz De Oliveira

Costa Neto¹

Oliveira Morais

Application of Quality Tools for Process Improvement to Reduce Scrap in an Aluminum Smelter

Keywords: Quality tools, Cause and Effect Diagram, Scrap reduction, Productivity, Process improvement

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

Introduction

Upon market opening and globalization, companies needed to upgrade and become more competitive, being forced to eliminate wastes in the entire production process, so the processes have become more streamlined, accurate and efficient. Such reality was experienced in Brazil as a developing country and became stronger with the phenomenon of globalization and, in the specific case of this nation, with the market opening policy adopted in 1990, during the term of President Fernando Collor de Mello. With the increasing requirements for high quality, an issue raised involving the entire organization and work project, defined as the function of specifying the activities for an individual or group in the organizational environment [START_REF] Richard | Production and operations management -A life cycle approach[END_REF].

Scrap, represented by parts rejected by quality control which are impossible to be reworked, is considered one of the biggest problems in the industry, as it demonstrates the inefficiency of the process. Also, we cannot disregard it or manipulate the numbers so they can be satisfactory; if such problem exists, it should be treated and minimized to the maximum extend possible This article presents a case of process improvement in an aluminum smelter using appropriate techniques, in particular the cause and effect diagram, whose methodology is attributed to Kaoru Ishikawa.

Theoretical background

The advancement in failure minimization for optimization can generate great rewards. For many companies, something that begins as an attempt to minimize a problem gradually evolves and becomes a coordinated effort to develop creative valuable solutions [START_REF] Savitz | A empresa sustentável: o verdadeiro sucesso é lucro com responsabilidade social e ambiental[END_REF].

Obviously all production processes deal with wastes, but they must be measured within standard limits for the production of a particular material. In the event of a product failure, a new set of customer needs arises: how to get service restored and how to be compensated for associated unwanted losses [START_REF] Juran | A qualidade desde o projeto: novos passos para o planejamento da qualidade em produtos e serviços -São Paulo: Cengage Learning[END_REF].

Deming emphasized the importance of product cost, which often does not consider such loss, thus directly affecting the company, burdening the product and passing the value to the customer [START_REF] Deming | a revolução na administração[END_REF].

All people involved in the organization must be aware of the problems and how they impact the company. The overall quality and operational performance planning, as well as its implementation, focuses completely on the needs and development of the entire labor force [START_REF] Paladini | Avaliação estratégica da qualidade -São Paulo[END_REF].

Factors such as manpower, raw materials, customer service, energy, etc. should be considered and evaluated, taking into account the delivery of the final product to the client, having the continuous improvement as an integral part of the quality management system [START_REF] Joseph | Administração da qualidade total: o aperfeiçoamento contínuo; teoria e prática[END_REF]. Regarding labor force, behavioral issues need to be closely linked to production processes for the development of a work design that is associated with the concept of empowerment involving work organization based on team. It occurs when employees that usually have juxtaposed skills collectively perform a specific task and possess high degree of description of how to actually perform the task [START_REF] Slack | Administração da produção[END_REF].

Reducing the cost of production, material and shoddy products increases the contribution margin, taking into account higher profits. The development of a customeroriented operational strategy begins with a corporate strategy that aligns the overall goals of the company with its essential processes.

Observing Figure 1, it is possible to understand the flow of competitive priorities: link between corporate strategy and operational strategy.

Methodology

This article used the action-research methodology, which is a type of empirically-based social research, designed and carried out in close association with an action or with the solution of a collective problem in which researchers and representative participants in the situation or problem are involved in a cooperative or participatory way [START_REF] Turrioni | Pesquisa-ação na Engenharia de Produção[END_REF]. This type of approach may be used in an organization (company or school, for example), in which hierarchy or groups with problematic relationships are present, in order to contribute to the best possible form of problem solving, including the arising of solutions and proposals for actions corresponding to solutions, since they represent the perfect strategy when issues such as how and why are raised, when the researcher has little control over events and when the focus is on contemporary phenomena inserted in some real-life context [START_REF] Thiollent | Metodologia da Pesquisação[END_REF].

This work refers to the description and deepening of knowledge in an industry of aluminum casting under pressure, referring to a particular item labeled as substrate.

After identifying the most relevant nonconformity of the process, the possible causes of non-compliance were mapped using brainstorming tools and Cause and Effect Diagram.

Results and discussion

An analysis conducted in company between February and August 2013 showed a high rate of housing product scrap, directly affecting the client and therefore the organization.

The referred values shown in Figure 2 are related to the production, scrap and scrap percentage. The flow analysis (Figure 3) led to the conclusion that the critical operation of the process generating the waste was the aluminum injection under pressure.

In fact, the five most relevant problems, their respective sections and the percentage of scrap were identified and are shown in Table 1. A Pareto analysis, even if visual, identified porosity as the problem evidenced in the injection section.

The scrap control spreadsheet identifies the number of cavities and the quadrant of the part, facilitating the indication and subsequent analysis of the most critical points of the product. The action focus was porosity, since it corresponds to the highest percentage of rejection. After the completion of data collection, a multidisciplinary team was composed of all the people in charge of all sections involved, in order to work on the existing problems, having porosity as the main focus, since it represents 71% of the problems found in the analyzed parts.

Developing people is not just giving them information so that they improve their knowledge, skills and abilities and become more efficient in what they do; it is above all things giving them basic training so they can develop new attitudes, solutions, ideas, concepts, modify their habits and behaviors and become more effective in what they do. [START_REF] Chiavenato | Teoria da Administração Geral[END_REF] The team used the Ishikawa diagram, shown in Figure 5, to help in the identification of possible causes and their potential effects on porosity, so that direct action on the issue could be taken.

Table 2 of equivalence was used to identify the criticality of the problem, adapted from FMEA 4th edition [START_REF] Aiag | [END_REF]. Equivalence Minor failure, probably will not affect customer's product. During September 2013 and January 2014 the improvement actions, which are not detailed in this article, and follow-up for analysis and verification were performed. After the improvements made in the process, were obtained the results shown in Figure 6. An Aspin-Welch test, as described in [13], applied not strictly regarding the absolute statistical accuracy, has proven, based on the values x1 = 19.81, x2 = 10.24, s 2 1 = 0.931, s 2 2 = 21.783, n1 = 7, n2 = 5, the significant reduction of the percentage of scrap to the level of significance of 1%, with clearance (t4 = 4.516 > t4,1% = 3.747). It is worthwhile to mention that the percentage of rejects after improvement actions are clearly decreasing, certainly due to the monitoring and identification of such improvements, reaching the acceptable level in January 2014.

Figure 1 :

 1 Figure 1: Quality, productivity and competitiveness. Adapted from [8].

Figure 2 :

 2 Figure 2: Material produced versus scrap materialFor the purposes of analysis and to perfectly know the process, a flow chart was made and is shown in Figure3.

Figure 3 :

 3 Figure 3: Flow of the customer order-to-delivery process

Figure 6 :

 6 Figure 6: Result after analyzing and taking action.

Table 2 :

 2 Equivalence of degree of relationship with problem.In the following analysis, the seriousness problem indicators have been associated with the causes identified in Ishikawa diagram, as shown in Table3.

	CAUSE	EFFECT	RELATIONSHIP WITH PROBLEM
	Out-of-spec. parameter	Incorrect adjustment	8
	Pulverization	Affects the filling of cavities	3
	Lack of nitrogen	Poor compaction of material	5
	Machine closure	Leak of material during injection	8
	Oil leak	Low pressure during injection	6
	Water leak	Lack of compression and cold joint	5
	Concentration of release agent	Lack of compression	6
	Lack of air bag	Accumulation of gases inside the cavity	6
	Aluminum temperature	Above specification: generates porosity Below specification: generates cold joint	10 6
	Excess return	Excess sludge, generating gases in raw material	9
	Lack of cleanliness in the bath	Gas accumulated in the bottom of the crucible	8

Table 3 :

 3 Degree of relationship with problemTable4summarizes critically the main steps of aluminum injection that should be checked and the direct actions to be taken to improve the score.

	Cause	Effect	Relatio
			nship
	Aluminum temperature	Above specification: generates porosity	10
	Excess return	Excess sludge, generating gases in the raw material	9
	Lack of cleanliness in the bath	Gas accumulated in the bottom of the crucible	8
	Out-of-spec. parameter	Incorrect adjustment	8
	Machine closure	Leak of material during the injection, lack of compression	8

Table 4 :

 4 Ranking of the most critical issues in degree of relationship with the problem.

Application of quality tools for process improvement to reduce scrap in an aluminum smelter.

Application of quality tools for process improvement to reduce scrap in an aluminum smelter.

-Conclusions

This paper tells as an aimed improvement in process was achieved in an actual industry condition, by using quality tools. To allow such goal, there were some changes in the process under study in relation to labor, process and concepts.

Increased contribution margin can be achieved with the optimization of production processes and a balanced cost reduction strategy that will provide the organization with a better management, thus making it more competitive in the market in which it operates. Furthermore, involving people is crucial for the effective success of the whole process.

There was an effective reduction in scrap, favoring a possible reduction in the price of the item, if necessary, or even a larger effective gain for the company. One should, however, proceed with the analysis so that further improvements are effectively proven.

Problem

Section Percentage The rate established by and acceptable to the company for the section of injection is 5% of scrap, the same value reported in product cost spreadsheet shown in Figure 2. In the period considered, such average percentage was 19.81%.

The authors developed a scrap control, shown in Figure 4, to check and indicate the regions with the highest porosity in the part. The verification worksheet details the part per quadrant and region, facilitating the visualization of the most critical point, thus making the scrap reducing action more effective. In the sheet it is possible to identify the area of the part, its cavity, and the total and produced amounts, as well as the percentage of scrap.


Vincent Cliville
email: vincent.cliville@univ-savoie.fr

Lamia Berrah
email: lamia.berrah@univ-savoie.fr

Laurent Foulloy
email: laurent.foulloy@univ-savoie.fr

Fuzzy Symbolic handling of industrial instantaneous and trend performance expressions

Keywords: Industrial objectives, Instantaneous performance expressions, Trend performance expressions, Visual management, Fuzzy logic. 1

This study subscribes to the performance expression and the control of the achievement of an industrial objective. Temporal trajectory is considered for describing such an achievement, which links the initial instant of the corresponding action plan to the final one. At each milestone, instantaneous and trend performances are expressed. The purpose is thus to simultaneously handle the previous kinds of expression in order to define a meaningful piece of information that takes into account the obtained results along the considered temporal horizon. A rule-based aggregation is retained in this sense. Moreover, according to the visual management principles, symbolic fuzzification and deffuzzification are used, and colored emoticons are proposed in this sense.

INTRODUCTION

This study deals with the simultaneous handling of "instantaneous" performance expressions and "trend" ones, with regards to the achievement of tactical industrial objectives. This achievement can be described by a temporal trajectory. Such a trajectory is defined in coherence with the duration of the execution of the associated action plan. At the initial instant, the objective achievement is planned as being null, while at the final one, it is supposed to be totally achieved, in accordance with the expected value.

In order to control the objective temporal trajectory, milestones are introduced. These milestones generally correspond to the end of sets of actions of the considered action plan, being thus a kind of check point for the decision-maker for reacting with regards to the expressed performances. Rightly, performance expressions are provided by Performance Indicators -PI's -and Performance Measurement Systems -PMS's - [START_REF] Neely | Performance measurement system design: a literature review and research agenda[END_REF], [START_REF] Nudurupati | State of the art literature review on performance measurement[END_REF]. These expressions are the result of comparison mechanisms of the expected objectives with the acquired measures [START_REF] Fortuin | Performance indicators, why, where and how?[END_REF], [START_REF] Berrah | Global vision and performance indicators for an industrial improvement approach[END_REF], [START_REF] Kaplan | The Balanced Scorecard: Measures that drive performances[END_REF]. They are conventionally computed under numeric formats, at each milestone. That is what we can call "instantaneous" expressions. In this work, we look for the definition of a kind of enriched perfor-mance expression that not only handles the instantaneous result but also the trend one, according to the obtained performances until the considered milestone. According to us, such an expression allows the decision-maker to have a more meaningful piece of information about the given objective achievement.

Subscribing to some principles of the visual management [START_REF] Greif | The visual factory, building participation through shared information[END_REF], [START_REF] Platts | Strategy visualisation: knowing, understanding, and formulating[END_REF], [START_REF] Tergan | Knowledge and Information Visualization: Searching for Synergies[END_REF], we choose to describe this enriched performance expression under a symbolic form, namely coloured emoticons. Fuzzy inference mechanisms are used in this sense. Indeed, for the sake of simplicity, graphical representation has been progressively introduced in manufacturing companies during the two last decades. Providing visual pieces of information has been highlighted with the Toyota Production System, namely the Kanban flow control or the 5S management [START_REF] Ohno | Toyota Production System: Beyond Large-scale Production[END_REF], [START_REF] Greif | The visual factory, building participation through shared information[END_REF]. For instance, the last version of the ISO 9000 standard explains how to formalise PI's through ten parameters, and gather them into visual scorecards. The visual representation is based on values, colours, curves, graphics or icons, by also considering trend data (see Fig. 1).

Fig. 1. Example of PI visual representation inspired by the French version of ISO 9000.

Besides, the industrial practice shows that many visual formats are used for expressing performances, such as the emoticons, the traffic lights or the weather symbols. Nevertheless, the association between performance expressions and symbols generally remains implicit, while a systematic formal processing would ensure a commensurate handling. Dealing with this drawback, this article is organised as follows. In Section 2, we present the proposed fuzzy formalism. The developed ideas are illustrated by examples extracted from the case study, which is submitted by a bearings manufacturing company, around the "manufacturing Capacity" action plan. Finally, we conclude by some remarks and prospective investigations.

FUZZY PROCESSING

Case study and background

The bearings manufacturing company being considered works for automotive and aeronautics companies, spatial and several other high-tech activities. One of the most important Original Equipment Manufacturers in Europe, its market shares have continuously grown over the last ten years. The different bearing families are produced in specific plants and the production of a given type of bearing is made in a dedicated line which ensures the whole customer demand. Due to the success of innovative products, the submitted problem has concerned the increase of the capacity of one production line, leading thus the plant manager, who is the tactical decision-maker, to the declaration of an objective of a capacity of 30 000 pieces par week at the end of 2013's last trimester; knowing that the capacity at the beginning of the trimester was 27 000 pieces. Fig. 2 gives the objective trajectory planned in this sense.

Fig. 2. Objective trajectory for the production line capacity

For the control of the objective trajectory, the plant manager has defined weekly milestones. The purpose is based on the idea of providing, at each milestone, meaningful pieces of information with regards to the obtained performance. Moreover, knowing the numerous people involved in this action plan, a visual performance representation is retained. To be more precise, let k be the milestone corresponding to the th k week, 1 to 13 k =

. And let ( ) o k , ( ) m k , ( ) p k and '( ) p k respectively be the objective, the measure, the instantaneous and the trend performance expressions, with regards to the production capacity. The idea developed here is to take advantage of the instantaneous performance behaviour to introduce some kind of weighting by the performance trend. The following processing is proposed.

1 ( ) p k and '( ) p k are fuzzified, into linguistic fuzzy subsets.

( )

p k and '( )

p k are aggregated in ) (k C
by means of a fuzzy rule base.

) (k C

is defuzzified into a coloured emoticon ( ) e k .

Instantaneous and trend performance expression fuzzification

We choose to express the instantaneous performance expression ) (k p by the ratio

) ( ) ( ) ( k o k m k p =
. The performance expression trend is obtained from the backward approximation of the first derivate with a first order accuracy and a period of 4 weeks is

used: ) 4 , min( )) 4 , min( ( ) ( ) ( , 0 k k k p k p k p k - - = ′ > ∀ . ( 1
)
The symbolic fuzzification goes the same way for the two expressions. The symbolic fuzzification of ) (k p denoted ϕ , relies on the fuzzy meaning of the linguistic terms, i.e. the membership function associated with each term [START_REF] Zadeh | Quantitative fuzzy semantics[END_REF]. Let Let the membership functions of these terms, i.e. their fuzzy meaning, be represented in Fig. 3. Using Zadeh's writing for discrete fuzzy subsets [START_REF] Zadeh | Outline of a new approach to the analysis of complex systems and decision processes[END_REF]

Fuzzy meaning for instantaneous expression

Fuzzy meaning for trend expression

Aggregation of the instantaneous and trend performance expressions

In order to aggregate the two linguistic fuzzy subsets representing respectively the instantaneous and trend performances, we choose to use a rule based aggregation. Such a mechanism captures, more easily, various cases. The rule base used in the case study presented here is given in Table 1. The typical cases are expressed as couples of linguistic values, for example (VG, D), where the instantaneous performance is Very Good but its trend is Decreasing. Each typical case is associated with a fuzzy evaluation defined on a set of emoticons 3 L = {☺, , }. Using a fuzzy set of emoticons instead of a unique crisp emoticon provides a more precise way to code the aggregation. For example, assume that for (VG, D), we consider that aggregated evaluation can be characterised as a happy one, i.e. ☺, but may be also a neutral one, i.e. , and certainly more happy than a neutral. This type of smooth natural language description can be captured by expressing that the fuzzy subset 0.7/☺ + 0.3/ is associated with (VG, D), according to Zadeh's conventional description one for discrete fuzzy subsets.

l l l R l B l A l C L l L L l l Τ =⊥ ∈ ∀ × ∈
with ⊥ a t-conorm and T a t-norm. Most often max-min operators are used as t-conorm and t-norm. It was shown in [START_REF] Foulloy | Building a class of fuzzy equivalence relations[END_REF] that other couples of operators can be used. In particular, )

1 , min( ) , ( ], 1 , 0 [ ] 1 , 0 [ , y x y x y x + = ⊥ × ∈ ∀ and y x y x . ) , ( = Τ
preserve Ruspini's fuzzy partitions [START_REF] Ruspini | A new approach to clustering[END_REF] and lead to:

) , , ( ). ( ). ( ) ( , 3 2 1 2 ) , ( 1 3 3 3 2 1 2 1 l l l R l B l A l C L l L L l l ∑ × ∈ = ∈ ∀ . ( 2

2.4

The emoticon-based scorecard

The idea is now to defuzzify the fuzzy subset defined on the set of emoticons into a unique colored emoticon whose smile, makes it easily understandable. Indeed, conventionally, two parameters characterise such an emoticon: its smile, on the one hand, and its colour one the other hand, knowing that there is a kind of equivalence between them . Let C be a fuzzy subset of 3 L , i α the grade of membership and Y y i ∈ a value, respectively associated with each emoticon. The symbolic defuzzification δ is defined by:

∑ ∑ = = i i i i i y C y α α δ . ) ( . (4)
Two symbolic defuzzifications are used at the same time. The first one refers to the intensity of the smile and the second one with the colour of the emoticon. The smile is drawn as part of an ellipsis which is associated with a parameter

] 1 , 1 [- ∈ s . When 1 = s
, the emoticon means full happiness. It means that the value 1 is associated with ☺. In the same way, -1 and 0 are respectively associated with and . Moreover, a "happy" emoticon means a satisfactory situation and the green colour is the conventional one for this type of case. If the colour is defined in the RGB space and each color component is defined in [0, 1], then the vector ]

0 1 0 [ = c
, representing the green colour, is associated with ☺. In the same way, red and yellow colours, i. It is interesting to note that the fuzzy approach makes it quite simple to capture human expertise for the aggregation of the performance and it trend. Nevertheless, the generated information is not trivial and would have been quite complex had it been represented by mathematical equations. Fig. 5 shows this point. It represents the surface of the emoticon parameter s, i.e. the smile intensity, in function with the performance and its trend. The colours of the surface are the emoticon colours.

Illustrations

Figure 6 summarises the instantaneous and trend performance expressions that correspond to the six first weeks of the Capacity action plan. Note that the same scorecard could be refreshed every week until the 13 th week of the year 2013. Then expres-sions are thus fuzzified thanks to the previous ϕ functions. Results , which is an orange colour very close to the red one. It produces the following unhappy emoticon,

. Thus the plant manager builds a scorecard (Fig. 7) which respectively gathers, for a considered week, the objective and measure

)) ( ), ( ( k m k o . On the left hand side of the scorecard, the performance and emoticon trajectories are displayed from the beginning of the action plan. As it can be seen, a strong and quick corrective action must be undertaken to improve the performance.

Conclusion

Taking trend performance expression into account can be seen as an enrichment of the traditional way of instantaneously expressing performances. Moreover, visual management is useful, in industrial improvement processes, to facilitate the decision. In this sense an information processing has been proposed which aggregates the instantaneous and the trend expressions based on fuzzification mechanisms and inference rules. This aggregated piece of information is displayed in the form of emoticons which ensure an easy and common understanding for most people involved in the improvement action plans. The case study is in progress and should give feedback about the interest and the practical difficulties to deploy this visual management in industrial company. Further development of this work concerns the generalisation of this type of visual temporal approach particularly when many objectives have to be simultaneously reached. An extension of this model is also envisaged for the performance analysis of the temporal trajectories being considered as a whole.

1 L 1 L

 11 by the set of linguistic terms = = {Very Good, Good, Medium, Bad}, for short = = {VG, G, M, B}.

  the term Very Good with a degree of 0.85 and by the term Good with a degree of 0.15. The symbolic fuzzification of the trend is a linguistic fuzzy subset of 2 L = {Decreasing, Stable, Increasing}, for short 2 L = {D, S, I}. The membership functions associated with these linguistic terms are given in Fig.3. For example, the performance trend is 41 e. the trend is stable with a small increase.

Fig. 3 .

 3 Fig. 3. Fuzzy meanings of the linguistic terms describing the performance expressions.

  e. vectors [1 0 0] and [1 1 0] are respectively associated with and . For example, given C = 0.95/☺ + 0.05/ + 0/ , we have 95 the left hand side emoticon in Fig. 4. In the same way C = 0/☺ + 0.8/ + 0.2/ produces the right hand side one.

Fig. 4 .

 4 Fig. 4. Examples of generated emoticons.

Fig. 5 .

 5 Fig. 5. : The smiley parameter surface

Fig. 7 .

 7 Fig. 7. Scorecard for the Capacity action plan at the 6 th week

Table 1 .

 1 Fuzzy rule base for the typical cases related to the Capacity action plan

											D										S							I
			VG				0.7/☺ + 0.3/							1/☺						1/☺
			G		0.4/☺ + 0.5/ + 0.1/		0.6/☺ + 0.4/				0.8/☺ + 0.2/
			M				0.5/ + 0.5/							1/							0.5/☺ + 0.5/
			B							1/								0.3/ + 0.7/				0.1/☺ + 0.3/ + 0.6/
	This table is the graph of a fuzzy relation R defined on the Cartesian prod-
	uct	1 L	×	2 L	×	3 L	. Let X be a fuzzy subset of L and	L l ∈ .	) X denotes the grade of (l
	membership of l in X. Let A be a fuzzy subset of 1 L and B be a fuzzy subset of 2 L .
	Thanks to Zadeh's compositional rule of inference [13], the aggregation process is
	represented by a function g such that	C =	g	, ( B A	)	with C being a fuzzy subset of 3 L
	and:		3		3	,	(	3	)	(	1	,	2	)	1	2	(	(	1	),	(	2	),	(	1	,	2	,	3	))

Table 2 :

 2 Instantaneous and trend performance expression for the first six weeks fuzzification of the trend performance expression

	for	ϕ	( p	'	)	are giv-


Tomáš Lojka
email: tomas.lojka@tuke.sk

Iveta Zolotová
email: iveta.zolotova@tuke.sk

Improvement of Human-plant Interactivity via Industrial Cloud-based Supervisory Control and Data Acquisition System

Keywords: Cloud manufacturing, database systems, data storage systems, network-attached storage, SCADA/HMI systems, SOA

Industrial companies look for the best way to be perfectly optimized, failure resistant, how to handle increasing amounts of information, and have more open and reliable union with their customers and suppliers. This paper focuses on the improvement of industry performance through the integration of SCADA/HMI (Supervisory Control and Data Acquisition/Human Machine Interface), SOA (Serviced Oriented Architecture) and cloud computing. This paper's contribution is in a failover and high availability solution for small and medium industry companies. The contribution is based on the integration of the cloud and SCADA/HMI, and contains a developed SOA load balancer for better accessibility to the cloud. This whole solution improves performance, reliability and availability. It is cost-effective and includes a mobile device implementation for controlling and monitoring systems.

Introduction

Industrial companies intend to reduce their operating costs and expenses. Therefore, they need solutions that will help them have full, real-time control over an entire plant [START_REF] Alcaraz | Managing Incidents in Smart Grids à la Cloud[END_REF]. The needed features of such solutions are stability, flexibility, fault-tolerance, high accessible storage of information and good connectivity. This will make every internal and external process more effective, highly available, and cost-effective. The communication interactivity and complexity will be enlarged. One of the recent technological waves, cloud computing, fulfils industrial companies' needs [START_REF] Decandia | Dynamo: amazon's highly available key-value store[END_REF]. Cloud computing brings the option of integration a SCADA/HMI and the cloud [START_REF] Youseff | Toward a Unified Ontology of Cloud Computing[END_REF]. The integration can reduce industrial companies' costs, increase reliability, security and system stability with fail tolerance to industrial companies' systems errors [START_REF] Alcaraz | Managing Incidents in Smart Grids à la Cloud[END_REF]. This leads to "smart" industrial companies like homes in IBM vision [START_REF] Drungilas | Cloud Interconnected Affect Reward based Automation Ambient Comfort Controller[END_REF]. In SDACA/HMI and cloud implantation, local parts of an industrial company's ICS (Information and Control System) are moved out to the cloud. The SCADA/HMI and cloud integration also brings a solution to the increasing demands for the amount of quick, easy and secured access to the information inside industrial companies, where information is important not only for critical control. The amount of information in an ICS increases every year and with new parts in the ICS. Industrial companies struggle with processing and saving large amounts of data and ensuring the security of manufacture information. Industrial companies easily overcome demands of increasing amount of information with hosting a SCADA/HMI (2) in the cloud with using cloud benefits (2) and risks (2.1).

We defined our SCADA/HMI cloud-based solution (3) with a failover SOA (Service Oriented Architecture) and a failover MySQL cluster (4) to reach improvements in performance, reliability and availability, and to find a cost-effective solution with the involved mobile device implementation for controlling and monitoring systems. The solution is aimed at small industrial companies which want to manage their own cloud. This solution was created to fulfil small industrial companies' requirements in a costefficient way [START_REF] Finn | Microsoft Private Cloud Computing Copyright[END_REF]. Moreover, this solution is open enough to supporters and customers, but not publicly open to the internet. In this solution, we chose a SOA and cloud (private, realized with VMware). Service-oriented architecture is also used for communication with mobile clients, and separated load balancer service.

Hosting a SCADA/HMI in the cloud

There are many options how to implement a SCADA/HMI system in the cloud to get all benefits from a cloud-based SCADA/HMI system. A cloud-based SCADA/HMI system provides robust remote access and independency of the client platform. We identified three option how to host a SCADA/HMI in the cloud to reach best contribution for our implementation:  Outside cloud-based SCADA/HMI is situated outside of the cloud, SCADA/HMI is connected to the cloud. Data is transmitted to the cloud and classified [START_REF] Youseff | Toward a Unified Ontology of Cloud Computing[END_REF]. Main purpose is data analysis and easy access to data. Data is mainly stored in the cloud to be always available and secure. Additional reporting and analysis services are implemented in the cloud to increase the efficiency of data acquisition and historization. Clients retrieve data from the cloud [3]  Inside cloud-based SCADA/HMI is running in the cloud and it is connected to the technological layer [START_REF] Decandia | Dynamo: amazon's highly available key-value store[END_REF]. In this solution, cloud applications are remotely connected to the technological layer. Commands are sent to the technological layer and then processed. Data is polled from the technological layer and remotely sent to the cloud.  Inside/Outside cloud-based SCADA/HMI is primarily running outside of the cloud, while some SCADA/HMI application runs in the cloud as well.

In our implementation, we focused on the inside cloud-based SCADA/HMI, which is depicted in Fig. 1. Our purpose was to integrate the benefits of the cloud, such as high availability, virtualization, load balancing, uptime etc. Integration provides multi-use remote access where the SCADA/HMI system is guest in the cloud environment. Hosting a SCADA/HMI in the cloud allows a user to track data with various hardware platforms (smartphones, tablets, notebook and so on).

Big benefit of a cloud-based SCADA/HMI solution is data accessibility. This accessibility ensures stable access to data. Data informational content in ICS is important for decreasing the risks of bad decisions due to no or insufficiently information.

The cloud supports sharing information and increases the speed of accessing manufacture data, also for customers. For example, if a customer (another industrial company) urgently needs to change their production and needs raw materials with other quality, then the industrial company can easily change the requirements of product quality in the supplier's industrial company.

An ICS has internal or external suppliers which maintain, explore and upgrade the ICS. In such situations, it is beneficial for suppliers to have a distributed ICS solution in the cloud due the increased complexity between the supplier and customer.

Another example, the supplier of conveyers can easily reach data about conveyers, analyse them, predict and prevent failures and decrease the downtime in production.

Implementing a SCADA/HMI in the cloud means reaching benefits such as optimization, flexibility, scalability, availability and better cost-efficiency [START_REF] Decandia | Dynamo: amazon's highly available key-value store[END_REF].

On the other hand, connection of the cloud and a SCADA/HMI has negatives as well. These are described in sub-section 2.1.

2.1

Risks of a cloud-based SCADA/HMI

We identified the risks of a cloud base SCADA/HMI implantation. First, the cloud makes a SCADA/HMI system more open. Commands and data in the cloud can be sniffed, modified, spoofed or lost during the communication. Moreover, the connection of a SCADA/HMI and the cloud opens a door into the ICS. The attackers then can access the technological and the SCADA/HMI layer of any ICS.

Integrating a SCADA/HMI into the cloud also has the same risks like a typical cloud realization. Data might be accessible with the same service with different security access for different industrial companies or humans. More specifically, another client has access to the same cloud, and the data is only internally separated. There might be a potential risk. Attackers can find and abuse services or applications running in the cloud.

Applications which run in the cloud might also have direct access to the ICS technological layer. In such a case, it is important to secure the ICS communication, because some protocols in automation are not secured. SCADA/HMI systems regularly use MODBUS/TCP, DNP3, IEC-140 for control and automation [START_REF] Alcaraz | Managing Incidents in Smart Grids à la Cloud[END_REF]. Some protocols lack protection [START_REF] Alcaraz | Secure Management of SCADA Networks[END_REF]. Industrial companies with some insecure communication protocols are more prone to attacks (man-in-the-middle (MiTM) attacks) [START_REF] Yang | Man-in-the-middle attack test-bed investigating cyber-security vulnerabilities in Smart Grid SCADA systems[END_REF].

The cloud offers big benefits for a SCADA/HMI or other layers of the ICS, but its security might not be reliable. The data is not the only thing that is supposed to be encrypted and secured inside the cloud. The connection to the technological layer and other parts of any ICS, which are not usually part of the cloud, require security measures as well. A simple solution for security is separating the data. Data which is important to suppliers or customers might be secured and placed in the cloud. Direct connection to the technological layer is risky. An alternative is creating a hybrid cloud. Another solution might be a gateway to field devices with a special protocol. This gateway creates two separated layers. The first one is for an internal SCADA/HMI part and the other layer is used for the cloud SCADA/HMI part [START_REF] Alcaraz | Managing Incidents in Smart Grids à la Cloud[END_REF].

Analysis of the cloud-based SCADA/HMI Solution and Connectivity in Laboratory Conditions

We implemented an inside cloud-based SCADA/HMI solution using a private cloud and the ICS with the SCADA/HMI system from Wonderware and Rockwell Automation [START_REF] Liguš | Information and control system of traverse and its integration into cybernetic centre[END_REF]. We extended the ICS with cloud benefits, to share information from the SCADA/HMI and MES (Manufacturing Execution Systems) layer and used it in education exercises. Clients can then work with data anywhere and extend their own SCADA/HMI solution with cloud stored data from real technology process. Technological process is without risks and the connection to the field devices is limited. Also, we consider the option if someone unauthorized gets access to the cloud stored data or some students try to do something unauthorized.

To design a cost-effective solution for a small company, and a solution with closed technological, layers we chose to use a private cloud. Another reason was the situation when providers do some changes in their security or service functionality. The SCADA/HMI and another layer of the ICS might be sensitive to such changes, which might endanger processes in the industrial company (for example slowing down query execution). We used our own private cloud solution and with OpenVPN (Open Virtual Private Net) access (for external customers and suppliers) to have better security, be more flexible in customization and see all needed sources for realization.

In our solution for the SCADA/HMI and the cloud implementation, we firstly created a storage place. We implemented a NAS (Network Attached Storage) with a CIFS (Common Internet File System) [START_REF] Pavlík | Supervisory control and data acquisition systems in virtual architecture built via VMware vSphere platform[END_REF]. A NAS is a storage device for VMware virtual machines. This implementation enables HA (High Availability) and gives independence to the SCADA/HMI application from the hardware implementation on the server side. If the physical server fails, another server will be used to continue processing data. Data is not bound to the server but to the data storage. In our solution, we implemented an outside SCADA/HMI cloud solution. This solution can be set in a small industrial company which needs to share large amount of data to their customers, suppliers or internal workers. The solution will be used to share data from the SCADA/HMI layer.

Fig. 2. Improvement of Human-plant Interactivity with better cloud accessibility.

Data storage systems should meet selected requirements (high availability, reliability and others) [START_REF] Decandia | Dynamo: amazon's highly available key-value store[END_REF]. These requirements might be in conflict. For example, availability, scalability and data consistency might be in conflict [START_REF] Alcaraz | Managing Incidents in Smart Grids à la Cloud[END_REF][START_REF] Decandia | Dynamo: amazon's highly available key-value store[END_REF]. In our solution, we used MySQL Cluster [START_REF] Davies | High Availability MySQL Cookbook[END_REF], where we gave more importance to data availability [START_REF] Petersen | Replicated database services for world-wide applications[END_REF].

Not only storing data is important, but also the infrastructure for accessing it. Because we chose the implementation of a private cloud in our experiment, we implemented a service oriented architecture (SOA) in our architecture with a service that retrieves data from the communication server. The communication server communicates with the technological layer of our ICS. The service is also used to saving data to the cloud storage and its retrieval. The service communicates with HMI clients.

Realised Solution in Laboratory

We created and tested solution, in which data is accessible to every client. We chose the database to store data from technological process, but we also chose NFS due to its advantage of quick saving of reports in the cloud. For users are the documents accessible from NAS with the utilities which NAS has. Data is available through MySQL servers, which were realized on virtual machines on an ESXI server from VMware.

Our solution is extended with an application server. The application server is intended to communicate with the technological process, HMI clients and data storage.

The technological layer consists of a laboratory controlled model. The model is controlled by a PLC (Programmable Logic Controller). The application server communicates with the PLC through an OPC server. Data is cached in the application server. If the value of same data changes, a new event occurs. The application server writes (updates/inserts) the data to the database placed behind the application server in the event.

The application server hosts a WCF (Windows Communication Foundation) service. To satisfy the failover requirement, we created a SOA load balancer. This balancer sends client requests to the service. If the balancer fails to communicate with the service or has insufficient low response from the service, it transmits the client request to another service. The balancer has memory where it saves a request after it was successfully sent. In our solution, we used service-oriented architecture (SOA) which is connected to the technological layer and to the data storage and also to the HMI clients. Inside the service, there is an implemented connection to the MySQL database and the HMI clients.

The MySQL database is placed on two independent virtual machines, which are clustered with the storage NAS. It is configured to use raid 10. Both virtual machines have their own MySQL instance and are connected together with a heartbeat connection [START_REF] Davies | High Availability MySQL Cookbook[END_REF].

These servers have one virtual IP address, which is used by the application server and MySQL clients (for example, MySQL report client). Virtual machines run Windows Server 2008 R2, but Linux can be used as well. Data is secured with MySQL security. MySQL data is accessible from every place inside the private network. The MySQL database stores data from the technological layer and critical controls commands from the HMI layer. This data is accessible for every SCADA/HMI application on a device or a PC.

MySQL client is not supported by many SCADA/HMI systems. However, there are libraries which can be implemented to allow the use of MySQL. The access to data ensures tolerance to faults, which is guaranteed with ours created cluster and the heartbeat connection of MySQL [START_REF] Davies | High Availability MySQL Cookbook[END_REF].

Fig. 3. Graphical interpretation of the SOA load balancer

The HMI clients can connect to the service through an installed application or through a website. These clients are used like mobile HMI applications for manufacture operators.

Clients can connect to the NAS (for example, with a web browser) and access files. Clients can use FTP, NFS and SMD protocols. These clients are mainly oriented for downloading created reports, saving and sharing business documents.

The last client type is a client application for a direct connection to the MySQL service.

Conclusions

The main purpose of every industrial company is to build an effective system and reduce its costs. This paper described solutions, benefits and risks of integrating a SCADA/HMI and cloud computing. Our selected solution was introduced as a solution for small industrial companies to store their production data through the SOA service, which is implemented over a realized SCADA/HMI from Wonderware System Platform. The benefit and contribution of this solution is in parallel data processing with a SCADA/HMI and the cloud, which doesn't influence the realized SCADA/HMI system, Others benefits are interactivity of the stored data with report analysis tools, web clients, NFS clients and safety of the data. This solution should increase the stability and speed in communication between an industrial company, customers and suppliers.

Fig. 1 .

 1 Fig. 1. Inside cloud-based SCADA/HMI system with the technological layer, communication server and firewall to protect the access to the technological layer. The SCADA/HMI application runs in the cloud and the cloud clients are connected to the application.

Fig. 4 .

 4 Fig. 4. Mobile web application client for model Magnet

Acknowledgments. This research was funded by a grant (No. 021TUKE-4/2012) from the KEGA (50%) and VEGA -1/0286/11 (50%).


Hugo Lafaye De Micheaux

Christophe Ducottet

Philippe Frey

ONLINE MULTI-MODEL PARTICLE FILTER-BASED TRACKING TO STUDY BEDLOAD TRANSPORT

Keywords: Particle filtering, multi-model tracking, multi-object tracking, detector confidence, bedload transport

Multi-object tracking is a difficult problem underlying many computer vision applications. In this work, we focus on sediment transport experiments in a flow were sediments are represented by spherical calibrated beads. The aim is to track all beads over long time sequences to obtain sediment velocities and concentration. Classical algorithms used in fluid mechanics fail to track the beads over long sequences with a high precision because they incorrectly handle both miss-detections and detector imprecision. Our contribution is to propose a particle filter-based algorithm including an adapted multiple motion model. Additionally, this algorithm integrates several improvements to account for the lack of precision of the detector. The evaluation was made using a test sequence with a dedicated ground-truth. The results show that the method outperforms state-of-the-art concurrent algorithms.

INTRODUCTION

Visual target tracking is a recurrent problem in computer vision, it has been used in many applications, e.g. video surveillance, sports analysis, or traffic safety. In particular, object tracking is used in fluid mechanics to track particles with techniques as PIV [START_REF] Westerweel | Particle image velocimetry for complex and turbulent flows[END_REF] and PTV [START_REF] Ohmi | Particle-tracking velocimetry with new algorithms[END_REF]. We focus here on bedload sediment transport experiments. The aim is to track all spherical beads (see Fig. 1) over a long time to obtain particle velocities and concentrations [START_REF] Frey | Particle velocity and concentration profiles in bedload experiments on a steep slope[END_REF], for studying bedload granular rheology [START_REF] Maurin | A minimal coupled fluid-discrete element model for bedload transport[END_REF], size segregation [START_REF] Bacchi | The effects of kinetic sorting on sediment mobility on steep slopes[END_REF] and associated morphology [START_REF] Recking | Antidunes on steep slopes[END_REF].

In this context, most of the proposed algorithms are deterministic and rely on a standard two step approach: (1) object detection, [START_REF] Ohmi | Particle-tracking velocimetry with new algorithms[END_REF] object tracking by solving a data association problem [START_REF] Hergault | Image processing for the study of bedload transport of two-size spherical particles in a supercritical flow[END_REF]. However, these are not robust enough to track objects over very long sequences with a good precision for object positions. This is mainly because they incorrectly handle miss-detections and do not take into account the lack of precision of the detector. In recent years, particle filter-based approaches have been successfully used in many applications [START_REF] Choset | Topological simultaneous localization and mapping (SLAM): toward exact localization without explicit localization[END_REF][START_REF] Rathi | Tracking deforming objects using particle filtering for geometric active contours[END_REF][START_REF] Lu | Tracking and recognizing actions of multiple hockey players using the boosted particle filter[END_REF]. The main benefit of these methods is to enable the estimation of the distribution of the target's system state incorporating a non linear motion model. In this context, Breitenstein et al. [START_REF] Breitenstein | Online multiperson trackingby-detection from a single, uncalibrated camera[END_REF] proposed a very efficient online multi-target tracking approach accounting for the detector confidence to handle missdetections. However, this method is not directly adapted to our problem mainly because it uses a single motion model unable to describe all occurring object interactions.

In this paper, using the same framework, we propose to introduce a multiple motion model dedicated to our simulation of bedload transport. Each motion model corresponds to a specific state of motion of our objects: resting, rolling or bouncing. We also introduce improvements to correctly handle the lack of precision of the detector providing tracking over long sequences with a high precision for objects position.

The paper is structured as follows. After discussing the related work in next section, Sec. 3 describes our algorithm and design choices. Sec. 4 presents the evaluation results of tracking performances and a comparison with concurrent algorithms. Finally, Sec. 5 concludes the paper.

RELATED WORK

Various visual tracking approaches have been reviewed [START_REF] Smeulders | Visual tracking: An experimental survey[END_REF][START_REF] Wu | Online object tracking: A benchmark[END_REF] and they can be separated in two categories: detection-based methods and Bayesian filtering ones. In fluid mechanics, researchers usually employ the first one, i.e. taking the object detector output as a straight truth and then solving the association problem on pairwise frames [START_REF] Hergault | Image processing for the study of bedload transport of two-size spherical particles in a supercritical flow[END_REF][START_REF] Ouellette | A quantitative study of three-dimensional lagrangian particle tracking algorithms[END_REF]. This deterministic approach lacks precision since it strongly relies on detectors that can be unreliable and imprecise.

Sequential monte carlo methods or particle filters were introduced to provide better estimations and predictions [START_REF] Doucet | Sequential Monte Carlo methods in practice[END_REF][START_REF] Gordon | Novel approach to nonlinear/non-gaussian bayesian state estimation[END_REF][START_REF] Isard | Condensation-conditional density propagation for visual tracking[END_REF]. Basically, they consist of a dynamic model for prediction and an observation model to evaluate the likelihood of a predicted state. The main steps are: random generation of a sample of potential states called particles, propagation of these particles through the motion model and resampling of the distribution according to the observation model. To handle difficult tracking situations in a multi-object context, Breitenstein et al. [START_REF] Breitenstein | Online multiperson trackingby-detection from a single, uncalibrated camera[END_REF] proposed an online and automatic particle filter-based algorithm that exploits the intermediate output of the object detector as a graded observation model. As most particle filter-based algorithms, it relies on a single motion model which can be problematic in an environment with complex dynamics.

To face this limitation, multiple dynamics models such as switching dynamical model approaches [START_REF] Isard | A mixed-state condensation tracker with automatic model-switching[END_REF], have been recently developed under particle filters for robotics and navigation [START_REF] Boers | Interacting multiple model particle filter[END_REF] or video surveillance [START_REF] Zhai | An object-tracking algorithm based on multiple-model particle filtering with state partitioning[END_REF]. These methods use the fact that object motions can be classified in different motion states according to the situation. Each motion state is dealt with specific state evolution model for prediction. However, it requires to know all motion states beforehand with a mathematical description for each. In contrast, our method exploits the mechanistic knowledge we have in our application.

MULTI-OBJECT TRACKING ALGORITHM

Our fully automatic multi-object tracking algorithm uses the same principle as [START_REF] Breitenstein | Online multiperson trackingby-detection from a single, uncalibrated camera[END_REF]. Each trajectory is estimated by an individual particle filter (tracker), automatically initialized when a new object is detected and terminated when the object is leaving the field of view. At each time step we perform: (1) object detection, (2) association of each detection to a tracker, (3) update of the state of each particle filter according to the motion model and the new detection.

Object detector

Black beads are detected by thresholding the image and taking the center of objects having an area close to the mean bead area. As transparent beads appear as faint dark rings of different shapes because of their neighboring beads, we use a specific chain of morphological operations to detect them. We apply a hconvex operator [START_REF] Soille | Morphological image analysis: Principles and Applications[END_REF] on the image, then a normalized cross-correlation with a ring-shape model and finally we keep the relevant maxima using an adjusted threshold. The object detector returns a set of detections D.

To handle missing detections on transparent beads, we use the detector confidence as a graded observation model [START_REF] Breitenstein | Online multiperson trackingby-detection from a single, uncalibrated camera[END_REF]. Based on the raw output of the detector, the detector confidence must give an estimation of the likelihood of a detection at each candidate pixel. In our case, for a given detection d ∈ D, we propose to define the confidence value as a decreasing function of the distance to the detection position x d a maximum equal to the cross-correlation output xcorr(d) of the detector, i.e. the correlation value before thresholding. Formally, for each position x of the image, the detector confidence density d c (x) is defined as:

d c (x) = 1 k D d∈D xcorr(d) exp(-λ x -x d ) (1)
where λ denotes the exponential decay constant (see Sec. 3.4), and k D is the normalization coefficient.

Data association

To assign at most one detection to at most one tracker, a data association process is needed. Due to the high number of detections and the long time series, a greedy algorithm was found to be an effective solution. Given the matching cost c(tr, d) between all tracker-detection pairs, the greedy algorithm iteratively selects the best candidate and removes the corresponding concurrent associations. To limit the number of possible tracker-detection pairs, the set of possible detections associated to a given tracker is limited to the detections located inside a circular region centered at the predicted position x tr given by this tracker. This predicted position is made assuming a constant velocity model. Given a tracker tr and a detection d, the matching cost is:

c(tr, d) = α x d -x tr r s distance term + β |v d | |v max | velocity term (2)
where v d is the measured velocity of detection d1 , the parameters α and β represent the proportion of each term (see Sec. 3.4), and r s is the radius of the circular searching region calculated from the fluid velocity. The distance term promotes the detections closest to the prediction. With the velocity term, we want to promote low velocities as it allows to have better association in case of beads collisions.

Particle filtering

Each tracker is described by a fixed number N of particles, having a state {x p , v p , s p } where x p = (x, y) denotes the position, v p = (u, v) the velocity and s p the motion state. We employ the Sequential Importance Resampling filter, also known as the bootstrap filter [START_REF] Gordon | Novel approach to nonlinear/non-gaussian bayesian state estimation[END_REF], to approximate the probability function. For one target, it works as follows: (1) Estimation of particle states, positions and velocities, (2) Particle importance weighting, (3) Normalization of weights, (4) Resampling, (5) Estimation of final state, position and velocity of the target. The main difference with [START_REF] Breitenstein | Online multiperson trackingby-detection from a single, uncalibrated camera[END_REF], is the use of the velocity estimation of a particle as an observation in the importance weighting.

State model. In motion-based stochastic tracking [START_REF] Odobez | Embedding motion in model-based stochastic tracking[END_REF], explicit motion measurements are used to guide predictions. In our application, beads have different behaviors according to their location, velocity and neighborhood. We can distinguish three distinct motion states: resting (not moving), rolling (rolling/sliding on others) and saltating (bouncing on others). To propagate the particles, we first update their state and then we apply a motion model to update the position and the velocity. To update the state, we draw the new state according to a conditional probability table (see Sec. 3.4). The motion models are:

resting: (x, y) t = (x, y) t-1 + ε rest (x,y) (3a) rolling: (x, y) t = (x, y) t-1 + (u) t-1 ∆t + ε roll (x,y) (3b) (u) t = (u) t-1 + ε roll (u) (3c) saltating: (x, y) t = (x, y) t-1 + (u, v) t-1 ∆t + ε salt (x,y) (3d) (u, v) t = (u, v) t-1 + ε salt (u,v) (3e)
where ε rest (x,y) , ε roll (x,y) , ε salt (x,y) are the process noises on the position and ε roll (u) , ε salt (u,v) are the process noises on the velocity, they are all independently drawn from zero-mean normal distributions ; ∆t depends on the framerate of the sequence.

Particle weighting. The importance weight w tr,p for a particle p of tracker tr is given by the conditional likelihood of the new observation given the propagated particle. Given detection d * associated to the tracker, we have: [START_REF] Maurin | A minimal coupled fluid-discrete element model for bedload transport[END_REF] where I(tr) is an indicator function that returns 1 if a detection is associated to the tracker and 0 otherwise. δ, γ and η are set experimentally (see Sec. 3.4).

w tr,p = I(tr) δp N (x p -x d * ) particle position + γp N (v p -v d * ) particle velocity +ηd c (x p ) det. conf
The particle position (resp. velocity) term calculates the distance between particle position (resp. velocity) and the measured detection position (resp. velocity), and is evaluated under a normal distribution p N . The detector confidence term evaluates the detector confidence density at the particle position.

Resampling and estimating. After the weighting, the resampling is used to solve particle degeneracy, namely removing the particles of small weight and reproducing those of large weights [START_REF] Milstein | Robust global localization using clustered particle filtering[END_REF]. Finally, the position and the velocity are estimated by averaging the resampled particles.

Implementation details

The number of particles N was fixed to N = 100, being a good compromise between computational cost and tracking reliability. The parameters in equations ( 1), ( 2) and ( 4) have been set experimentally and remained the same for the different experiments used in Sec. 4.1. λ was set to 1 in eq. ( 1). In eq. ( 2), α and β were set respectively to 0.75 and 0.25 to give more importance to the distance term. The proportion parameters (δ, γ, η) in eq. ( 4) were fixed at (20, 1, 1). Therefore, when a detection is associated, the particle weight is mainly influenced by its position and also a little by its velocity, to reduce the imprecision of the detection position.

Each motion state in eqs.

(3) has its own variance for the process noise on position and velocity. The initial particle states were set as rolling, and their initial positions and velocities were drawn from a Normal distribution with positions centered at the detection center and velocities centered to null velocity. To handle the difficulty of dealing with new trackers, we increased the variances to make the motion model more flexible during the first 3 frames. A tracker survives only 10 frames without associated detection and is then automatically terminated.

For a given particle, the transition from one state to another is controlled with conditional probabilities. We have estimated these probabilities on a representative training sequence. Concerning the particle velocity at the beginning of a track, the estimation was set to the measured particle velocity (i.e. the displacement between the particle position and the estimated position at previous time step).

RESULTS

In this section, we present the results of the proposed tracking algorithm with three motion models (3MM) (see Sec. 3.3) against two simplified versions using only one motion model: one with a constant velocity model (1CVM) and the other with a null velocity model (1NVM). These simplified versions can be considered as direct adaptations of Breitenstein et al. [START_REF] Breitenstein | Online multiperson trackingby-detection from a single, uncalibrated camera[END_REF] algorithm. The results are compared to a ground truth to have information about the false positives and false negatives. We also use the CLEAR MOT metrics [START_REF] Bernardin | Evaluating multiple object tracking performance: the CLEAR MOT metrics[END_REF] to evaluate the tracking performance.

Experiments and ground truth

We worked on a 1000-frames sequence recorded at 130 fps with approximately 400 beads per frame (about 300 coarse and 100 small beads). The sequence is split in two parts, one for optimizing the parameters, and the other part for evaluation. We created a ground truth on the sequence by selecting manually the detections on each frame. To get the ground truth of trajectories, we applied a simple data association algorithm on the ground truth of detections just created. 98.35% 0.64px 0.07% 0.16% 4 99.77% 1CVM [START_REF] Breitenstein | Online multiperson trackingby-detection from a single, uncalibrated camera[END_REF] 95.05% 0.77px 0.09% 0.17% 23 99.72% 1NVM [START_REF] Breitenstein | Online multiperson trackingby-detection from a single, uncalibrated camera[END_REF] 89.90% 0.89px 0.14% 0.54% 84 99.28% Table 1. Tracking evaluation results for the three algorithm configurations. It shows the percentage of correct tracks (i.e. more than 95% of the track is correct) and the CLEAR MOT metrics [START_REF] Bernardin | Evaluating multiple object tracking performance: the CLEAR MOT metrics[END_REF] such as precision (MOTP), false negative rate (FN), false positive rate (FP), number of mismatches (Id Sw.) and accuracy (MOTA).

Evaluation of the tracking algorithm

In Tab. 1, we present the evaluation of the three tracking algorithms 3MM, 1CVM and 1NVM. The results show that 3MM is always better than the two others. Especially for the percentage of correct tracks (a track is considered as correct on the total length if more than 95% of it has no false negatives or mismatches), the 3MM reaches 98.35%. We also computed the CLEAR MOT metrics to evaluate the precision score MOTP (average error in estimated position) and the accuracy score MOTA (accounts for all object configuration errors made by the tracker, false negatives, false positives and mismatches). Here again, the 3MM appears to be the most precise and accurate.

In Fig. 2, we plotted the precision MOTP of the tracking of transparent beads for each motion state described in Sec. 3.3. The precision depends on the motion states, the higher the velocity (saltating > rolling > resting), the worse the precision. However, our 3MM performs better on each motion state especially on saltation.

In Fig. 3, we varied the threshold of the transparent beads detector in order to see the tracking performance with different levels of detection. It illustrates the influence of this threshold on the percentage of correct tracks and the preci- sion MOTP on transparent beads. Again, 3MM performs better even when the miss detection rate increases due to the increasing threshold.

CONCLUSION

We have presented a new online particle filter algorithm based on multiple dynamic models for automatic multi-object tracking over long sequences. Having a priori information about the object mechanical dynamics, we were able to approach the real trajectories. This allows us to study bedload transport with higher confidence.

Our multiple motion model based algorithm provides a high tracking precision and accuracy when applied on detectors of different quality. Moreover, the approach has been shown to outperform state-of-the-art algorithms presenting a single motion model such as constant or null velocity model.

A possible extension would be to use the state of neighboring objects as an information to help choosing between motion states and bring more estimation precision. Finally, the tracking algorithm could be applied on very long sequences to observe lower frequency phenomena.

Fig. 1 .

 1 Fig. 1. Example of trajectories for two tracked beads (cropped images). Green color is for a coarse black bead and red is for a smaller transparent bead.

Algo

Fig. 2 .

 2 Fig. 2. Precision score MOTP on transparent beads tracking according to motion state (resting, rolling, saltating) for each algorithm model (3MM, 1CVM, 1NVM).

Fig. 3 .

 3 Fig. 3. Evaluation of tracking performance on transparent beads for different detection thresholds. The percentage of correct tracks (bars, left scale) and the precision score MOTP (curves, right scale) are plotted.

The measured velocity v d corresponds to the displacement between the detection position x d and the estimated position at previous time step.

This research is funded by Irstea, labex OSUG@2020 and by the Rhône-Alpes region as part of its Environment Academic Research Community.


Mohamed Ouzineb
email: mohamed.ouzineb@gerad.ca

Fatima-Zahra Mhada
email: f.mhada@um5s.net.ma

Robert Pellerin
email: robert.pellerin@polymtl.ca

Issmail El Hallaoui
email: issmail.el-hallaoui@polymtl.ca

A hybrid method for solving buffer sizing and inspection stations allocation

Keywords: Inspection, Production lines, Quality, Combinatorial Optimization, Meta-heuristics

The buffer sizing problem in unreliable heterogeneous production lines is an important, indeed, complex combinatorial optimization problem with many industrial applications. These applications include quality, logistics and manufacturing production systems. In the formulation of the problem, the system consists of n machines, n fixed-size buffers and m inspection station in series. The objective is to minimize a combined storage and shortage costs, and also specifying the optimal location of inspection stations in the system. The present paper aims at optimizing a generalization of the model previously proposed in (Mhada, Malhamé, & Pellerin, 2014) using a novel approach. In this approach, we combine Tabu Search (TS) and Genetic Algorithm (GA) to identify search regions with promising locations of inspection stations and an exact method to optimize the assignment of buffer sizes for each location. This approach provides a balance between diversification and intensification. Numerical results on test problems from previous research are reported. Using this approach, we can reduce the solution time by more than 97% in some cases.

Introduction

Apart from rare exceptions ( [START_REF] Kim | Integrated quality and quantity modeling of a production line[END_REF][START_REF] Kim | Analysis of long flow lines with quality and operational failures[END_REF], [START_REF] Colledani | Impact of statistical process control (spc) on the performance of production systems-part 2 (large systems)[END_REF], 2006a[START_REF] Colledani | Performance evaluation of production systems monitored by statistical process control and offline inspections[END_REF][START_REF] Colledani | Integrated analysis of quality and production logistics performance in manufacturing lines[END_REF]), the current and standard quality analysis models tend to consider separately the problem of developing strategies for the quality preservation in production lines (positioning stations inspection for example) and the development of strategies to optimize the production problem (kanban, CONWIP, or others). Yet as noted it so well ( [START_REF] Kim | Integrated quality and quantity modeling of a production line[END_REF][START_REF] Kim | Analysis of long flow lines with quality and operational failures[END_REF] and [START_REF] Colledani | Impact of statistical process control (spc) on the performance of production systems-part 2 (large systems)[END_REF], 2006a[START_REF] Colledani | Performance evaluation of production systems monitored by statistical process control and offline inspections[END_REF][START_REF] Colledani | Integrated analysis of quality and production logistics performance in manufacturing lines[END_REF]), both whole decision are interdependent. We illustrate this interdependence through the example of the analysis of kanban strategies introduced by Toyota in the sixties and have since become the paradigm of "lean manufacturing": they essentially advocate areas of limited storage between successive machines in a production line. The objective of these storage areas is to allow certain degree of decoupling between machines to increase productivity of the line (limitation of the effects of parts shortage for downstream machines or blocking machines upstream a broken down one). These stocks should be limited because they are associated with a frozen capital, a storage costs and a parts extended transit times in the workshop. In a "just in time" ideal, there would be no intermediate stock and finished parts would be pulled from the system as they are produced. However, hazards, such machinery breakdowns and lack of raw material or operators, will come to question this idealized vision, unable to ensure a sufficient continuity of the workshop output. The sizes of the storage areas are directly related to the statistics of these hazards, as well as the estimated costs of the service losses that may result. So if, we choose to size the kanban by ignoring totally the production quality dimension in the Please note that the LNCS Editorial assumes that all authors have used the western naming convention, with given names preceding surnames. This determines the structure of the names in the running heads and the author index.

problem, we risk likely to overestimate the security service level with a storage areas which may contain important quantities of defective parts. These defective parts play a negative role for at least two reasons: on one hand they correspond to a misused production line time, since they decrease the efficiency of individual machines; they systematically undermine the "efficiency" of the intermediate storage for its ability to help increase the productivity of the line. On the other hand, as the investments associated with production line come from the same source, the costs associated with storage within the line are going to burden the budget associated with the improvement of the quality and vice versa. [START_REF] Inman | Survey of recent advances on the interface between production system design and quality[END_REF] present a survey of recent advances on the interface between quality and production systems design, they provide evidence that production design impact quality and quality impact production design. Also the location of the inspection station affects both the expected production cost per item and the production rate of the line. They are many research (see [START_REF] Mandroli | A survey of inspection strategy and sensor distribution studies in discrete-part manufacturing processes[END_REF]) that focus in determining the optimal inspection station position in n serial production lines with or without: i) scrapping, ii) rework, iii) off-line repair, without considering the concept of buffer sizing. Like the work of [START_REF] Kim | Integrated quality and quantity modeling of a production line[END_REF][START_REF] Kim | Analysis of long flow lines with quality and operational failures[END_REF], we propose to work with a continuous production models (fluid models). However, the analogy with [START_REF] Kim | Integrated quality and quantity modeling of a production line[END_REF][START_REF] Kim | Analysis of long flow lines with quality and operational failures[END_REF] stops there. In [START_REF] Kim | Integrated quality and quantity modeling of a production line[END_REF][START_REF] Kim | Analysis of long flow lines with quality and operational failures[END_REF], although the models are continuous, quality, remains attached to a discrete part and we see this as a potential source of contradictions in the modeling. In our case, we consider a tandem machines where every machine has to satisfy a demand rate of good parts per time unit. We consider the problem of sizing the inventory level taking into account that the stock is mix of good and defective parts; we assume at first all outstanding in the production line continuously observed. Here, the modeling becomes more complex given that there is generally elimination of defective parts along the line by positioning a number of inspection stations. A steady effort was made to develop methods of decomposition, to reduce the analysis of the line to a series of equivalent machine that can be isolated and sequentially analyzed [START_REF] Mhada | Joint assignment of buffer sizes and inspection points in unreliable transfer lines with scrapping of defective parts[END_REF]. The present paper efficiently solves a generalization of the model proposed in [START_REF] Mhada | Joint assignment of buffer sizes and inspection points in unreliable transfer lines with scrapping of defective parts[END_REF] where the question of the optimal position in the production line of a number m of inspection stations will be treated (m also must be optimal). We combine Tabu Search (TS) and Genetic Algorithm (GA) to identify search regions with promising locations of inspection stations and an exact method to optimize the assignment of buffer sizes for each given location. Hybridizing TS and GA has been proven to be very effective for high-dimensional combinatorial optimization problems. Actually, when the number of solutions is huge, which is the case in this paper, this step aims at locating promising search regions. This approach provides a balance between diversification and intensification. First, the selection of solutions by GA allows the identification of promising regions in the search space. One intended role of using GA is to facilitate the exploration by guiding the search to unvisited regions with good potential. This leads to a certain diversification in terms of subspaces to explore. Second, TS intends to search intensively around good solutions found in the past search. This leads to intensification by exploiting the neighborhood of each solution selected by GA. The exact method of [START_REF] Ouzineb | An exact method for solving the bffer sizing and inspection stations allocations problem[END_REF] has been shown to be efficient when dealing with the small instances of buffer sizing and inspection stations allocation. This approach is an Exhaustive Search Method (ESM) because the search is guaranteed to generate all possible locations of inspection stations. For each fixed location, the problem is reformulated as a network flow optimization problem that can be efficiently solved by a fast polynomial algorithm. Actually, the space that will be searched is finite by very large and the exhaustive search method may need hours for large instances. The approach proposed in this paper finds near optimal solutions in a fraction of time compared to the exhaustive method proposed in [START_REF] Ouzineb | An exact method for solving the bffer sizing and inspection stations allocations problem[END_REF]. The remainder of the paper is organized as follows. In Section 2, the problem statement is presented. A short description of the proposed approach is given in Section 3. Numerical results are reported in Section 4 and some conclusions are drawn in Section 5.

Problem Formulation

Figure 1 represents the production system studies, it consists of n machines separated by n -1 buffers and contain (m+1) inspection stations. Machines can be either up or down, starved or blocked. A machine M i is starved if one of the upstream machines is down and all buffers between this machine and the machine M i are empty. M i is blocked if one of the downstream machines is down and all buffer between this machine and the machine M i are full. When a machine is neither starved or blocked and operational, it transfer parts from the upstream buffer to the downstream in a continuous way. We assume that the first machine can never be starved and an inspection station is located after the last machine to ensure the conformity of parts received by the customer. All machines M i , i = 1...n could be modeled as a continuous time Markov chain that produce a Fig. 1: The production line single part type with two different quality levels: conforming and non conforming with the same predefined of non-conforming parts to conforming parts β. We consider that all the machines have the same maximal production rate k, failure rate p and repair rate r. We denote d the demand rate for good parts from the last buffer, x i the inventory level on the buffer i, di the long term average number of parts pulled per unit time from the stock x i , c p the storage cost per time unit and per part, c I the inspection cost per pulled part, and a n des the required conforming finished parts availability rate. A binary variable λ i determine whether or not there is a station before the machine M (i+1) to ensure that all the parts be processed by M (i+1) are conform. We suppose that m inspection stations are dispersed along the line (m is not known) i.e. The optimization problem is the minimizing of the long term per unit time average global cost of storage , production shortages, and inspection. Meaning, the cost to be minimized is:

J T ( di,λi) = lim T →∞ 1 T n i=1 E[ T 0 (c p x i (t) + c I di λ i )dt]
(1) under conditions:

n-1 i=1 λ i = m, m ∈ {0, 1, ..., (n -1)} and λ n = 1
The average long term combined storage, shortage costs and inspection costs in (1) expressions can be written after development and calculation (see article [START_REF] Mhada | Joint assignment of buffer sizes and inspection points in unreliable transfer lines with scrapping of defective parts[END_REF]) as:

J(a, λ) = n-1 i=1 T (i) (a, λ) + T F (a, λ) + c I n-1 i=1 λ i di (2)
T (i) (a, λ) = c p k (r(1-ai-1)+p) ai-1 σ i (k -di ai ) (r+p) ai-1 - k (1 -a i ) σ i (k -di ai ) - 1 σ i - (1 -a i ) (r+p) ai-1 σ 2 i (k -di ai ) ln (r(1-ai-1)+p) ai-1 di ai r (k -di ai ) - σ i (r(1-ai-1)+p) ai-1 di ai (r+p) ai-1 r (1 -a i ) , i = 1, ..., n -1 (3) T F (a, λ) = ρ n c p ( kn (1-exp(-µn(1-ρn) zn(a des n )) 1-ρn -(r+p) an-1 z n (a des n ) exp(-µ n (1 -ρ n ) z n (a des n )) (r+p) an-1 (1 -ρ n exp(-µ n (1 -ρ n ) z n (a des n ))) (4)
with:

σ i = ( (r+p) a i-1 ) di a i -k r (k-di a i ) di a i , ρ n = r(k-dn a des n ) (r(1-a n-1 )+p) a n-1 dn a des n , µ n = (r(1-an-1)+p) an-1(k-dn a des n ) and z n (a des n ) = - ln 1 ρn 1- (1-ρn ) (1-a des n )( (r+p) (r(1-a n-1 )+p) )
µn(1-ρn)

a i , i = 1...n -1 is the total parts wip availability coefficient at buffer x i ; this coefficient has a lower and an upper bounds [START_REF] Sadr | Unreliable transfer lines: decomposition/ aggregation and optimisation[END_REF]:

The upper bound : the minimum of a i is achieved when the levels of intermediate stocks are at zero, in this case a i is therefore equal to a i-1 r (r+p) . i.e. a i > a i-1 r (r+p) . Also a i must be smaller than 1. So a i-1 < min ai(r+p) r , 1

The lower bound : a i-1 must guarantee the feasibility of demand di by M i , i.e di < a i-1 k r (r+p)

then (r+p) di r k < a i-1 . Also a i > a i-1 r (r+p) and we suppose that a 0 = 1 , then a i-1 > r (r+p) i-1 . So : a i-1 > max r (r+p) i-1 , (r+p) di r k .
di , i = 1...n is the long term average number of parts pulled per unit time from stock x i . The di , i = 1...n expression depends on the selected position along the line of the m inspection stations. So if e j , j = 1...m the inspection station's position, i.e.

λ i = 1 if i = e j , j = 1...m 0 if not (5) then: di =                d(1 + β) n if 1 ≤ i ≤ e 1 d(1 + β) n-e1 if e 1 < i ≤ e 2 . . . . d(1 + β) n-em-1 if e m-1 < i ≤ e m d(1 + β) n-em if e m < i ≤ n                (6)
The problem can be formulated as follows: find the minimal average global cost system structure (a, λ, m) that satisfies both constraints. That is, minimize J(a, λ, m) (7)

subject to n-1 i=1 λ i = m ∀m, 1 ≤ m ≤ n -1, ( 8
) max r (r + p) i-1 , (r + p) di r k < a i-1 ≤ min a i (r + p) r , 1 , ∀i, 1 ≤ i ≤ n, ( 9
)
λ n = 1 and a n = a des n , (10)

λ i ∈ {0, 1} ∀i, 1 ≤ i ≤ n -1. ( 11
)
a i ≥ 0 ∀i, 1 ≤ i ≤ n, ( 12
)
This problem is a Mixed Integer Nonlinear Programming (MINLP) problem which refers to a mathematical programming with continuous and discrete variables and nonlinearities in the objective function ( 7) and constraints ((8), ( 9), ( 10), (11), and ( 12)). This problem simultaneously optimizes the system structure: the location of the inspection stations (discrete ) and parameters and the buffer sizing (continuous). The variables a i , 1 ≤ i ≤ n, λ i ∈ {0, 1} 1 ≤ i ≤ n -1 and m are the decision variables. The constraint (10) represents the final conditions set by the customer.

The constraint ( 9) is a nonlinear constraint function which represents the line configuration, it is a cumulative constraint type that represents a guarantee the functioning of the production line.

The vector of binary variables (( 8),( 11)) is connected to the line structure.

Solution methodology

As mentioned earlier, the objective function to minimize is the average long term combined storage and shortage costs, while also specifying the optimal location of inspection stations that meets a specified final condition set by the customer. The goal is to solve the optimization problem given by Eqs. (7-12) for a large test problem with 20 machines. The exact method of [START_REF] Ouzineb | An exact method for solving the bffer sizing and inspection stations allocations problem[END_REF] has been shown to be efficient when dealing with the small instances of buffer sizing and inspection stations allocation. This approach is an Exhaustive Search Method (ESM) because the search is guaranteed to generate all possible locations of inspection stations. This approach is an Exhaustive Search Method (ESM) because the search is guaranteed to . It is clear that while the exhaustive exact method (ESM) of [START_REF] Ouzineb | An exact method for solving the bffer sizing and inspection stations allocations problem[END_REF] finds optimal solutions to small instances in reasonable times, the running time appears to be unreasonable for larger ones. In fact, ESM generate all possible locations of the inspection stations. If we especially increase the number of machines, this method becomes drastically inefficient. The number of possible locations of the inspection stations, which is exponential, exploses. It is observed that the large amount of these locations are not profitable. For solving the combinatorial optimization problem formulated in 7-12, it is important to have an effective and fast procedure to smartly locate the extra m inspection stations. To do so, we propose a combination of Genetic Algorithm (GA) and Tabu Search (TS), which has been proven to be very effective for high-dimensional combinatorial optimization problems. For each fixed location, we use a network flow problem, that can be efficiently solved as the standard shortest path problem to find the optimal assignment of buffer sizes. Because of such a combination, this method is said to be hybrid. Hereunder, we will refer to this hybrid method as EM/TG, EM and TG being acronyms of Exact Method and Tabu-Genetic, respectively. This approach finds optimal or near optimal solutions to the same instances in a fraction of time compared to the exhaustive method proposed in [START_REF] Ouzineb | An exact method for solving the bffer sizing and inspection stations allocations problem[END_REF] as will be shown by the experiments. The hybrid method is presented in details in the next section.

Hybrid optimization method

The genetic algorithm used in this paper is based on the method commonly known as the steadystate GA or GENITOR [START_REF] Whitley | Genitor: A different genetic algorithm[END_REF]. Starting from a randomly-generated initial population (feasible solutions), the genetic algorithm applies iteratively four operators: selection, crossover, mutation and culling to produce a new population of solutions.

The search space S is composed of all possible λ i values, for i ∈ {1, ..., n -1}. The production line can contain inspection stations located at the exit of buffer B i and the provisioning point for machine M i+1 . The presence or absence of these stations is captured by a binary variable λ i that takes 1 if there is an inspection station at the exit of the buffer B i and 0 if not, respectively.

To avoid creating infeasible solutions after the crossover operator, we choose to generate solutions with same address. We divide the solution into two same parts and we create an address for each solution as follows:

The address of λ is defined by: Address

(λ) = ( n/2 l=1 λ l , n l=n/2+1 λ l ).
Compared to standard genetic algorithm, the mutation step is replaced in EM/TG by Tabu Search. These operators can be summarized as follows:

1. Selection operator: it randomly selects, from the population, two solutions of same address named parent 1 and parent 2 that will "reproduce" to create a new solution. 2. Crossover operator: it produces a new solution (child or offspring) from a selected pair of parent solutions. We use the so-called one-point crossover operator, which, as illustrated in Table 1, creates the child string O for the given pair of parent strings λ 1 and λ 2 by: (a) Copying string elements belonging to the first fragment from λ 1 ; (b) Copying the rest of string elements from λ 2 .

Parent string λ 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 Parent string λ 2 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 Child string 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 Table 1: An example illustrating the 1-point crossover procedure 3. Tabu Search (TS) (this replaces the Mutation operator): it looks for the best solution in the subspace associated with the new child using the TS algorithm described previously. The best solution found becomes the new child. 4. Culling operator: it generates the new population. Each new solution obtained by TS is decoded to obtain its fitness value. The fitness value, which is in fact a measure of quality, is used to compare different solutions. This fitness is evaluated according to the objective function J(a, λ) optimized as a subproblem with an exact method (for more details see Section 3.2). If the new solution obtained by TS is better than the worst solution currently in the population, it replaces it, else it is discarded. After N rep new solutions have been produced, new randomly constructed solutions are generated to replenish the population, and a new genetic cycle begins. The GA is terminated after N c genetic cycles. The final GA population contains the best solution.

Flow optimization model

For a fixed location λ, the subproblem used to evaluate the fitness can be reformulated as a network flow problem. Consider the connected network G(E, V ) consisting of a set of nodes E and a set of links V as illustrated by Figure 2. Each column i corresponds to a set of possible buffer levels for a machine i, such that:

a i1 = 100 × max(( r r + p ) i-1 , d k r + p r
) and a ini = 100 × min( a i (r + p) r , 1).

Each node is connected to all nodes in the next column. To each link is associated some real number c i,i+1 that corresponds to the shortage costs and inspection costs, such that:

c 0,1 = 1, c i,i+1 = T i (a i , a i+1 , λ) + C I × λ i × d i and c n-1,n = T F (a n-1 , a n ).
The main objective is to find for each λ the shortest path between a 0 and a n .

Numerical Results

To analyze the solution method introduced in this paper, we tested it on a large problem with 20 machines, one of the problems benchmarked in previous research. This problem was first introduced and solved by the exact ESM method in [START_REF] Ouzineb | An exact method for solving the bffer sizing and inspection stations allocations problem[END_REF]. The exact method applied to this problem takes hours while the new approach finds optimal or near optimal solutions in a fraction of time. Our algorithm was implemented in C++. The numerical tests were performed on an Intel Core i7 at 2.8 GHz with 8 Gbytes of RAM running under Linux.

Table 2 shows the parameters used for the experimentation. To compare the proposed hybrid approach EM/TG to ESM, we re-implemented ESM and re-tested it and EM/TG in the same conditions (computer, programming language, operating systems, etc.). This allows us to determine Table 2: system parameters n p r k βi d cp cI a des n 20 machines 20 0.2 0.9 9 0.1 1 0.1 0.2 0.95 the optimal solutions to compare to. We define two ratios in terms of the objective value and CPU time to determine which solution method performs better:

MPCI = 100% × (Minimal ESM Cost -Minimal EM/TG Cost) Minimal ESM Cost . ( 13
) MPTI = 100% × (Minimal ESM Time -Minimal EM/TG Time) Minimal ESM Time . ( 14
)
Comparison results are given in Table 3 . The column m indicates the number of inspection stations to use. We varied this number between 1 and 10. We see that EM/TG obtains optimal solutions in 90% of the cases in less time. It reduces the solution time by huge factors up to 40 compared to ESM. 4 shows the results obtained for the test problems with 20 machines by using the proposed hybrid method and the exact approach limiting the running time to 3600 seconds. In all test cases, EM/TG performs as well as ESM in 40% of the test cases and better in the remaining 60% of the test cases when we limit the solution time to one hour. m 1 2 3 4 5 6 7 8 9 10 EM/T G 8.3125 6.2645 5.9802 6.0663 6.2772 6.5230 6.7959 7.0965 7.5000 7.7947 ESM 8.3125 6.2645 5.9802 6.0663 6.2774 6.8639 7.3566 7.8709 8.4458 8.9299 Table 4: The results obtained by the proposed method and exact approach for 20 machines during 3600 seconds N.B: For instance (m=9) the algorithm has converged locally after 1322 seconds and could not improve this solution even after more time.

Conclusions

This paper proposes an efficient hybrid approach based on an exact method and methaheuristics to solve the buffer sizing problem in unreliable heterogeneous production lines with several inspection stations. This is a very hard mixed integer nonlinear program. The proposed approach uses ideas from genetic algorithm and tabu search to identify profitable configurations (locations of the inspection stations). For these locations, we use an exact approach to decide the optimal sizes of the buffers to use. Our final goal is to find an optimal design.

This hybrid approach provides a balance between diversification and intensification that shows to work well on such heterogeneous production lines with up to 20 machines. When compared to the exhaustive exact method, the hybrid approach results are superior in terms of CPU time.

Future research will focus on applying our heuristic to solve larger instances (up to 30 machines and a variable number of inspection stations).

  m, m ∈ {0, 1, ..., (n -1)} and λ n = 1 .

Fig. 2 :

 2 Fig. 2: The production line

Table 3 :

 3 Comparison results for 20 machines Table