Pierrick Guégan

Daniel Lebreton

Franck Pasco

Ramzi Othman

Steven Le Corre

Arnaud Poitou

P Guegan

S Le Corre

Metallic energy-absorbing inserts for Formula One tyre barriers

Keywords: Formula One, crash, tyre barriers, race car circuit

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

INTRODUCTION

It seems that in the literature there is little on the subject of tyre barriers. However, Wright and Mellor [1-3] studied, in laboratory, many integral tyre barrier configurations by crashing a trolley with initial velocities of 60 and 80 km/h. They showed the improved energy contribution of a thermoplastic tubular insert compared with when tyres were used alone; therefore the barrier rigidity is better with inserts. Thus, the force applied during the crash is more important, but the trolley stopped while acquiring an allowable deceleration. Moreover, the inserts improve the integrity of the barrier, as the tyres are held in position. However, the insert used generates a larger trolley rebound, sometimes equal to an energy ratio of 20 per cent of the initial energy. During a race, this could cause a race car to return to a dangerous position on the race way.

Thus, the aim of this study concerns the improvement in the energy absorption properties of the tyre barriers by optimization of its inserts. Before studying a new insert, which is able to produce a lower rebound energy, the actual insert behaviour must be determinate by static and dynamic tests.

BEHAVIOUR OF THE PRESENT INSERTS UNDER STATIC LOADING

The insert that is now in operation matches the Fe ´deration Internationale de l'Automobile (FIA) Standard 8861-2000 [2]. This document includes the insert specifications and the static test conditions for validation by the race car circuit manager. The recognized solution is a tube made of thermoplastic-type polyethylene (PE) with specific dimensions adapted to the internal tyre column. Initially, this product was validated by an FIA crash test [3]. Thus, a tube with the following properties has been selected for experimental investigation: material, PE-HD 100; external diameter D 0 5 315 mm; thickness e 5 12.1 mm; length L 0 5 1 m (cut, 6 m original).

For the static loading, the following FIA standard parameters were used: a loading rate S of 2 mm/s and a radial force in the middle of the tube applied by a rigid square plate indenter of 250 mm6250 mm 2 (Fig. 1(a)). To be accurate to specifications, the PE tube must supply a minimum energy of 4 kJ and a maximum radial force of 35 kN, for a radial strain of 0.8 (ratio of the radial displacement DD to the external diameter D 0 ). *Corresponding author: GeM Research Institute in Civil and, Mechanical Engineering, UMR 6183 CNRS, Ecole Centrale Nantes, 1, rue de la Noe ¨, BP 92101, Nantes Cedex 3, 44321, France. email: pierrick.guegan@ec nantes.fr An Instron 5584 static machine was used for these tests on three PE tube specimens (Fig. 1(b)). Each specimen was tested at a different radial strain level of 0.2, 0.5, or 0.8. The operation consists in loading the specimen from 0 to the required radial strain and then unloading to 0 at the same speed. Figure 2(a) shows the evolution of the radial force with the radial strain. First, the accuracy of the selected thermoplastic tube was verified; for a radial strain of 0.8, the maximum force is 33.9 kN (lower than 35 kN) and the supplied energy is 4948 J (greater than 4 kJ). Then, this procedure gives information on the supplied energy E s and the dissipated energy E d , which is the effective absorption parameter of the tube insert.

The ratio of the dissipated energy E d to the supplied energy E s shows the ability of the insert to dissipate energy for different crash levels. For the three tested specimens, the ratios are as follows: for a radial strain of 0.2, E d /E s 5 48 per cent; for a radial strain of 0.5, E d /E s 5 65 per cent; for a radial strain of 0.8, E d /E s 5 80 per cent. The energy ratio is better for a radial strain of 0.8 because plastic alteration appears at a radial strain of 0.5 (see Fig. 2(a)). The combination of the material behaviour, the tube geometry, and the square indenter causes an amplification of local plastic deformation above this radial strain. Thus, the energy dissipation of the PE tube insert is better for a high radial strain above 0.5. Below this strain level, the PE tube insert has almost elastic characteristics, and so it does not fulfil the criterion for being a suitable absorber. Indeed, a significant part of the absorbed energy is released after the test.

BEHAVIOUR OF THE PRESENT INSERTS UNDER DYNAMIC LOADING

The static investigations were completed by two dynamic tests on similar tubes, realized on the vertical bench at the Ecole Centrale de Nantes (Fig. 3). The experimental conditions are the same as for the static tests, except for the impact speed. The potential energy is produced by a mass M t of 320 kg, dropped at an initial height h. A high-speed video camera records the test at a frequency of 1000 frames/ s (Fig. 4). Post-treatment of the pictures gives an expression for the mass height during the test (position X 1 , X 2 , and X 3 ), and also an expression for its rebound. For the two dynamic tests, the energy dissipation ratios are explained in Fig. 5 and Table 1.

As for the static test, the energy dissipation of the PE tube insert is better for a high strain, greater than 0.5.

In conclusion, the PE insert has an almost elastic behaviour for deformations below 0.5. This explains the increase in the rebound length noticed during experimentation on a barrier including these inserts [1].

METALLIC SOLUTIONS

In fact, a problem of the PE tube insert is the high elasticity of the PE material. This is acceptable with regard to the recovery of the barrier after a crash, but not suitable for optimum energy dissipation. The material has to be changed to improve the energy dissipation of the insert. The creation of a new insert with the same geometry implies using a material that assures some structural integrity during the crash (and therefore without rupture), has a rigidity when used with the weighted force, and, in particular, possesses a minimum elastic return during unloading. That is why metallic materials were chosen as they have a better elastoplastic behaviour. For this study, two metallic materials were selected: stainless steel type 304 and aluminium alloy 5754-H111. These materials are stainless (no corrosive problems in use) and their strain failure levels are compatible with crash applications because they withstand a large plastic strain before rupture (greater than 20 per cent). Four prototypes have been made with the following parameters [4]: external diameter D 0 5 321 mm, plate rolled and tungsten-inert-gas welded; thickness e 5 2.5 mm for stainless steel 304 and e 5 3 mm for aluminium alloy 5754-H111; length L 0 5 1 m. The thicknesses were initially estimated by an analytical approach and finite element calculations with the explicit software ABAQUS, with the static conditions defined by the FIA as references.

BEHAVIOUR OF THE METALLIC INSERTS UNDER STATIC LOADING

The experimental specifications are the same as for the tests on the PE inserts. A metallic tube is used for the operation, which is divided into three steps, according to three consecutive cycles of loading and unloading at the same speed, for radial deformation levels of 20 per cent, 50 per cent, and 80 per cent.

Figure 6 shows the force in terms of the radial strain for the two prototypes tested in static loading. First, the plastic alteration observed on the PE curves at a radial strain of 0.5 (see Fig. 2) is not visible in these new results, because the material plastic strain is clearly initiated since the beginning of the test.

For the two static tests on these first prototypes, the global energies used are under the minimum specification for the PE tube (3464 J for the stainless steel insert and 2507 J for the aluminium alloy insert). This difference is probably due to a variation in the metallurgical state between the materials limit design and the real behaviour of the tested tubes. An increase in the insert thickness would be enough to obtain a final energy equal to that of the PE tube if needed. However, these static tests show that the energy dissipation E d /E s ratio for the three consecutive cycles gives better results with the metallic inserts than with the PE tube (Table 2): 85 per cent and 81 per cent for the tested metallic tubes versus 65 per cent for the PE insert at a radial strain of 0.5; 91 per cent and 92 per cent versus 80 per cent at a radial strain of 0.8. The PE insert tested at a radial strain level of 0.2 has an energy dissipation ratio of 4-9 per cent below those of the metallic materials to date. The dynamic tests were realized with the same specifications as for the PE inserts. In the quasistatic tests at a radial strain of 0.8, the metallic inserts dissipate almost completely the supplied energy: 94 per cent and 96 per cent (see the video sequences in Fig. 7 and the results in Table 3). In contrast, the dynamic test carried out on PE tube specimen 05-114 yielded an energy dissipation ratio of 71 per cent for a radial strain of 0.64.

CONCLUSION

Although the crash energy of the prototypes designed for this first study is slightly lower than the FIA energy specifications of the PE tube, the energy dissipating power of a metallic insert under quasi-static and dynamic loading is definitively higher than that of the PE insert used now. In quasi-static conditions, the gain is very interesting at a medium crash level (20 per cent better dissipation at a radial strain of 0.5) and remains significant for a larger crash (increase of 10 per cent at a radial strain of 0.8). It is also positive for a very weak radial strain (6 per cent average of the additional contribution at a radial strain of 0.2). In dynamic conditions, the energy dissipation is almost full scale, with a mean for the two metallic inserts of 95 per cent at a radial strain of 0.89. Now, the real contribution of this improvement to the general behaviour of the tyre barrier in crash test must be determined. The next steps of this study could be to adjust, if necessary, the metallic insert behaviour, by increasing its thickness, to validate the solution by new quasi-static and dynamic tests, and to realize a crash test on a tyre barrier fitted out with these new inserts, under conditions in conformity with the FIA specifications [3].

ACKNOWLEDGEMENT

Fig. 2

 2 Fig. 2 Results of the three static tests showing (a) the force as a function of the radial strain and (b) the energy as a function of radial strain: test 1, tube specimen 05-110; test 2, tube specimen 05-111; test 3, tube specimen 05-116

Fig. 3

 3 Fig. 3 (a) Dynamic test parameters; (b) PE tube on the vertical bench

Fig. 5

 5 Fig. 5 Definition of the energy dissipation ratio E d /E s

Fig. 6

 6 Fig. 6 Force as a function of the radial strain: (a) stainless steel insert specimen 06-050; (b) aluminium alloy insert specimen 06-052

Fig. 7

 7 Fig. 7 Video sequences of dynamic tests on a metallic tubular insert on a vertical bench (test parameters for a high rebound: stainless steel insert specimen 06-051; falling height h 1276 mm; contact velocity, 5.0 m/s) (test parameters for a low rebound: aluminium alloy insert specimen 06-053; falling height h 800 mm; contact velocity, 4.0 m/s)

Table 1

 1 Parameters and results of the dynamic tests on the PE inserts

	PE insert specimen		Radial strain
	number	h (mm)	DD/D 0	X 1 (mm)	X 2 (mm)	X 3 (mm)	E d /E s (%)
	05 114	1580	0.64	0	1781	1271	71
	05 115	805	0.43	0	940	532	57

Table 2

 2 Results of static tests on PE, stainless steel, and aluminium alloy inserts

			E d /E s (%)
	Radial	Stainless steel	Aluminium alloy	PE insert specimen
	strain	insert specimen	insert specimen	05 110, 05 111,
	DD/D 0	06 050	06 052	and 05 116*
	0.2	57	52	48
	0.5	85	81	65
	0.8	91	92	80
	*The values for PE inserts are given for comparison.

  Special thanks are due to Mr Franck Corcelle of the FIA for his valuable help. Gue ´gan, P., Lebreton, D., Pasco, F., Othman, R., and Poitou, A. Structure amortisseur de chocs, en particulier pour les circuits de compe ´titions automobiles. Fr. pat. 07/00547, 26 January 2007.

	REFERENCES
	1 Wright, P. G. and Mellor, A. Barrier testing. SAE
	technical paper 983061, 1998.
	2 FIA Standard 8861-2000. FIA energy absorbing
	inserts for Formula One tyre barriers standard,
	Fe ´de ´ration Internationale de l'Automobile, Paris,
	26 January 2000, available from www.fia.com/sport/
	Regulations/standregs.html.
	3 FIA safety barriers standard, Fe ´de ´ration Inter-
	nationale de l'Automobile, Paris, 26 January 2000,
	available from www.fia.com/sport/Regulations/
	standregs.html.
	4 APPENDIX
	Notation
	D 0	external diameter of the insert
	e	thickness of the tubular insert
	E d	dissipated energy
	E s	supplied energy
	h	falling height on the vertical bench
	L 0	length of the insert
	M t	falling mass of the vertical
		bench 5 320 kg
	PE	polyethylene
	PE-HD	high-density polyethylene thermo-
		plastic material
	S	loading rate
	t	time reference in dynamic loading
	X 1	height of the high position before
		rebound
	X 2	height of the low position before
		rebound
	X 3	height of the high position after
		rebound
	DD	radial displacement
	DX r	indenter displacement during
		rebound
	DX s	indenter displacement during falling

Table 3

 3 Results of dynamic tests on stainless steel and aluminium alloy inserts

	Insert	h (mm)	Radial strain DD/D 0	X 1 (mm)	X 2 (mm)	X 3 (mm)	E d /E s (%)
	Stainless steel specimen 06 051	1276	0.84	0	1547	1449	94
	Aluminium alloy specimen 06 053	800	0.94	0	1101	1060	96


Antti Pulkkinen

Ville Vainio

Noora Rissanen

Case Study on the Relation of PLM Maturity, Architecture and Business Processes

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

Introduction

Product lifecycle management (PLM) was being studied through the analysis of six industrial cases. The focused factors of PLM were the maturity of PLM, business types and PLM systems' architectures.

Motivation was to find out the potential combinations of factors in the above. The research questions of the paper are: what kind of business processes are the main customers of PLM, how mature is the PLM approach and what kind of changes are taking place in PLM architectures of case companies?

The paper continues with literature review, which substantiates the research approach and outlines the details of the factors, which serve as a means of analysis. The research method is outlined and results presented. The conclusions summarize the findings, estimate the effects of the changes in the architectures of PLM systems and compare the aspired situation with the overall diversity of business processes taking place in the case companies.

Three PLM factors: maturity, business and systems architecture PLM is the activity of managing products effectively across their lifecycle [START_REF] Stark | Product Lifecycle Management: 21st Century Paradigm for Product Realisation[END_REF]] or a strategic business approach, which applies business solutions, collaborative creation, management, dissemination of product definition information throughout the PLC [CIMdata 2011].

Essentially, Product Data Management (PDM) is the core activity of PLM [START_REF] Stark | Product Lifecycle Management: 21st Century Paradigm for Product Realisation[END_REF]] and PDM system an essential IT platform for PLM. A PDM project is composed of two main stages [START_REF] Crnkovic | Implementing and Integrating Product Data Management and Software Configuration Management[END_REF]]: evaluation and deployment. As the implementing and utilizing PLM is not only a software project, we consider PLM as a continuous process that comprises of several IT-projects, as well as strategic and organizational initiatives. Generally, the productivity of PLM is a sum of the efficiency of implementation projects and effects attained by the utilization of PLM in business. Hence, we chose to assess the maturity of PLM in different cases, the type of business and the architecture and integration of PLM subsystems (CAE, PDM, etc.).

PLM maturity

For this research, a four level PLM maturity model was put together by [START_REF] Vainio | Comparative research of PLM usage and architecture[END_REF]. It is based on the two models presented by [START_REF] Stark | Product Lifecycle Management: 21st Century Paradigm for Product Realisation[END_REF] and [START_REF] Batenburg | PLM roadmap: stepwise PLM implementation based on the concepts of maturity and alignment[END_REF]. The five dimensions of the model characterize the state of PLM systems and organisations in a company. The synthesized model is presented in the Table 1. In the analysis, the position in the table above presents the maturity of the PLM in a company regarding the dimension of maturity.

Type of businesses

It is important to understand the business processes, because the industrial characteristics define the context of PLM in a company. This is why we characterize the main business processes into two main areas. The case companies create and deliver value by selling and delivering:

-Tangible products in the beginning of PLC.

-Service products (operations and spare parts) in the middle of PLC. Service business has steadily gained importance instead of the plain manufacturing of investment goods. In practice, it is important to know the share of service business in a company's turnover.

In the sales-delivery processes the products can be engineered, configured and/or assembled to order or made to stock (ETO, CTO & ATO, MTS). However, the pre-recognized sub-domain of above characterization, which is typical for Finnish industry, is partial configuration, i.e. the use of configured products as sub-elements of projects. Therefore, the kinds of product definition processes for the analysis were 1. ETO in project deliveries 2. Partial CTO in project deliveries 3. CTO in ATO 4. Fixed / Standard products / MTS The abovementioned typology of product definition does apply to both tangible products and services. Also services can be engineered or configured to order (e.g. in the upgrading of a plant or maintenance of an investment product) or standardized (e.g. standard service programs in automotive industry).

The architecture of PLM system [START_REF] Vainio | Comparative research of PLM usage and architecture[END_REF] characterized the relations of PLM applications with the synthesis of two architecture integration models [START_REF] Crnkovic | Implementing and Integrating Product Data Management and Software Configuration Management[END_REF][START_REF] Bergsjö | Architectures for Mechatronic Product Data Integration in PLM Systems[END_REF]] as three major trends of integration: legacy, single source and service-oriented architecture. Table 2 illustrates which of the definitions are essentially describing the same architecture types. The synthesis is used in the analysis, which is presented also in the table (case state and transition in italics). For example, case company A will either remain to have loose integrations between best in class systems (A→A') or transform to single source architecture (A'').

Research method and material

We applied different methods for collecting the raw data and for the analyzing of it. The data was collected with eight of structured interviews (3-4 hours) and six benchmarking sessions (six of each). The benchmarking sessions involved the participants of all the case companies. In a session the hosts presented the PLM approach of a company and answered consequent questions. The active audience (typically 15-25 PLM experts) consisted of practitioners, managers, consultants, and researchers. The benchmarking sessions gave more accurate information on the PLM in a company than the interviews. All the sessions were recorded, notes were taken and presentation material (e.g. presentation slides) collected. The collected data was processed and reported (6 reports of 20-30 pages). Four people were involved in the processing of the material. Their expertise varied from novice in transcribing audio recordings to senior researcher correcting the reports. Finally, the reports were sent for validation and verification to the interviewees. The reports were the basis of the analysis and therefore are the essential material for this research.

The application of benchmarking was considered positive by all participants. The practitioners got the direct feedback and insight on level of PLM in all the companies. So, they could attain other experts' ideas for the benefit of their own PLM processes. For the researchers there was a large set of experience taking place in the sessions. The quality of questions was high and new issues arose in the discussion resulting with a large set of material. However, the common themes are recognizable in the material.

The cases were analyzed with the application of comparative case study method. A more detailed description on the utilization of Qualitative Comparative Analysis (QCA) by [START_REF] Ragin | The Comparative Method. Moving beyond qualitative and quantitative strategies[END_REF] for our purposes is presented in [START_REF] Rissanen | Testing a Framework for Analyzing PLM Architecture in Global Manufacturing Companies[END_REF]. In short, the essence of the method is the set of truth tables documenting the properties of the cases with Boolean logic (best illustrated with the Table 4 of the results). The tables of the cases are summed up as matrices, which are comparable to tabular formats of other fields. The combinations of tables present the properties of cases with a matrix that is conceptually close to the utilization of morphological matrices in product development [Pahl & Beitz 1996]. The combinations of case properties are similar to possible configurations in matrix based product configuration methods [e.g. [START_REF] Bongulielmi | Die Konfigurations-& Verträglichkeitsmatrix als Beitrag zur Darstellung konfigurationsrelevanter Aspekte im Produktentstehungsprozess[END_REF]].

Results and analysis: maturity, processes and architecture

We present the studied cases with figures and tables, which are based on the frame of analysis, which consists of the factors of research. Each factor is dealt separately and conclusion combines them.

The maturity of the companies is analyzed in five dimensions represented with the five directions of the Table 3. The range of maturity is according to Table 1 from level 0 to level 3. The most mature PLM approaches were recognized in cases D, A and E.

Involvement and understanding

2 1 1 3 2 1
Organisational integration

2 2 2 3 3 2

Level of interoperability

2 1 1 3 2 1
General description

2 1 1 3 2 1
In the Table 3, the sales-delivery type is according to previous combination. Many of the companies utilized configuration in ETO projects, which is visible in the table (cases A, C & D). In these cases there is an indicator (1) in the both of the rows designated for ETO and CTO.

Table 4 The type of business vs. case companies

Business vs. Cases

A B C D E F Sales-Delivery type 2 1 2 2 3 1 -MTS 0 0 1 0 0 0 -ETO 1 1 1 1 0 1 -CTO 1 0 1 1 1 0 Service business > 50% 1 0 0 1 0 0
The share of service business is higher than the 50% of turnover in two companies (A & D). The share of turnover is characterized with options ranging from less than (0) to more than (1) half of the turnover. We had more accurate data on the share of service business that could be used in fuzzy-set QCA more precisely. Actually, the row presenting sales delivery type as a whole combines the approach with a more precise manner (1 for MTS, 1 for pure ETO, 2 for CTO in ETO, 3 for pure CTO). Concerning PLM architecture the present and future dimensions were presented already in the Table 2.

Conclusions

According to the sample of study the sales-delivery (ETO) projects applying partial configuration are the main customers of PLM. The most mature company (at least PLM wise) is making its turnover mostly by service business. Pure project based business seem to be less mature. However, the sample is small and statistic verification is impossible with it. It seems to be a sound strategy to approach PLM is to first systematize products and processes along with the increase of PLM awareness and the readiness of adoption in an organization. Focusing only on changing PLM architecture may lead to mismatch that lies within the compatibility of IT architecture and the diversity of product lifecycle (PLC) related business needs the companies are running.

Obviously, maturity is a matter of aligned initiatives (see Table 3). A company cannot focus the one dimension of maturity and omit the development in another. In all dimensions the most mature company appeared to be the case D, which had started its PDM/PLM process already in early 1990's. However, the PDM/PLM process of another company (case F) had begun already in the same years, but the maturity of case F was much lower. Apparently, long history of PLM does not ensure the maturity in a company. The companies that utilized configuration (in sales-delivery projects) had the higher degrees of PLM maturity.

There are some research findings that are not reported in the results of this paper. One of them is that the deployment processes are actually long chains of consecutive development projects. The consecutive projects can be considered as the reason of legacy architectures, which are comprised of several independent pieces of software integrated loosely by the companies, consultants and vendors.

Application integration is an important factor in PLM. The dominant trend seems to be the transition from legacy to single source architecture. This has advantages, such as data correctness and the ease administration of PLM systems. However, the disadvantages of the single source architecture, see e.g. [START_REF] Silcher | B.A Service-Based Approach for Next-Generation Product Lifecycle Management[END_REF] and [START_REF] Bergsjö | Implementing a service-oriented PLM architecture focusing on support for engineering change management[END_REF], may lead to difficulties in the PLM processes of companies (especially with ETO products). The companies may not be aware or lack of trust in service oriented architecture.

Based on our study it appears to be so that the product configuration based businesses are supported quite well with legacy architecture. Moreover, the maturity analysis suggests that the dominant issues in companies are related to the management of PLM systems, which is one of the advantages of single source architecture. However, the notion that the emerging changes in PLM architectures may appear difficult to validate for some business functions. The role of PLM as the support of business processes should not be forsaken. Another future challenge is the configuration of services, such as maintenance and spare parts, in the middle of PLC. This requires the updating of PLM systems, e.g. data models. However, it opens new business opportunities instead of just relying on the limited markets of green field installations.

The applied research methods were very welcome way of collaborating between industry and academia. Especially the novel ap-proach of benchmarking in data collection served all the participants. The analysis of the collected material appeared tedious. The crisp-set QCA seems to apply poorly to the material (see Table 3). Instead, for screening the material we used a frame consisting of three dimensions with values ranging from 0 to 3 (see e.g. Table 2, which is based on the PLM maturity dimensions). This approach could be transformed as a fuzzy-set QCA supported by a survey.

Table 1 The PLM maturity definition model

 1

		Level 0	Level 1	Level 2	Level 3
	Application of	Non-existent	Local initiatives	Company-wide	PLM is seen as a
	PLM		exist, but there is	understanding of	business problem
			no overall vision	the importance of	spanning the whole
				product data is tak-	product lifecycle
				ing shape
	Involvement	From few to none	Few people un-	It is clear for eve-	Widespread under-
	and understand-	people involved	derstand PLM	ryone where the	standing of PLM in
	ing			company is and	the company and in
				where it wants to	its extended enter-
				be	prise
	Organisational	No integration	Simple depart-	Integration be-	PDM tools are ful-
	integration		mental integra-	tween PDM tools	ly integrated and
			tions between	and simple integra-	there is widespread
			some PDM tools	tions with for ex-	integration with re-
				ample ERP	lated systems such
					as ERP
	Level of	Between individual	On a depart-	On a cross-	Across the extend-
	interoperability	tools only	mental level	departmental level	ed enterprise
	General de-	There is no PLM in-	PLM is realized	PLM is understood	PLM is integrated
	scription	vestment and individ-	as individual ap-	relatively well and	across the supply
		ual legacy systems are	plications inte-	integrated on a	chain. PLM is uti-
		used.	grated on a de-	cross-departmental	lized in state-of-
			partmental level.	level	the-art ways, for
			There is no over-		example in a
			all PLM vision.		closed-loop fash-
					ion.

Table 2 Synthesis of the architecture definitions and analysis of case PLM architectures [adapted from Vainio 2012]

 2

		No integration	Loose integration	Full integration
	Best in	Has typically resulted in	One to one ad-hoc integra-	One system as an integrator
	class	Legacy Architecture	tions. Cases: A→A', B &	(standard integration inter-
		Case: F→F'	C→C', D	face). Cases: C'', E''
	Peer to		Service Oriented Archi-
	Peer

tecture (SOA). Case: B'' All in one Typically Single Source architecture. Case: A'', B', D', E→E'

Table 3 The PLM maturity of studied companies

 3

	Maturity vs. Cases	A	B	C	D	E	F
	Application of PLM	3	2	2	3	2	1

Acknowledgments

We thank all the participants of benchmarking and Finnish funding Agency for Technology and Innovation for funding the research.


Haiqing Zhang
email: haizhang@univ-lyon2.fr

Yacine Ouzrout
email: yacine.ouzrout@univ-lyon2.fr

Abdelaziz Bouras
email: abdelaziz.bouras@univ-lyon2.fr

Antonio Mazza
email: antonio.mazza@unisannio.it

Matteo Mario Savino
email: matteo.savino@unisannio.it

PLM Components Selection Based on a Maturity Assessment and AHP Methodology

Keywords: PLM Maturity Model, AHP Methodology, Key Performance Indicators, TIFOS Framework

The benefits of Product Lifecycle Management (PLM) have been noted for improving business, creating collaboration, and reducing energy and time by making transcendent decisions through the process of product life cycle. This work aims to propose a PLM Components Maturity Assessment (PCMA) model to gain comprehensive maturity results and reduce the complexity in obtaining maturity scores. According to PLM functionalities, we divide PLM into fifteen components. PLM components can be cataloged into five main fields: 'TechnoWare', 'InforWare', 'FunctionWare', 'OrgaWare', and 'SustainWare' (TIFOS Framework). With PCMA model we analyzed PLM components and proposed mature content of each dimension, obtaining specific key performance indicators for each dimension. This work has been also useful to solve decision-making issues based on AHP methodology, such as: selecting the optimal PLM components in TIFOS Framework, obtaining the components ranking weight, getting components maturity score, and comparing it with the actual situation to give constructive business suggestions. These business suggestions include strengths and weakness of PLM components and conducting selection of PLM components. Experimental studies have been conducted to verify maturity scores for each component and to achieve component-ranking weights.

Introduction

The concepts of PLM are very extensive [START_REF] Stark | Product Lifecycle Management[END_REF]. PLM manages and accesses product information to make companies run smooth and secure. PLM guarantees persistent integrity of product definitions and related information during the life of a product. The functionalities of PLM include maintaining business processes, such as: creating, managing, disseminating, and sharing product information [START_REF] Stark | Product Lifecycle Management[END_REF]. The foundation components are used to construct these PLM functionalities. The integration of several components is a PLM solution. Selecting right PLM components lead to a better PLM solution, which has substantial opportunity to meet company requirements. In contrast, misuse of PLM components will cause products to malfunction or fail.

The main purpose of this work is to help companies to select the right PLM components with their different goal oriented objectives. To achieve this aim, four basic research questions need to be addressed:

1. What are the full PLM functionalities that have to be considered in relation to PLM capabilities?

2. How many components constitute these PLM functionalities? 3. How can we identify the strengths and weaknesses of PLM components? 4. Which one is the most suitable PLM component for a company?

To answer the first research question, two important literature works are presented and a new framework is proposed in section 2.1. To answer the second question, the basic literature on PLM components is presented and fifteen PLM components are proposed in section 2.3. To answer the third question, a PLM maturity model has been proposed by analyzing characters and KPIs of PLM components in section 3. To answer the fourth question, AHP (Analytic Hierarchy Process) methodology is developed in section 4. Section 5 gives the case study and section 6 concludes our work.

TIFOS Framework and PLM components

TIFOS Framework

Firstly, from Sharif's perspective [START_REF] Sharif | Technology Strategy in Developing Countries: Evolving from Comparative to Competitive Advantage[END_REF], technology can be classified into four categories: TechnoWare, InforWare, HumanWare, and OrgaWare.

 TechnoWare: contains components, equipment (manual and powered), vehicles, machinery, IT and other facilities;  InforWare: contains documents or knowledge records that reflect facts and formulas (design parameters, standards), principles of physical and social phenomena; computer software; technical information; theories and state-ofthe-art knowledge for innovation;  HumanWare: describes the skills to comprehend and use the job related components; the ability to utilize technology components; have the motivation to improve the work performance;  OrgaWare: consists in organizational techniques, work assignments, education, and experience-based work facilitation; has the means for using and controlling factors of production, systems analysis, organization of products, processes, and components. Secondly, from Vengugopalan et al.'s perspective [START_REF] Vengugopalan | Application of AHP for PLM Tools Selection. Product Lifecycle Management: Fostering the culture of innovation[END_REF], the functionalities of PLM are classified into four major categories based on TIFO Framework (TechnoWare, InfoWare, FunctionWare, and OrgaWare). They mixed the initial HumanWare with the OrgaWare components and added a new FunctionWare category:

 FunctionWare: depth and breadth of functionalities. Every product life cycle is characterized by three phases: beginning of life (BOL), middle of life (MOL), and end of life (EOL). Most previous works focus on the BOL (design and manufacturing) phase [START_REF] Kiritsis | Report from workshop 2: Sustainable products and production, services and management[END_REF]. However, in order to get tangible products, achieve top range performance, and obtain optimum product lifecycle, businesses must extend to EOL phase, which is PLM sustainability [START_REF] Kiritsis | Report from workshop 2: Sustainable products and production, services and management[END_REF]. Next, we give the reasons why sustainability should be added into PLM functionalities.

PLM sustainability is the potential for a long-term maintenance of product lifecycle [START_REF] Trotta | Product Lifecycle Management: Sustainability and knowledge management as keys in a complex system of product development[END_REF]. To meet the requirements of product performance, present designer decisions heavily impact upon product design (BOL phase) as well as on environmental aspects (EOL phase). To minimize efforts, time, and costs for improving product quality, businesses need sustainable, stable process management, and product development. Analysis, synthesis, evaluation and improvement of product lifecycle design, DFE (Design for Environment), TRIZ (Theory of Inventive Problem Resolution), and LCA (Life Cycle Assessment) need to be integrated and collaborated with PLM.

Based on what was mentioned above, we extend the TIFO framework into TIFOS and add a new category called SustainWare. The content of SustainWare is:

 SustainWare: reducing waste and pollution; designing eco-friendly products; using new materials and supply chain; minimizing damage to environment and human; consuming low energy.

Successful Sustainability indicators to obtain sustainable PLM

In current literature studies, sustainability indicators and concepts have been studied and defined based on five dimensions: economy, ecology, society, technology, and performance management. Number these five dimensions in sequence: 1, 2, 3, etc. First, we will discuss presently acceptable and better recognized indicators for sustainable PLM. Efforts are made by multiple organizations. An effort by the United Nations Environment Program (UNEP) and the United States nongovernmental organization called Global Reporting Initiative (GRI) (GRI, 2011) has defined more than 100 indicators and focused the first three dimensions. Other efforts by the National Institute of Standards and Technology (NIST) is the Sustainable Manufacturing Indicator Repository (SMIR) (SMIR, 2012), which defined extensively available indicator sets by using the five dimensions.

Efforts have been made by researchers to study system sustainable indicators. Laurent et al. studied the ability of carbon footprint emissions as an indicator, eager to find out the correlation between carbon footprints and other environmental impacts [START_REF] Laurent | Carbon footprint as environmental performance indicator for the manufacturing industry[END_REF] [START_REF] Abramovici | Decision Support Framework for PLM Harmonization Projects within Industrial Companies[END_REF]. After comprehensively analyzing PLM functionalities and reviewing the works, which have been done by the other researchers, fifteen different types of PLM components have been collected and showed in Table 2.

Table 2. TIFOS Frameworks and corresponding components

A PLM maturity model needs to be proposed to measure the current maturity situation of each PLM component, which can help the company identify strengths and weaknesses of PLM components. Evaluation of the integration and maturity of different components is essential and advantageous. For instance, PDM (Product Data Management) maturity models [START_REF] Stark | Product Lifecycle Management -21 st Century Paradigm for Product Realisation[END_REF] define the activities that a company needs to carry out at each stage and also defines a generic five-step process per stage; related to the as-is situation and to-be situation of the studied company. CPI (Collaborative Product Innovation) maturity model [START_REF] Sharma | Collaborative Product Innovation: Integrating Elements of CPI via PLM Framework[END_REF] proposes three unique stages of CPI based on collaborative maturity. Batenburg [START_REF] Batenburg | PLM roadmap: stepwise PLM implementation based on the concepts of maturity and alignment[END_REF] developed a PLM framework to assess and guide PLM implementations. Sä ä ksvuori Model (Sä ä ksvuori & Immonen, 2008) determines the maturity of a large international corporation for a corporate-wide PLM development program and develops business and PLM related issues. Other maturity models include Savino model [START_REF] Savino | PLM Maturity Model: a Multi-Criteria Assessment in Southern Italy Companies[END_REF] and BPMM (looy et al, 2012). But it should be mentioned that none of these maturity models have solved the following questions:

1 Complete degree of PLM areas: how many dimensions that need to be studied to cover all of the necessary PLM themes to get comprehensive results; 2 Relative importance of dimensions to the overall PLM maturity level: needed to strategize for allocation of structural weights of different dimensions based on different business needs. Next step, we will propose a maturity model which can solve these two questions.

Maturity Model to Assess Maturity Level of PLM Components

This paper has considered viewpoints of different maturity models, analyzed success factors and key performance indicators of each component, then proposed a PLM Maturity Model called PLM Components Maturity Assessment (PCMA). This maturity model follows the principle structure of capability maturity model by using the same maturity levels and structured questionnaires. CMMI defined process maturity is developed incrementally from one level to the next level and it does not allow for skipping levels. This limitation of CMMI will result in misleading interpretations. This work gives detailed information of fifteen components in each maturity level in which the maturity is assessed separately, and the items of maturity descriptions are outlined in Table 3. 4 summarizes on what needs to be accomplished for "People" dimension in each maturity level. In order to simplify assessment work, avoid missing information, and improve the measurement of progress, we propose KPIs for each dimension, develop questionnaires, and obtain maturity scores based on KPI. For example, we outline the overall KPI of "people" dimension; the maturity score range of "Level 1" is 0-1, the maturity score is 0.5 for each KPI, the maturity score of "People" dimension is the average of all KPIs' score. Similarly, we can obtain the maturity score of every dimension.

Selection the Optimal PLM Components based on Company Requirements

The AHP method is a multi-criteria, multi-item decision-making technique [START_REF] Vansnick | A Critical Analysis of the Eigenvalue Method Used to Derive Priorities in AHP[END_REF]. It involves in structuring multiple criteria into a hierarchy and assessing the relative importance of these criteria, while comparing alternatives for each criterion, and obtaining an overall ranking of the alternatives. This process has been conceptualized as a hierarchical composition of 'Goals', 'Criteria', and 'Alternatives'. Selecting the optimal PLM components based on business profits can be approached by the AHP method. The objective is to choose PLM components in the TIFOS framework represented by O1 (TechnoWare), O2 (InforWare), O3 (FunctionWare), O4 (OrgaWare) and O5 (SustainWare). The features of O1-O5 can be selected as "Criteria" in the second hierarchy. Each criterion is individually connected to the competing alternatives, which come from PLM components (T1-T15), (limited in the examples given in this paper to T9).

We first determine the priorities of each PLM component. Priorities for each criterion are calculated from their importance in reaching the goal. The priorities are then combined throughout the hierarchy to get an overall priority for each component. The component with the highest priority will be the best alternative, and the ratios of PLM components' priorities indicate their relative importance to the goal. The decision process is described in depth in Figure 1.

Fig. 1. AHP calculation steps

In figure 1, the equation to get overall weights (step 6) is:

(1)
Where, W j is the priority value of the alternative j; W i is the priority value of criteria i; a ij is the priority value of the alternative j related to criteria i. m is the number of alternatives and n is the number of criteria.

) ,..., 2 , 1 ( ∈ ∀ ) ,..., 2 , 1 ( ∈ ∀ = 1 = m j n i a w W n i j i i j ∑

Case Studies

This section focuses on case studies. Two parts are studied in this section: evaluating PCMA for a particular unit to get a maturity score; and choosing the right PLM components from the defined business targets. Experimental data and important information have been collected by interviewing the managers of an Italian prefabrication company.

We calculate final maturity score per PCMA dimension by calculating the weighted sum of the KPIs in each dimension; and determine the overall PCMA maturity as the mean score of the fifteen dimensions. The result can be seen in the radar chart (figure 2) showing the level of achievement for each dimension (limited in the examples given in this paper to T6).

Our work developed AHP methodology and derived priorities of PLM components. Describe the components' weight by using the descending order in figure 3. We define business profit goals as 'Reduce time-to-market' and achieve features of it as criteria, while adopting fifteen PLM components as alternatives. PLM components' weight is shown in figure 4.

Figure 2 shows the average score over all assessments. The yellow line represents the as-is situation. Among six dimensions, PLM applications are scoring highest with 3.8, and financial management scores lowest with 1.9. The overall maturity score is 2.76. From figure 3, we can obtain which PLM component is relatively important in the TIFOS framework. Figuring out strengths and weaknesses of PLM components in figure 2 and analyzing components relative importance in figure 3; we can work out future maturity scores of PCMA (blue dash line in figure 2). According to figure 2 and figure 3, the PLM application component helps to gain more profits than the other components, therefore, recommending the company to strengthen management of this component. In figure 4, when a business profit goal is 'Reduce time-to market', the optimal PLM components that should be selected are: PLM Applications, and Business Management.

Business actions are blind to many PLM components. However, this model, it is convenient to figure out which component is more important and improve. In conclusion, it is beneficial for the companies to make well educated choices when choosing the right PLM components by using less effort and time.

Conclusion and Future Work

This research work proposes an extension of the TIFO framework by adding Sustainability. This new framework, TIFOS, can cover entire functionalities of PLM and contains all PLM components. We introduced PCMA maturity model to evaluate the performance of each PLM component based on TIFOS. PCMA maturity score is given by assessing the characters and KPIs, which can entirely cover all PLM areas and reflects the strengths and weaknesses of PLM components. Then we selected optimal PLM components in TIFOS by developing AHP methodology, which is a weighting process in competing alternatives via pair-wise comparison matrices. Finally, we have done an experimental study to achieve PCMA as-is and to-be maturity scores, to select the optimal PLM components based on weight priorities.

The future work will use more realistic data to examine the effectiveness of the PCMA Model, concentrate on the consistency ratio of AHP, and test criteria and KPIs validations. Then we will develop Fuzzy AHP method to handle the uncertainty of the collected data.

Fig. 2 .Fig. 3 .

 23 Fig. 2. PCMA Maturity Score

Fig. 4 .

 4 Fig. 4. PLM components' ranking based on 'Reduce time-to-market' goal

Table 1

 1 . Fang et al. developed sustainable manufacturing metrics to measure sustainability performance in entire product lifecycle based on the first three dimensions (Fang et al., 2010). Trotta et al. analyzed important tools to formalize information and knowledge for sustainable new product development in companies (Trotta et al., 2010). We investigated the literature studies to give a list of 19 successful sustainability indicators based on four dimensions (

Table 1 .

 1 ). Successful sustainability indicators to obtain sustainable PLM from literature Now we will define how many important components PLM has and what they are on the basis of the TIFOS framework. Stark et al. presented that PLM is a holistic approach, which contains nine PLM components: products, data, applications, processes, people, work methods, and equipment (Stark et al., 2011). Abramovici et al. defined five PLM levels; every PLM levels is described by several concrete PLM components that can have interdependencies with other components

	Dimensions Sustainability indicators	Dimensions Sustainability indicators
	Economy	Investment	Society	Labor Practices
		Economic performance		Human Rights
		Product Presence in the		Social influence
		market
		Green Process Design		Product Responsibility
		Green Manufacturing		Eco-design Responsibility
	Ecology	Energy emissions		Innovative new materials
				care
		Carbon Foot Print	Technology Life Cycle Assessment
		Waste Reduction		Design for Environment
				tools
		Water Usage		Zero Emissions &Waste
		Compliance
	2.3 PLM components

Table 3 .

 3 PCMA Maturity Level and Corresponding ContentPCMA serves the goal of measuring, monitoring, and comparing PLM components in relative and absolute terms. It provides a holistic assessment for fifteen PLM components based on a comprehensive set of key performance indicators (KPI) in each maturity level. Table

	Maturity Levels	CMMI(Short Description)	Our Work (Items for Maturity Levels)
				The activity is done with expediency
				Nobody is responsible for PLM
	1 ad-hoc	Process unpredictable		Documentation is at the lowest point to satisfy operational needs
				PLM software system and processes have
				deficiencies


Yu Yan
email: yu.yan@irccyn.ec-nantes.fr

Emilie Poirson

Fouad Bennis

Integrating User to Minimize Assembly Path Planning Time in PLM

Keywords: path planning, virtual reality tools, assembly, manipulation, perception assessment

Assembly and disassembly verification plays an important role in Product Lifecycle Management (PLM). Mass customization and personalized production require greater agility of industrial manufacturers, and consequently the time consumed in assembly processes (which often dominates costs) is of growing importance. Narrow passages which commonly exist in assembly tasks become a bottleneck in the assembly planning process reducing the time saved by using virtual assembly. In this paper, we present a novel interactive motion planning methodology for virtual assembly and disassembly operations. In our method, user's manipulation with force feedback device in difficult scenario is liberated by relaxing collision constraints. The rough path is retracted by our random retraction method and then connected by BiRRT algorithm. For each user's operation, a path successfully passing through the narrow passage is presented, or geometrical interference information in failed case is provided for motion re-planning and design modification. Significant improvement for trajectory planning of non-convex object is observed in challenging 2D scenarios with narrow passages.

Introduction

Path planning in assembly and disassembly has significant influence on many processes in product lifecycle from virtual assembly for design verification [START_REF] Ferré | Progresses in Assembly Path Planning[END_REF] to parts removal for maintainability studies [START_REF] Santochi | Computer Aided Disassembly Planning State of the Art and Perspectives[END_REF] and robot assembly for automatic production [START_REF] Kohrt | An Online Robot Trajectory Planning and Programming Support System for Industrial[END_REF], shown as Fig. 1. Assembly is capstone process in manufacturing and one of the most cost effective approaches to high production flexibility [START_REF] Hu | Assembly System Design and Operations for Product Variety[END_REF]. In recent decades, virtual prototyping is already widely applied in industry to lower the cost of production and shorten the production cycle time. The virtual assembly based on 3D CAD model can make the designer intuitively verify the assembly or disassembly operations. However, due to disappearance of some perceptions and shortage of human-computer interaction technology, the virtual assembly presents new challenges to the designers as well [START_REF] Lim | Haptic Virtual Reality Assembly-Moving Towards Real Engineering Applications[END_REF]. Some of the manual manipulation of 3D object in complex virtual environment is extremely difficult [START_REF] Ferré | Progresses in Assembly Path Planning[END_REF].

Defining the assembly process as a precise description of how to move the target part gradually from its initial location to the goal location while never touching the obstacles, sampling based motion planning algorithm search a discrete path with connectivity in part's configuration space. Among this category of algorithm, Rapidly Exploring Random Trees (RRTs) have been successfully used to solve high level degree of freedom motion planning problems [START_REF] Kuffner | RRT-connect: An Efficient Approach to Single-Query Path Planning[END_REF]. However, narrow passages which commonly exist in assembly tasks become a bottleneck restricting time reduction of assembly process in PLM. Despite that different heuristics have been created to improve the performance of automatic algorithms, narrow passages are still major issue for sampling based method.

Fig. 1. Path planning for assembly/disassembly applied in product lifecycle

In contrast, humans have the abilities to globally plan motion in complex environment. Based on experience and perception to 3D environment, humans can make fast judgments and response. The skills human lack is accurate computation on geometry. Humans and computer may both encounter trouble in narrow passages. However, when relaxing collision constraints, it's easier for humans to find a solution.

Moreover, the PLM process impulses on information sharing with all the internal and external actors of companies [START_REF] Duigou | A Constraints Driven Product Lifecycle Management Framework[END_REF]. However, the automatic algorithms cannot fulfill the gap between users, designers and assembly experts. For example, the designers have to take into account the emotion and perception evaluation of user in maintenance study. At present time, it's difficult to model humans' preferences and perceptions in assembly process, even with semantics description. In [START_REF] Duigou | Generic PLM System for SMEs: Application to an Equipment Manufacturer[END_REF], authors indicated that the closed-loop PLM is more valuable when the interaction is direct between the company and the end user of product. Therefore integration of user into planning process is essential.

In this paper, we present a new interactive frame. Combined with human manipulation, retraction and RRT planners, we allow users guide the computer in difficult scenarios. Human's participations can accelerate the algorithm as well as make final path in compliance with users' operating preferences. And in reverse, the interaction process can indirectly extract the experience knowledge from assembly experts and operational preferences of end users.

The paper is organized as follows: in section 2, we provide a brief survey of related work in interactive planning. In section 3, we descript the interactive loop which integrates human manipulation, our random retraction method and BiRRT planner. Simulation results are presented and analyzed in section 4. Section 5 is dedicated to an outlook on future work and the conclusion.

Related Work

User's participations in motion planning process emerge in different prior works. Algorithm in [START_REF] He | Haptic-Aided Robot Path Planning Based on Virtual Tele-Operation[END_REF] allow users specify some critical via configurations or sub-goals in workspace visually with haptic devices to accelerate the exploration of sampling based algorithm. However, in practical implementation, via configurations in tightly clustered environment is unlikely to be found by human.

A preliminary workspace discretization is done based on decomposition algorithm, and then a corridor between initial configuration and goal configuration is found. Harmonic functions are formulated to provide force feedback, or sampling based method explores this corridor to find a feasible path [START_REF] Vazquez | Haptic Guidance Based on Harmonic Functions for the Execution of Tele-operated Assembly Tasks[END_REF].

Method proposed by [START_REF] Patil | Interactive Motion Planning for Steerable Needles in 3D Environments with Obstacles[END_REF] is successfully applied to interactive motion planning for steerable needles, but difficult for non-convex assembly object. Although method proposed in [START_REF] Taï X | Human Interaction with Motion Planning Algorithm[END_REF] simultaneously allows cooperation between user and algorithm, it's still unable to tackle the situations when user and algorithm both get into trap.

As far as we observed, the existing work can neither apply to highly complex packaging scenarios in mechanical industry nor drive design for assembly processes. The proposed method integrates user to significantly reduce the assembly path planning time in different phases of product lifecycle. Based on the feedback of geometric interference information and ease of operation for inexperienced users, our method strengthens the information flow between user, designer and assembly expert.

Interactive Motion Planning Process

Approach Overview

The global view of our interactive assembly motion planning framework is presented in Fig. 2. The more detailed description of process is presented in Fig. 3. The path marked green is user manipulated path. This rough path is then retracted to produce seeds (marked blue) on C-contact space by our Random Retraction Method. BiRRT algorithm explores between every neighboring two seeds to find a connecting path. The algorithm either finds a solution from 1 q to 8 q shown as Fig. 3 (a), or return the nearest configuration pair (marked red) shown as Fig. 3 (b).

User Manipulation

Based on the fact that user can effectively finish the assembly task in a loose space, we firstly allow user manipulate mechanical parts with some penetration into obstacles. In this manner, user will quickly find a rough path with some configurations in-collision and close to the boundary of C-obstacle space. At the same time, the rough path satisfies user's operating habits and preference. In this process, users can choose any kind of interactive devices, no matter using cheap haptic devices or expensive movement tracking system. Moreover, we take a strategy that raise the sampling rate during capture of the human assembly process when user's operations encounter collisions more frequently and decrease it in opposite situation. This strategy will increase computational efficiency as well as guarantee a perfect description for human's operations in narrow passages.

Algorithm: Random Retraction Method (RRM) input: Path J(q 1 ,…,q i ,…,q n ), Obstacles; for all i do if collision(q i ) = true then PD = Penetration_Depth(q i ,Obstacles); *[SL T ,SL R ] = initial(); while PD > threshold(PD) do D random = Random_direction(SL T , SL R ); q new = Move(q i ,D random ); PD new = Penetration_Depth(q new , Obstacles); if PD new < PD then q i = q new ; (SL T ,SL R ,PD) = (SL T *2,SL R *2,PD new ); else q new = Move(q i ,~D random ); PD new = Penetration_Depth(q new ,Obstacles); if PD new < PD then q i = q new ; (SL T ,SL R ,PD) = (SL T *2,SL R *2,PD new ); else (SL T ,SL R ) = (SL T /2,SL R /2); end if end if end while end if end for J = Smooth(J) end * T SL Translation step length, R SL Rotation step length.

Random Retraction Method

Due to the high computational complexity of global penetration depth, retraction based planners use simple heuristics to explore C-contact space [START_REF] Rosell | Motion Planning for Haptic Guidance[END_REF]. For example, the algorithm starts from a rough solution and iteratively refines it through shrinking the obstacles and relaxing the collision constraints [START_REF] Ferré | Progresses in Assembly Path Planning[END_REF]. Algorithm proposed by [START_REF] Bayazit | Enhancing Randomized Motion Planners: Exploring with Haptic Hints[END_REF] allows users generate path by shrinking the object, then improve user-generated path by pushing the in-collision configuration directly to collision-free.

Through defining certain types of distance metric on configuration space, retraction process can be formulated as an optimization problem. In [START_REF] Zhang | An Efficient Retraction-based RRT Planner[END_REF], authors use geometric method simulating optimization to get the nearest collision-free configurations in C-contact space. As the boundary of feasible solution region is the C-contact space, and the computation of C-contact space is too complex at present time. Conventional optimization algorithms are either impossible to implement or time-consuming. We provide a randomly retracting method which is based on penetration depth. Compared to pattern search optimization algorithm which uses mesh at each iteration to search a descent direction, our randomly retracting method uses random direction at each step which makes penetration depth value decrease. We also enlarge the step-length when search is successful and reduce it when search is failed. Variable step-length can effectively overcome burdensome computation of penetration depth. Our method will find a solution which is on C-contact space and near to the optimal one.

Seeds Connection

After retraction, the user manipulated path is transformed into seeds which consist of some collision-free configurations and some configurations on C-contact space. The following process is similar to multi-tree RRT. We use BiRRT algorithm [START_REF] Kuffner | RRT-connect: An Efficient Approach to Single-Query Path Planning[END_REF] to connect every neighboring two seeds. Since the neighboring two seeds are close to each other, it's pretty easy for BiRRT planner to find a path between them. In case of that motion planner fails to find a solution within a limited time, we return the nearest configuration-pair in workspace. The interference information is easy to obtain through contact between the configuration-pair and obstacles. The user can make movement adjustments or modify the design size of parts according to the information.

Implementation and Results

The following section describes how our interactive system works for the motion planning of a non-convex part passing through a narrow passage. We also demonstrate that the interaction with user equipped by a force feedback joystick can greatly decrease the search space.

All the experiments are performed in the software platform Matlab and on a PC Dual Core, 2.4 GHz and 2 GB ram.

User Manipulation

In implementation, user manipulates the part in 2D environment with Logitech Force 3D Pro force feedback joystick. The moving object is allowed to have limited penetration into obstacles, which means that the maximum penetration is set by user and any part of the moving object is forbidden to penetrate through the obstacle. And we allow moving object have large penetration into obstacle, but only have collision with one obstacle at the same moment. User can decide the beginning and end of the motion recording time.

Collision check is realized by detecting the intersected edges between two polygons. Penetration depth is realized by calculating the area of overlap region between two polygons.

Results

In the situation of Fig. 4, user has to manipulate an L shape part passing through a hole of a wall in 2D environment. The moving part has three degrees of freedom. In this case, the hole is narrow enough that the planning with strict collision detection is time-consuming for both user and basic BiRRT planner. By relaxing the collision, user can quickly manipulate the part pass through the hole, as shown at Fig. 4(a). This rough path manipulated by user is then retracted as shown at Fig. 4(b) and corresponding path in configuration space shown at Fig. 4(d). As the number of configuration recorded for retraction is small, the retraction process doesn't require much time. From every neighboring two configurations of retracted path, two trees (marked green and blue) are grown by BiRRT algorithm to connect each other, as shown at Fig. 4(e). A path successfully passing through the hole is found quickly by our interaction method shown at Fig. 4 (c) (f). In reason that our retraction process provides guidance to exploration of BiRRT, the number of visited configurations and tree search time of BiRRT algorithm are greatly reduced, as shown in Table 1. This result can be observed intuitively through comparison between the exploration trace of basic BiRRT algorithm in Fig. 5 and our interactive process in Fig. 4. From Table 1, we can also find how fast the random retraction process is, which only takes 1.239 seconds for 5 times retraction. We also make the comparison in cases of different radius of hole. For each radius of hole, we run both of the algorithms 5 times respectively, and take the average time. The results are demonstrated in Table 2 and Fig. 6. In challenging situation when the radius of hole is 5, the basic BiRRT will spend more than one hour to find a feasible solution. While in opposite, our method runs about 10 seconds. Moreover, in easy situations, our method also needs less time for planning. Through comparison, our interaction method appears more robust and efficient in planning motion of non-convex part in narrow passage.

In Fig. 7, the hole is designed too small for the part to pass through. However, intuitively detecting the infeasibility is difficult for user in advance of planning. In condition of relaxed collision, user can manipulate the part passing through the hole shown as Fig. 7 (b). After retraction process (shown as Fig. 7 (c) (d)) and connection process (shown as Fig. 7 (e)) of our method, the nearest configurations respectively locating at entrance and exit of the narrow hole can be returned to user, shown as Fig. 7 (f). As a result, the designer can understand the size limitations of accessibility for a product design.

Conclusion and Future Work

In this paper, we present an interactive path planning framework for assembly/disassembly process of PLM. Based on randomly retracting method, our method can make user and automatic planner efficiently work together to overcome narrow passages with very tight tolerances. Planning time for assembly task can be greatly reduced. Moreover, our method provides visualized geometric interference information feedback to designer, thereby facilitating designer's understanding to change and shortening design cycle time. As the generated paths comply with user's operating habits and preferences, some ergonomic issues can be quickly checked at early phase.

In future work, we will implement our interaction method in industrial cases within virtual environment. It is possible to implement different interactive device for user in virtual world such as 6dof haptic devices or motion tracking system. It is also necessary for us to make a choice on different penetration depth algorithms that can be applied to our retraction method. Although our system performs perfectly in 2D environment, it still faces some challenging issues in 3D, which includes providing deeper insights on measuring human perception in virtual assembly and facilitating user understand environment from feedback.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Interactive motion planning process

Fig. 4 .Fig. 5 .

 45 Fig. 4. Successful case for an L shape part passing through a narrow passage

Fig. 6 .

 6 Fig. 6. Comparison between basic BiRRT and our interactive process

Fig. 7 .

 7 Fig. 7. Failed case for an L shape part passing through a narrow passage

Table 1 .

 1 Comparison between basic BiRRT and our interactive process in case of radius = 5

							T all	(s	)			T C	(s	)	R T	(s	)	S T	(s	)	node Num	R Num
	Basic BiRRT				111.253			109.87	N/A		1.383	354	N/A
	M-interactive			13.023			9.1900	1.239		2.594	93	5
	T		T	,	T		T	,	T		T	,	Num		Num	,	Num		Num
	C		Connection	R		Retraction		S		Smooth		node			searched	R	Retraction

Table 2 .

 2 Comparison between basic BiRRT and our interactive process in case of different radius

					Mean
	Hole Radius				5	6	7	8	9	10
	Basic BiRRT:	T	(s	)	>2,901	>1,090	280.397	17.735	15.838	12.268
	M-interactive: ) (s T	13.91	15.314	13.965	11.676	6.291	6.771


Mickaël David
email: mickael.david@univ-nantes.fr

A Few Guidelines for a Good Usage of PLM Software

Keywords: PLM Tools, NPD Process, Informational Integration, Agency, Rules of use

Softwares providers offer PLM solutions to support the homonym organizational approach, especially during New Product Development (NPD) process. However these tools are not a panacea. This communication takes its theoretical and methodological foundations in management science. We seek to understand how managers can influence the users so they make a good use of their PLM tool. We analyze the case of a car manufacturer that has purchased a PLM software eight years ago. Our qualitative approach has allowed us to highlighting the importance of managerial action and regulation for an efficient use of PLM tools. On a theoretical level, we use the PLM features in line with Grieves to determine the informational integration effectiveness permitted by the tool. We propose some extensions to the sociomaterial typology of agencies recognized in Information Systems literature. Finally, we propose some managerial guidelines for a good use of PLM tools.

Introduction

Many industrial companies have to produce more and more complex goods, while optimizing development costs and reducing time to market [START_REF] Hatchuel | Design-oriented organizations[END_REF]. A major concern in this sector is being able to handle the various facets of a product (manufacturing, logistics, recycling...) in a comprehensive manner as soon as its design phase. However, the New Product Development (NPD) process is distributed among different organizational functions, and regularly inter-organizational [START_REF] Merminod | How does PLM technology support knowledge transfer and translation in new product development? Transparency and boundary spanners in an international context[END_REF]. Informational integration including sharing of updated documents is thus critique. IT vendors offer packaged Product Lifecycle Management (PLM) solutions to meet this challenge [START_REF] Ameri | Product lifecycle management: closing the knowledge loops[END_REF]. The Literature recognizes three functional subsystems within these solutions: 1°) Organizational Memory System (OMS) with storage, classification and research features; 2°) Project and Resources Management System (PRMS), with workflow, monitoring and milestones features, and 3°) Collaborative Work System (CWS), with viewer features and management of files by their status [START_REF] Nambisan | Information Systems as a Reference Discipline for New Product Development[END_REF], [START_REF] Pavlou | From IT leveraging competence to competitive advantage in turbulent environments: The case of new product development[END_REF]. However these softwares sold in the market are not a panacea, their potential must be activated [START_REF] Leonardi | Activating the Informational Capabilities of Information Technology for Organizational Change[END_REF]. In management science, many researchers consider the organizational performance as an emergent, technical and social, construction [START_REF] Desanctis | Capturing the Complexity in Advanced Technology Use: Adaptive Structuration Theory[END_REF]. In this communication, we seek to understand the construction of a performing use of the PLM softwares (i.e. here, a use permitting to improve the informational integration of NPD process). To do this, we have to identify the different causes enacting the idiosyncratic usage of the PLM software in an organization (see 3.1). We are not trying to determine what a good tool is but what a good use of this PLM tool is. Finally, we wish to be able to propose guidelines for a good use of PLM tools.

State-of-the-art

The potential of these complex softwares must be activated during the implementation project. A "fit" between the users' practices (and others organizational specificities) and the IT solution must be created [START_REF] Strong | Understanding Organization-Enterprise System Fit: A Path To Theorizing the Information Technology Artifact[END_REF], [START_REF] Garetti | Organisational change and knowledge management in PLM implementation[END_REF]. However, a perfect fit seems impossible to obtain. The user's practices are too different and conflicting between them and with the organizational interest. This irreducible "misfit" is called "imposition" [START_REF] Strong | Understanding Organization-Enterprise System Fit: A Path To Theorizing the Information Technology Artifact[END_REF]. This potential of the software must be also activated by a good use of this solution. The term "infusion" of the technology is generally used to denote the complete appropriation of the tool spirit by users [START_REF] Cooper | Information Technology Implementation Research: A Technological Diffusion Approach[END_REF], which leads them to propose new developments of the solution or new virtuous uses of the existing solution [START_REF] Leonardi | Activating the Informational Capabilities of Information Technology for Organizational Change[END_REF]. A collective appropriation of the software (i.e the users' capacity to effectively use the solution's functionalities when it's necessary, and only when it's useful) is an important asset for an organization [START_REF] Pavlou | From IT leveraging competence to competitive advantage in turbulent environments: The case of new product development[END_REF]. This appropriation need to be managed [START_REF] Jasperson | A comprehensive conceptualization of postadoptive behaviors associated with information technology enabled work systems[END_REF]. In this vein, workaround phenomena and resistance to use the tool are not necessary blamed. They can result from a second type of misfit called "deficiency" [START_REF] Strong | Understanding Organization-Enterprise System Fit: A Path To Theorizing the Information Technology Artifact[END_REF]. These phenomena can be the premise of the invention by users of new virtuous uses which are not foreseen by the solution designers [START_REF] Ferneley | Resist, comply or workaround? An examination of different facets of user engagement with information systems[END_REF], [START_REF] Boudreau | Enacting Integrated Information Technology: A Human Agency Perspective[END_REF].

Construction of our analytical model

Our analytical model is composed of a typology of causes of the IT use (independent variables) and of an informational integration model (dependent variable).

The causes of the idiosyncratic use of a PLM tool

We mobilize the concept of agency from the structurationist paradigm as it has been regularly used to answer this issue of the idiosyncratic use of PLM tools [START_REF] Desanctis | Capturing the Complexity in Advanced Technology Use: Adaptive Structuration Theory[END_REF], [START_REF] Leonardi | When Flexible Routines Meet Flexible Technologies: Affordance, Constraint, and the Imbrication of Human and Material Agencies[END_REF]. Agency is conceptualized as a spatiotemporally located expression of a material or social structure influencing determination of actual action, in this case the use of the tool. Leonardi [START_REF] Leonardi | When Flexible Routines Meet Flexible Technologies: Affordance, Constraint, and the Imbrication of Human and Material Agencies[END_REF] makes a distinction between material agency and human agency. We separate the individual form of human agency and its organizational form represented by prescribed or emergent collective rules of use (Fig. 2). We make again two distinctions in order to refine our analytical model: first, on the subject of these organizational rules between NPD process and PLM tool use; second, between intrinsic material agency (resulting from the basic structure of the tool) and extrinsic material agency (resulting from tool parameter settings wanted by the organization, and therefore which is a transfiguration of an organizational agency to a material agency). Regulations are then captured by the organizational agency (NDP or PLM) and by the extrinsic material agency of the PLM tool. The intrinsic material agency and the individual agency allow us to put into perspective the need of managerial rules (by increasing it or decreasing it).

Informational integration per se

Informational integration is often inferred from consequences presumed to cause (including coordination [START_REF] Hoopes | Shared knowledge, "glitches," and product development performance[END_REF]), but it is rarely grasping per se [START_REF] Patnayakuni | Managing the Complementarity of Knowledge Integration and Process Formalization for Systems Development Performance[END_REF]. Inspired by the characteristics of PLM tool, Grieves proposes six characteristics of product information integration: correspondence, singularity, traceability, differentiated availability, cohesion of representations and reflexivity [START_REF] Grieves | Product lifecycle management: driving the next generation of lean thinking[END_REF]. These characteristics are consistent with the four phases of organizational memory generally used in the literature [START_REF] Walsh | Organizational Memory[END_REF] as well as with the Patnayakuni, Ruppel et Rai's model of informational integration [START_REF] Patnayakuni | Managing the Complementarity of Knowledge Integration and Process Formalization for Systems Development Performance[END_REF]. However, the characteristics of PLM tool have two advantages over the current informational integration model: the consideration of the acquisition phase and the consideration of the notion of parsimony by the differentiated availability of items (Fig. 1).

Fig. 1: Comparison of informational integration models (adapted from references).

The information acquisition must be comprehensive. The correspondence* 1 is required between the information richness contained in PLM tool and the complexity of reality. The information acquisition must also be non-redundant. A singularity* of objects for the same information facilitates their updating. The information storing represents an informational integration with past tasks/phases. This integration is characterized by an easy accessibility to historical data design#, especially permitted by their traceability*.

1 * items from Grieves [START_REF] Grieves | Product lifecycle management: driving the next generation of lean thinking[END_REF], # items from Patnayakuni, Ruppel et Rai [START_REF] Patnayakuni | Managing the Complementarity of Knowledge Integration and Process Formalization for Systems Development Performance[END_REF]. The information diffusion must be efficient. Under condition of information portability#, only the information needed must be presented at user, and in a relevant way. The availability is differentiated* by the user's interest. However, this personalization should not prevent the cohesion of virtual representations* and it should preserve the coherence of the logical model#. The aim is mutual understanding of different trades without loss of semantic information#. Finally, informational integration implies that any change to the environment captured by the system is communicated# in order to produce the necessary consequences about its use (the reflectivity* in the Grieves' terminology).

The Results of the Case Studied

The case is a car manufacturer SME that designs, manufactures and assembles kits. The design and methods office is divided into four products families. There are forty PLM tool users; half of them work in the design and methods office.

The solution has been implemented between 2002 and 2004 by a phased deployment is Smarteam of Dassault Systemes. The available PLM functionalities are limited compared to functionalities offered on the market (no workflow, no project monitoring). In addition, the junction with the enterprise system is not carried out. Then, the PLM tool is used as an electronic documents management server offering some collaborative features. The results will be presented successively depending on the informational integration model (Fig. 2).

Information Acquisition

The correspondence (or completeness) is examined in width and breadth. The principle of formalization is inherent to design office work; the individual agency and the NPD organizational agency are congruent. The PLM functionalities (interfaced with CAD software) lead Smarteam to almost exclusively support technical information on product, such as CAD or DXF (Drawing eXchange Format) files, plans, test and accreditation reports; an intrinsic material agency supports the correspondence of this information with reality.

With regards to the information depth, the expected level of product detail by major car manufacturers is greater than that expected by this enterprise for its product on own-brand. Major car manufacturers require their parts are fully defined. However, a part's product on own-brand is described in order to provide ease of assembly. Thus there is a NDP organizational agency on a more or less important detail degree of CAD files. These agencies coincide for that product information has a good correspondence with reality, both in width and breadth (less for the products on own-brand).

The information singularity is in particular obtained by the absence of multiple individual agencies. There is only one designer per team because the design and methods office is divided into products families (NPD organizational agency). In these conditions the PLM tool becomes the single source of product information without difficulties (as wanted by the organization) through its shared server and its indexed incrementing of files (intrinsic material agency). However, interoperability problems sometimes require records in various formats and/or on different servers (adverse intrinsic material agency).

The acquisition phase of product information meets the correspondence criterion and meets relatively well the singularity criterion. This effectiveness is enabled by the overall convergence of various organizational, material and individual agencies. However, the information singularity appears to be the result both of the reduced structure of the organization and of the intrinsic properties of the tool.

Information Storage

The documentary retrieval and the traceability are only partially effective. The documentary ontology of PLM tool (extrinsic material agency) supports generally the various attributes of product information. The users dispose of search unique keys as plan number for example. However, designers are allowed to create their own folder in the tool directory tree (no extrinsic material agency). Thus, designers are free to organize the project folder as they want, to store anything they want in this folder, but especially they are free to name their files the way they want (individual agency/absence of PLM organizational agency). Eight years after the implementation of PLM tool, this absence of standardization of PLM use rules leads to time-consuming consequences. The designers have difficulty to retrieval a document if they are not the creator of it or if the document is "stored" in a folder which they are not accustomed. The peripheral users, such as those of manufacturing workshop or warehouse, use only the search keys and refuse a visual search in the directory tree without being leading by a designer by phone. Documents such as procedures have not attributes offering specific search keys. They are therefore particularly susceptible to problems resulting from the weak structuring of the directory tree. In addition, the NDP organizational agency promotes an accounting perspective on the project perimeter: a project is an annual expenditure commitment. Then there are as many folders as calendar years for a same technical project. This causes an expansion of the directory tree increasing the difficulty of visual search.

Storage and retrieval are therefore only partially effective (because it is sometimes laborious) despite the various features offered by PLM tool (intrinsic material agencies). It seems that the company has relied too much on the intrinsic properties of the tool. Despite the small size of the company, several users work on the same project and must access to the same documents. This common tool requires common rules of use (i.e. standards that counteract the multiplicity of individual patterns of use) especially in structuring of directory tree and in description of items.

Information Diffusion

Differentiated availability is only partially effective too. We analyze it with two points of view: static and dynamic.

Only documents having the last index are available for manufacturing workshop. However, despite the structuring of organization by products families, everyone has access to the folders of others products families. User profiles are not fully utilized (partial extrinsic material agency). In a dynamic point of view, the PLM tool does not contain workflow functionality (not intrinsic material agency). The information transfer by PLM tool is mainly pulled by manufacturing workshop or quality department. The designer (individual agency) is the pilot of the design and he pushes the information when he needs it, especially for prototyping. A procedure of electronic diffusion of technical notes via email (with a link to the document in Smarteam) has recently been implemented (PLM organizational agency). For some, the e-mail inbox provides a more efficient search engine than the one of Smarteam.

The partial formalization of the availability is based on the individual responsibility.

In the retrieval case, the users have to differentiate useful information and in the filing case, they have to find the appropriate location storage of the document.

Cohesion of virtual representations (not mental) calls several objects of representation: the directory tree, the product geometry or the technical domain of product. The directory tree of a project is the same regardless of the user, so there are no distinct representations. However, we have seen, the directory tree is subject to the accountant constraint (adverse PLM organizational agency). Then the geometric vision of object in 2D (plan) is automatically generated from the CAD file (favorable intrinsic material agency). Finally, the electrical design is not integrated in mechanical CAD files because the CAD softwares (respectively Electra and Catia) are not interfaced (adverse intrinsic material agency). Due to the weak coupling of these two technical areas, the electrical design is realized according to the CAD file after mechanical design (adverse NPD organizational agency).

In information diffusion phase, the criterions of differentiated availability and of representations cohesion are only partially effective. Differentiated availability is only permitted by individual efforts and the pressure exerted by individuals to build better practices of PLM use. Regarding to cohesion of representations, only one between the plan and the CAD file seems to be sought by the organization.

Information Use

The criterion of information reflectivity translates into an automatic mechanism by the tool: an alert for updating of all products using a part/item which has just been modified (intrinsic material agency). This constraint of tool is not always respected because the added value of the operation is too weak compared to the time required to do it. This is legitimized by the collective criterion of weak impact on the product manufacturing. A NPD organizational agency counteracts the intrinsic material agency for time consuming tasks. Products having a long life-series have therefore a large number of inconsistency markers between the different versions of the parts and assemblies. In addition, the absence of intrinsic material agency regarding the technical integration of PLM tool with ERP tool does not permit to draw all consequences in terms of use cases and nomenclatures.

Summary of the results

The figure 3 summarizes the results. The intrinsic material agency -the inherent properties of the tool -contributes to the effectiveness of informational integration in its various phases. However in this case, this contribution is lower on the last phases because there is neither workflow nor integration of CAD softwares and nor integration with ERP. The individual agency -the will of the individuals -has an ambivalent contribution: it generates a heterogeneity of practices (singularity, storage and retrieval), but it is also at the initiative of adaptive and palliative behaviors to functional deficiencies of the tool (storage, search and retrieval, differentiated availability).

The extrinsic material agency -the parameter settings of the tool -does not seem necessary for the acquisition or use phases. However, it is necessary to optimizing the directory tree, the ontological structure of the database and the differentiated access to information by the individuals' digital profile.

The PLM organizational agency -the rules of PLM tool use -is important for enforcing shared use practices of the tool (singularity), especially for imposing the filling of attributes and naming files standards and standards of structuring of directory tree (storage and documentary retrieval).

The NPD organizational agency -the rules related to the NPD process -defines the degree of correspondence and the updating degree of parts (reflectivity). It regulates the information needing by structuring the project teams (singularity) and it defines the scope of project and related product information (storage and documentary retrieval).

Discussion

After eight years of using the solution, information retrieval is more difficult. Informational saturation is a risk in the medium term. The company has opted for a weak formalization and standardization of PLM uses to increase the chances of acceptance of tool by users. The daily users have integrated the underlying logic of the tool and they have gradually created virtuous uses. For instance, they use this for constituting a catalog of standard parts or for sharing documents formalizing information on the project progress or on manufacturing workshop's constraints.

It is necessary to exceed the ambivalent character of the regulation by distinguishing between aspects of the usage of PLM software that require strict rules of use and those for which users' leeway is preferable in order to activate the potential of PLM software. The leeway given to users to create, to organize their folders and to store any document (if the required documents are present) into the PLM tool seems to be a good management practice, especially for appropriation of the tool by users. However, this implies strict rules for naming files and filling of their attributes in order that retrieval functionalities can effectively operate. The consequences are that is also necessary to ensure the adaptation of the ontological structure of the tool to new uses and to formalize tasks for ensuring the maintenance of the information content of the tool.

Conclusion

This communication takes its theoretical and methodological foundations in management science. By a qualitative approach, we study how users are influenced when they use the tool and what is the performance of this use in terms of informational integration. We have developed a model to assess the informational integration; it must also be validated by more systematic studies. Although they must to check them on other cases, this case study allows us to consider a few managerial guidelines for optimize the use of the solution.

The technical integration of the PLM software with CAD and ERP softwares must be wanted because it is necessary for enabled various functionalities of PLM software.

The modeling of (changing) practices and informational environment of the NDP process should be accurate, inserted and updated in parameter setting in the tool. Some usage rules must be put in place (the filling of attributes, the naming of files and the structuring of the directory tree). It is important to not formalize the contents of the tool in order to let users set up their own personal space and uses it to develop virtuous usages of the tool. These tools are not able to forget; it's important to formalize tasks for ensuring the maintenance of the information contained in the tool.

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Fig. 2 :

 2 Fig. 2: Our analytical model (the three shaded variables are the managerial variables)

Fig. 3 :

 3 Fig. 3: Summary of the results