Vincent Wagner ♮ †

Maher Baili ♮

Gilles Dessein ♮

Daniel Lallement

Behaviour laws comparison for titanium alloys machining: Application to Ti5553

The aircraft industry uses materials more and more efficient. This trend affects the majority of parts such as structure parts. Titanium alloy (Ti-5AL-5Mo-5V-3CR) is now used for the production of landing gear. There are many goals in this paper. First, the physical and mechanical properties of the material will be presented. Secondly, we show the relationship between material properties and machinability. Third, the Ti5553 will be compared to Ti64. The Ti64 is α+β alloy group and Ti5553 is a metastable beta but we have chosen to compare these two materials. Ti64 is the most popular of titanium alloys and many of works were been made on its machining. After, we have cited the Ti5553 properties and detailed the behaviour laws. They are used in different ways, with or without thermal softening effect or without dynamic terms. We have to define the best model to use in cutting force model. Differents models are compared for two materials (steel and titanium alloy). To define the model, two methods exist that we have compared. The first is based on machining test however the second on Hopkinson bar test. These methods allow us to obtain different ranges of strain rate, strain and temperature. This comparison will show the importance of a good range of strain rate, strain and temperature for behaviour law, especially in titanium machining.

Introduction

The aircraft industry uses materials more and more efficient. This trend affects the majority of parts such as structure parts. Titanium alloy (Ti-5AL-5Mo-5V-3CR) is now used for the production of landing gear. The poor titanium alloys machinability is explained by ezugwu in [START_REF] Ezugwu | Titanium alloys and their machinability -a review[END_REF]. The Ti5553 can be classified in hard to cut material and there is a low knowledge in Ti5553. Arrazola ([2]) compares the Ti5553 and the Ti64 alloys: the Ti5553 machinability is very poor compared to Ti64 one. No cutting force model has been defined in his work. However, some works have been made on the cutting model and especially on Ti64 machining ( [START_REF] Özel | A methodology to Determine Work Material Flow Stress and Tool-Chip Interfacial Friction Properties by Using Analysis of Machining[END_REF]). The machining is a processus where stress appears according to strain, srain rate and temperature. The temperature is the result of the high level of strain, strain rate and stress. The cutting model must have a law that defines this phenomenon. There is a lot of behaviour laws and they are never used in the same ways. Moreover, few researchers study the influence of the behaviour law in model of cutting force and cutting temperature. Espacially, in hard machining material where the cutting force is very sensitive to cutting conditions. Changeux ([4]) shows the influence of behaviour law in cutting force modelling. However, his work has been made for austenitic steel. In his work, Poulachon ([5]) explains that the identification methods of behaviour law can be classified by the strain rate range. He shows the difference beetween machining strain rate and identification methods strain rates. To allow a higher range of strain rate many works ( [START_REF] Özel | A methodology to Determine Work Material Flow Stress and Tool-Chip Interfacial Friction Properties by Using Analysis of Machining[END_REF][START_REF] Tounsi | From the Basic Mechanics of Orthogonal Metal Cutting Toward the Identification of the Constitutive Equation[END_REF]) detail a method to identify the constants of behaviour law from machining.

There is many goals in this paper. First, the physical and mechanical properties will be presented. [START_REF] Fanning | Properties of TIMETAL 555 (Ti-5Al-5Mo-5V-3Cr)[END_REF] shows the Ti5553 material properties but for a non treated Ti5553. We show the relationship between material properties and machinability. The Ti5553 will be compared to Ti64. The Ti64 is ❛+❜ alloy group and Ti5553 is a metastable beta but we have chosen to compare it with this material. Ti64 is the most popular of titanium alloys and many works were made on its machining. After, we have shown the Ti5553 properties and we have seen the behaviour laws. They are used in different ways, with or without thermal softening effect or without dynamics terms. The target is to define the best model to use in cutting force model. Different models are compared for two materials (steel and titanium alloy). An other important point is the model definition. There are different ways to define the constant model. We compared two methods. The first is defined from machining test and the second from Hopkinson bar test. This comparison will show the importance of a good range of strain rate, strain and temperature for behaviour law.

Physical properties

Phase diagram

The Ti5553 is a metastable beta with a low transus beta (occurs at 845°C). The titanium alloy Ti64 belongs to ❛+❜ alloys group, its transus beta occurs at about 990 °C . In machining, this difference between the two alloys can be important. In his paper, Ozel ( [START_REF] Özel | A methodology to Determine Work Material Flow Stress and Tool-Chip Interfacial Friction Properties by Using Analysis of Machining[END_REF]) uses the Oxley model ( [START_REF] Oxley | Mechanics of Machining an Analytical Approach to Assessing Machinability[END_REF]) to estimate the cutting temperatures. He shows in [START_REF] Özel | A methodology to Determine Work Material Flow Stress and Tool-Chip Interfacial Friction Properties by Using Analysis of Machining[END_REF] that the cutting temperatures of Ti64 machining are range from 750°C to 940°C. Consequently, they are always less than the transus beta temperature. So, the titanium structure ❛+❜ and its concentration do not change.

The mechanical properties of Ti5553 compared to the Ti64 alloy are higher and the physical properties are almost the same (table 1). The cutting temperatures will be also higher when machining Ti5553 alloy. In addition to that, they are superior than the transus beta temperature, as a result, the alloy structure will be changed. The beta phase concentration becames more important. For Arrazola ([2]), the differences of structures with a variable quantity of the alpha phase and the morphology of the transfromed ❛+❜ phase can explain the poor Ti5553 machinability. This modification of phase will be important, especially in machining of structure part.

Thermal conductivity

The Ti5553 alloy have a poor thermal conductivity and can be classified like heat resistant material. The figure 1 (a) shows the thermal conductivity of Ti5553 and Ti64 alloys. Indeed, according to temperature, we can see that whatever the steel thermal conductivity is the highest. It decreases when temperature increases whereas the titanium thermal conductivity increases. If we compare the titanium values, the Ti5553 thermal conductivity is always higher than the Ti64 one. This can be a problem in machining. This poor thermal conductivity limits the heat evacuation in chip. In his paper [START_REF] Ezugwu | Titanium alloys and their machinability -a review[END_REF], Ezugwu depicts the distribution of thermal load when machining titanium and steel. In titanium machining, a large proportion (80%) of the heat generated is conducted in tool. However, in steel machining only 50% of heat generated is conducted in tool. This difference can be explained by the higher thermal conductivity of tool (60 W/m/°C) compared to titanium alloy thermal conductivity (8 W/m/°C). Whereas, for the used machining tool, the thermal conductivity compared to steel one are quite the same. The heat is being quickly conducted in tool, so the thermal softening can be easily obtained. In their models, [START_REF] Boothroyd | Temperatures in Orthogonal Metal Cutting[END_REF] and [START_REF] Oxley | Mechanics of Machining an Analytical Approach to Assessing Machinability[END_REF] demonstrate that temperatures in shear plan and at the tool-chip interface are function of thermal conductivity (equations 1 and 2).

T AB = (1 -β)F s cosα ρSt u wcos(φ -α) (1)
β = 0.5 -0.35log( ρSV t u K tanφ) (2)
Where: T AB = Average temperature in shear plan; ρ = Density; S = Heat capacity; V = Cutting velocity; t u = Undeformed chip thickness; K = Thermal conductivity; φ = Shear angle; α = Rake angle; w = width of cut; F s = Shear force.

Equation 2 defines the heat rate conducted into the part. However, equation 1 represents the average temperature in primary shear plan. When K increases, the proportion of heat conducted into the part (β) is higher and leads to a reduction of temperature in primary shear plan (T AB ).

Heat capacity

The figure 1 (b) shows a comparison between heat capacity of steel and titanium alloys. To the contrary of thermal conductivity, the heat capacity of the three materials increases according to temperature. The steel heat capacity is higher for low temperatures (575 J/kg/°C) whereas the Ti64 is the lowest (460 J/kg/°C). When the temperature increases, the Ti5553 heat capacity becomes highest (775 J/kg/°C at 600°C). This value is 20% upper than Ti64 one. For Ti5553, the increasing heat capacity between low and high temperatures is more than 35%, whereas it is only about 15% for Ti64.

In [START_REF] Boothroyd | Temperatures in Orthogonal Metal Cutting[END_REF][START_REF] Oxley | Mechanics of Machining an Analytical Approach to Assessing Machinability[END_REF] models, the cutting temperature is inversely proportional to the heat capacity (equation 1). We can see that increasing heat capacity leads to reduction of the cutting temperature. Like thermal capacity, with a high heat capacity it is difficult to obtain the thermal softening. The cutting temperature can be limited by these high values and can be less than beta transus.

Mechanical properties

Tensile test

Figure 2 shows the true stress according to true strain. This value was obtained with ambient temperature and with constant deformation speed. The Young modulus, strain, tensile yield stress (TYS) and ultimate tensile stress (UTS) were identified from the tensile test. The values are noted in table 2. First, we can say that the Ti5553 material properties values are higher compared to Ti64. The ultimate tensile stress and tensile yield stress are 20% higher. The second point is the low ductility: 0.01%. In comparison with Ti64, this value is very low and show that the Ti5553 is a brittle material. The material properties influence the machining responses and can explain the high cutting force values. The Ti5553 ultimate tensile stress is also higher even at 400°C in machining and the cutting forces are also higher. Another consquence oh high mechanical properties and poor ductility, it will be difficult to get a segmented chip.

Behaviour law

There are two goals in this section. First, we will determine the best model defining the cutting forces and temperature in machining. Secondly, we will propose the best solution to define the behaviour law.

The behaviour laws are used to determine the stress according to strain, strain rate and temperature. Some different laws are used in modeling of cutting forces and cutting temperatures. [START_REF] Oxley | Mechanics of Machining an Analytical Approach to Assessing Machinability[END_REF] uses the Hollomon model and neglects the temperature and strain rate effects. [START_REF] Puigsegur | Caractérisation Thermique d'un Procédé d'Usinage par Tournage Approche Analytique et par Identification de Système non Entiers[END_REF], [START_REF] Joyot | Modélisation Numérique et Expérimentale de l'Enlévement de Matière[END_REF] and [START_REF] Özel | A methodology to Determine Work Material Flow Stress and Tool-Chip Interfacial Friction Properties by Using Analysis of Machining[END_REF] use the Johnson-Cook law. Other models can be considered. Lindholm model defines stress according to strain and strain rate. However, it does not take into account the temperature. The Norton-Hoff law can also be considered. Johnson-Cook model seems to be the best to model the cutting forces.

σ = A + B(ε) n 1 + Cln ε ε0 1 - T -T 0 T m -T 0 m (3)
However the Johnson-Cook model (equation 3) is used in different ways. In their works, [START_REF] Puigsegur | Caractérisation Thermique d'un Procédé d'Usinage par Tournage Approche Analytique et par Identification de Système non Entiers[END_REF] and [START_REF] Joyot | Modélisation Numérique et Expérimentale de l'Enlévement de Matière[END_REF] consider an adiabatic process and neglect the heat influence in primary shear plane. They determine the shear flow stress along primary plan from the restricted Johnson-Cook law. The thermal softening effect is not inserted in restricted Johnson-Cook model. In [START_REF] Özel | A methodology to Determine Work Material Flow Stress and Tool-Chip Interfacial Friction Properties by Using Analysis of Machining[END_REF], Ozel used also this model but in its complete definition with thermal softening effect. The target is to verify these assumptions and to see if it is always true in high mechanical and poor thermal properties materials. The titanium alloys have a poor thermal conductivity and a high heat capacity. The heat is rapidly conducted in tool ( [START_REF] Ezugwu | Titanium alloys and their machinability -a review[END_REF]). The Johnson-Cook model must have the thermal softening effect to define the cutting shear flow stress. The tensile test depicts that the titanium alloy are brittle. The strain rate constant (C) must be integrated in the model.

In this first part, we set the parameters to insert into the model. To define the best model, we have compared two materials: AISI1045 steel and Ti64 titanium alloy. For each material, the Johnson-Cook model have been used in three different ways and we have compared the theoretical results (σ JC , σ JC1 , σ JC2 ) and the experimental results (σ AB ), where σ AB is effective flow stress in primary shear plan defined in Oxley model from machining ( [START_REF] Oxley | Mechanics of Machining an Analytical Approach to Assessing Machinability[END_REF]). σ JC represents the stress obtained with the Johnson-Cook model. σ JC1 and σ JC2 are the stress obtained without the thermal softening effect and without the strain effect (equations 4 and 5). In [START_REF] Özel | A methodology to Determine Work Material Flow Stress and Tool-Chip Interfacial Friction Properties by Using Analysis of Machining[END_REF], the Johnson Cook model used is defined by Hopkinson bar test.

σ JC2 = A + B(ε) n (4) σ JC1 = A + B(ε) n 1 + Cln ε ε0 (5)
σ JC = A + B(ε) n 1 + Cln ε ε0 1 - T -T 0 T m -T 0 m (6)
The results for the two materials and the three models are presented in figure 3. Figure 3(b) shows the comparison between theoretical results and the experimental results (σ AB ) for Ti64. However, figure 3(a) depicts the same comparison for AISI1045. For steel, the best model seems to be the complete Johnson-Cook model. The errors between the values defined in machining and with the Johnson-Cook models are σ JC = 7%; σ JC1 = 15% and σ JC2 = 9%. For steel, the second model (σ JC1 ) is the worst one. The best values obtained for Ti64 are also obtained with the complete model (equation 6). The errors between the values defined in machining and with the Johnson-Cook models are σ JC = 5%; σ JC1 = 30% and σ JC2 = 5%. Like for steel, the worst model is the model without thermal effect.

First, this analysis shows the importance of thermal softening effects in shear plan model. Without thermal effect, the effective flow stress values is higher. It seems to be important to use the complete Johnson-Cook model in steel and in titanium alloy. Moreover, the mechanical properties of titanium remains high even at high temperature.

The figure 3(a) depicts that the titanium model seems to be more sensitive to the behavior law. The good fit for steel is due to the good range of strain rate, strain and temperature of Johnson-Cook model. The used model is defined at test strain up to 10 4 s -1 and a temperature up to 600°C. The strain rate and the temperature defined in cutting modeling are often in this range (3399 < ε AB < 12653 and 428 < T AB < 494). For Ti64, the material law is defined for a strain rate of 2000s -1 and a temperature up to 1100°C. Our calculations show some strain rate values up to the strain rate model (1780 < ε AB < 84993) and a temperature between 531°C and 671°C. The difference between model strain rate range and machining strain rate range is the error explanation. It seems to be very important to define correctly the range of strain rate and temperature. Especially, when the machining generates high strain rate. The constant of Johnson-Cook model can be defined by different methods. Poulachon ([5]) explains that the method must be chosen according to the strain rate (figure 6). The split Hopkinson bar test is the most commonly used method for determining stress according to high rates of strain. The Taylor test may be also considered. It allows to obtain higher strain rate (5 × 10 3 s -1 < ε < 5 × 10 6 s -1 ) ( [START_REF] Nistor | Identification Expérimentale et Simulation Numérique de l'Endommagement en Dynamique Rapide : Application aux Structures Aéronautiques[END_REF]). An other method can be considered. Indeed, Ozel ( [START_REF] Özel | A methodology to Determine Work Material Flow Stress and Tool-Chip Interfacial Friction Properties by Using Analysis of Machining[END_REF]) and Tounsi ([6]) have developed a method to define the Johnson-Cook material model from machining test. There are different advantages with these First, the strain rate and temperature are always those obtained in machining. Secondly, the impact test is not always feasible for brittle material. The increasing of temperature can rise the ductility of the material. Thus, impact test becomes possible.

We have compared two material models. The first model has been defined with Hopkinson bar test and the second from machining tests. We have chosen to use the model defined in [START_REF] Özel | A methodology to Determine Work Material Flow Stress and Tool-Chip Interfacial Friction Properties by Using Analysis of Machining[END_REF]. This test has been made on titanium alloy (Ti64). σ AB is the effective flow stress at primary shear zone and has been determined from Oxley model. σ HB is the stress defined from Johnson-Cook model and σ machining , the stress obtained with behaviour law identified from machining.

Figure 4 shows the stress obtained from the two models. The tests have been made in different cutting speed (Vc) and different undeformed chip thickness (tu). For steel, σ machining and σ HB are quite equal. The identification method does not seem to influence the results. For, Ti64, it can be observed that sometimes σ machining is better and sometimes σ HB is the best. A analysis shows that the results are function of strain rate values. For low strain rate values (Vc15-tu0.1, Vc15-tu0.08), the best model is the model obtained with Hopkinson bar test. Whereas, for high strain rate (Vc15-tu0.02; Vc60-tu0.02) the best model is one that is defined from machining test. This analysis show the importance of the good definition of model range. The Hopkinson bar test allows a maximum strain rate of 2000s -1 while strain rate machining is 85000s -1 . Moreover in analysing, the behaviour law obtained from machining test limits the influence of strain rate constant (C HB = 0.028 and C machining = 0.000002125). In high strain rate, the stress is also reduced with increasing of strain rate. This observation seems to be coherent with machining tests and explains the stress decreasing.

The other point is the temperature effect. To explain the difference between the two materials some response surfaces have been plotted. The figures 5 (a) and (b) show the stress plotted according to strain rate and temperature. In machining, σ machining is always lower at σ HB . The two surfaces show the difference between two identifications methods. In studied range temperature and strain rate, the difference between the stress is different for the material. The figure 5 (a) shows that the two surfaces obtained are close and almost parallel. They are closer to high temperatures. In machining test, σ machining and σ HB are the same, the results seems to be coherent. For Ti64, the two surfaces are more remote and the slope is different. Increasing of temperature reduces the gap between the two surfaces. However, in comparison with steel, the gap is higher. This analysis shows the importance of thermal softening above all in titanium alloy machining and the importance of a good beahaviour law. The modeling of cutting force in titanium alloy machining is more sensitive to behaviour law. The complete model must be used to define the shear flow stress along primary zone. The behaviour law must be defined with Hopkinson bar if strain rate values are good (figure 6). However, another point to consider is the temperature. It is very important above all in machining of titanium alloy where the strain rate seems to be higher. For Ti5553, the first terms of Johnson-Cook has been made. A is the yield stress when B and n represent the effects of strain hardening. These values show the high properties of Ti5553. If compared with Ti64 yield stress, the Ti5553 one is higher. The table 2 illustrates that the effect of strain hardening in Ti5553 is higher compared to Ti64. These values show the poor ductility of Ti5553. Moreover, the effect of strain hardening is higher for Ti5553. In using those results and works established in [START_REF] Johnson | A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures[END_REF], we have defined the strain obtained in Ti5553 machining. The test has been made with constant undeformed chip thickness (t u = 0.2mm), constant rake angle (α = 13°) and a low edge preparation. We can denote that Ti5553 machining creates a very high strain rate (table 3). Those results show the importance of the behavior law definition. In this case, Hopkinson bar test do not allows the good strain rate. To get the good strain rate, two methods are possible, the Taylor test which permits us to get very high strain rate (5×10 3 s -1 < ε < 5×10 6 s -1 ) [START_REF] Nistor | Identification Expérimentale et Simulation Numérique de l'Endommagement en Dynamique Rapide : Application aux Structures Aéronautiques[END_REF] or to define model with machining tests. We have chosen to use test machining to define behavior law. These methods allow us to define the behavior law in good range (strain rate and temperature) but especially to increase material ductility with the increasing of temperature.

Conclusion

This paper shows the influence of behaviour law in cutting force model. We have compared different models of shear stress along primary plan. These tests have shown that the model must have the thermal effect especially in titanium alloys machining. Moreover, the model strain rate range must be the same as machining. To limit error, we have shown that the best method to define the behaviour law is the definition from machining. This method allows the good stain rate and the good temperatures.

We have shown that observations are very important in Ti5553 machining. Indeed, the strain rate seems to be very high compared to Ti64. So, we have chosen to define a complete Johnson-Cook model based on machining tests. Other tests must be made to define the Johnson-Cook law constract. They make us to define the influence of cutting conditions on cutting forces ant cutting temperature. The

Figure 1 :

 1 Figure1: Thermal conductivity and heat capacity comparison[START_REF] Tricot | Thermo-mechanical Treatments of Titanium Alloys[END_REF]

Figure 2 :

 2 Figure 2: Tensile test Ti64 and Ti5553

Figure 3 :

 3 Figure 3: Behaviour law comparison

Figure 4 :

 4 Figure 4: Comparison between two identification methods

Figure 5 :

 5 Figure 5: Response surfaces

Figure 6 :

 6 Figure 6: Strain-rate range reached in metalworking and limitations of the standard mechanical tests [5]

Table 1

 1

			: Material properties of Ti5553 and Ti64
	Material	TYS	UTS	Modulus	Elongation	Hard.	TYS
		(MPa)	(MPa)	(GPa)	(%)	HB±5	400°C
							(MPa)
	Ti5553	1250	1320	110	0.01	370	860
	Ti64	1050	1200	105	18	241	550

Table 2 :

 2 Johnson Cook Law[START_REF] Özel | A methodology to Determine Work Material Flow Stress and Tool-Chip Interfacial Friction Properties by Using Analysis of Machining[END_REF]

	Material	A (MPa)	B (MPa)	n
	Ti5553	1250	403	0.47
	Ti64	783	498	0.28

Table 3 :

 3 Strain rate for Ti5553

	Test	Co	εAB (s -1 )	Fc (N)	Ft (N)
	V c = 25m/min	36	34104	1899	1238
	V c = 35m/min	47	62029	1905	1358
	V c = 40m/min	37	55492	1898	1245
	V c = 45m/min	38	65201	1903	1268
	V c = 50m/min	42	77808	1906	1302
	V c = 55m/min	46	94438	1886	1321
	V c = 60m/min	36	79871	1873	1210
	V c = 65m/min	38	92228	1875	1240
	V c = 75m/min	35	98571	1882	1210
	V c = 85m/min	41	129057	1841	1247
	V c = 95m/min	49	175614	1829	1321

Johnson-Cook law will be defined from these tests where cutting temperature has been recorded with thermocouples. The strain rate and strain will be defined from Oxley model ( [8]).


Yue Ming
email: yue.ming@enit.fr

Bernard Grabot
email: bernard.grabot@enit.fr

Raymond Houé
email: raymond.houe@enit.fr

Towards a collaborative MRP for supply chain coordination

The necessity to increase collaboration in nowadays supply chains is emphasized both by academics and practitioners, but most of the supply chains are still managed through cascades of classical MRP/MRP2 systems. Interviews in the aeronautical sector have shown us the existence of many hidden practices aiming at satisfying local constraints which would be better addressed through collaborative processes. We suggest in this communication to define a "collaborative MRP" which would not only provide a better global performance than purely local planning, but take into account the autonomy of the involved partners which is not always respected by centralized approaches using APS (Advanced Planning Systems).

I.

INTRODUCTION

Many recent studies on Supply Chain Management converge on the fact that information sharing, joint-planning, cooperation and strategic partnerships over the entire supply chain are conditions for building more efficient and reactive supply chains [START_REF] Ding | Information sharing and profit allotment based on supply chain cooperation[END_REF]. Such partnership, where trust replaces strict customer/supplier relationship and where many decisions are taken in common, is often summarized by the concept of "collaborative supply chain" [START_REF] Ding | Information sharing and profit allotment based on supply chain cooperation[END_REF]. As a consequence, several approaches have been suggested by both academics and practitioners in order to allow cooperative planning within supply chains, the most well known being for instance CPFR (Collaborative Planning, Forecasting and Replenishment), see for instance [START_REF]Collaborative Planning, Forecasting & Replenishment (CPFR®) Committee[END_REF].

Nevertheless, it seems when looking at real supply chains that the projects launched (mainly by large companies) in order to increase the quality of partnership between supply chain members do not always result in increased trust and increased exchanges of information, especially when Small and Medium Enterprises are involved in the supply chain. Through interviews in companies working for the aeronautic sector in the South-West of France (see section II), we have seen that huge efforts were made by large companies for promoting the MRP2 (Manufacturing Resource Planning) method as the unique mean for planning production all along the supply chain (see section II. B).

We have also seen that most of the small and medium companies (SMEs) involved in these chains need to use local (but hidden) processes for coping with their local constraints, which they can hardly do within a strict application of the MRP method.

In section III, we suggest to include local processes performed by the SMEs in order to satisfy their internal constraints in a "collaborative MRP method" which could in our opinion provide a better balance between the local objectives of each supplier and the global objectives of the chain, usually represented by the final assembler, and as a consequence should lead to a better overall performance of the chain.

II. AN ANALYSIS OF INDUSTRIAL PRACTICES IN THE AERONAUTIC SECTOR

A. Context of the aeronautic sector

The aeronautic sector has been a domain of major changes in the next fifteen years since the necessity to decrease costs and cycle times has emerged rather recently in this rather protected domain. A specificity of the aeronautic sector (especially if compared to the automotive one) is that many SMEs are involved in the supply chains, since they are usually very reactive [START_REF] Dangayach | Manufacturing strategy literature review and some issues[END_REF] and may have high and specific technical skills. Furthermore, companies do not usually need large capacity in this sector, since products like aircrafts, rockets or satellites are built in relatively low quantities. Even if they include many different components, the demand on each specific part is so relatively low and can be fulfilled by SMEs.

The involvement of SMEs in aeronautic supply chains have drastically changed through time. It was first dedicated to subcontracting of manufacturing operations: the customer was sending raw materials or semi-finished components to the subcontractor who was performing the operation, then was sending back the parts. The consequence was a high coordination effort from the customers, who decided through years to transfer to their suppliers the full responsibility on their own providers. This evolution required the SMEs to develop their competences on the management of more complex products (sub-systems described by bills of materials), but also to be able to manage their suppliers, including sending them forecasts and supply plans. As a consequence, "supplier development" (term introduced in [START_REF] Leenders | Supplier development[END_REF]) began to be a major issue in the sector. Supplier development summarizes the efforts made by a customer in order to increase the number of viable suppliers and improve supplier's performance or capability [START_REF] Krause | The relationship between supplier development, commitment, social capital accumulation and performance improvement[END_REF]. Lean manufacturing is a major constituent of supplier development programs [START_REF] Jensen | Implementing lean manufacturing in SME companies[END_REF][START_REF] Von Axelson | Developing lean production implementation methodology for SME learning networks[END_REF] but is not enough for giving the capacity to control the suppliers: planning methods and especially MRP and MRP2 [START_REF] Orlicky | Orlicky's Material Requirements Planning[END_REF], supported by ERP (Enterprise Resource Planning) systems, are required to process information at each level of the supply chain. As a consequence, it is usually considered that SMEs must switch from simple financial plans to forecast based planning [START_REF] Thakkar | Supply Chain Management in SMEs: development of constructs and propositions[END_REF]. In that purpose, using an ERP system including an MRP module is now seen as mandatory if a SME wants to join a supply chain [START_REF] Lenny Koh | Change and uncertainty in SME manufacturing environments using ERP[END_REF]. Nevertheless, for Arend and Wisner [START_REF] Arend | Small business and supply chain management, is there a fit[END_REF], SCM implementation can be negatively correlated with SME performance. Reasons can be that the requirements regarding business processes may be differently implemented in large and small companies. This point has been confirmed by interviews which are summarized in the next section.

B. Collaboration in the aeronautic industry

Analysis of the effects of the efforts of large companies for developing their small suppliers have been performed through two main projects:

-a "supplier development" project initiated by a large manufacturer of complex sub-systems for aircrafts. Ten small suppliers were selected and have been the object of an intensive development program mainly based on audits of their processes, training on the MRP method, then implementation of production management systems (or improvement of their use for some of them).

-an analysis of collaborative practices in the aeronautic industry, conducted with an Association of companies of the aeronautic sector and with a public body aiming at SMEs development. The objective of the project was to analyze the problems linked to the cooperation between partners of aeronautical supply chains on two main domains: collaborative design and product flow management. Twenty companies were visited in that purpose: 7 large ones and 13 of middle (around 200 employees) or low (less than 100 employees) size. If the relatively low number of visited companies does not allow to fully guarantee the generality of the identified problems and situations, we think that it nevertheless allows to show that some existing problems are not yet fully taken into account by existing practices.

Use of MRP as promoted by the large companies

Supply chains can be managed through centralized or decentralized approaches. Using a centralized approach, all the companies send their local information to an APS (Advanced Planning System) which optimizes the part flow management through all the supply chain [START_REF] Stadtler | Supply Chain Management and Advanced Planning[END_REF] and communicates a local planning to each member. This method allows a global optimization, but requires to share information usually considered as confidential (concerning costs for instance), and is poorly adapted to the context of the coordination of autonomous entities, most of the time working for several supply chains. Therefore, it is mainly used inside industrial groups, in order to coordinate sites having a low level of autonomy.

Therefore, the usual solution which is promoted for coordinating the partners is through a cascade of local MRP2 (Manufacturing Resource Planning) systems [START_REF] Marcotte | Cooperation models for supply chain management[END_REF] (see Figure 1). Forecasts based on the expected customer's demand are built by the focal company of the chain (usually the final assembler in the aeronautic sector) then processed using the MRP2 principles. After the MRP (Material requirement Planning) step, planned orders allow to build a supply plan (including forecasts) which is sent to the tier (n+1) partners.

In the aeronautic sector, the end-products are manufactured on the base of firm orders but also forecasted orders. Forecasts are usually built on a 1-3 years base and include a firm period (during which the orders cannot be changed), a flexible period (with allowed variations) and a free period, communicated for information only. Let us take an example for illustration (see Figure 2): the focal company A builds his sales forecasts based on firm orders and expected ones at long term. If the cycle time of its product (for instance an aircraft) is one year, the firm period of the forecasts should be at least one year (but preferably more). Let us suppose that this cycle time is the addition of an internal assembly process lasting for six months plus external supplies requiring six more months. Let us consider that these six months are divided into two months for the internal work of supplier B, and four months for the supply of the raw materials (supplier C). If the customer does not confirm a forecasted order expected on month 13, company A will have to cancel an internal load positioned on months 7 to 13, together with an order sent to B due on month 5. This order Fig. 1. Supply chain management through a cascade of MRP systems [START_REF] Marcotte | Cooperation models for supply chain management[END_REF] was to be released on month 4 at supplier's B. As a consequence, B will have to cancel an order he planned to send to his raw material supplier next month (left part of Figure 2).

The lead time of the suppliers, so that the prices, are discussed during the RFQ (Request For Quotation) process. The contract concluded with the selected suppliers includes a decrease through years of both cycle times and prices. Indicators aiming at measuring the performance of the suppliers (mainly based on a service ratio) are also defined. All these parameters, cycle times and prices, but also firm period, characteristics of the flexible period etc., are included in the contract which may include penalties in case of late deliveries.

According to this "theoretical" framework, the key issue is to check that each partner of the supply chain (and especially the smallest ones) is able to process his forecasts and turn them into an internal load planning and an external supply planning using the MRP process. As it will be shown in next section, reality is somehow different and more complex.

Anomalies and additional local practices

The first issue identified during the interviews is that the parameters of the forecast horizons, but also the practices which result from these parameters, may be quite different from one large company to another. Reality appears to be often less consistent that the principles illustrated in Figure 2, since it is the market (and not always the focal company) which decides on the lead time acceptable by the customer. We have for instance seen the case of a company manufacturing small (and highly customized) aircrafts with a firm order horizon of 12 months, whereas their supply time for the motors was 14 months, the variant of the motor being chosen by the customer. This pressure set by the market is sometimes transmitted to the suppliers, e.g. for raw materials. During several years, a relative scarcity of some aeronautical alloys together with a lack of capacity of companies providing casting parts made that the supply time of raw materials increased up to 12 months in some cases... In spite of this, the firm period of the forecasts sent by the customers to their suppliers remained constant, around 3 months, forcing the suppliers to take the risk to order materials on the base of flexible forecasts, or to be sure to be late. Some (rare) companies use the difference between the firm period received from their customers and the one sent to their suppliers as a way to protect their smallest suppliers. For instance, a large tier 1 company was mentioning that the importance of one his customers obliged him to accept that all orders (even firm ones) could be cancelled until it was received by the customer... Such a constraint can obviously not be transmitted to a SME. Therefore, the company did not set into question the firm horizon sent to his suppliers, but introduced high flexibility ratios (±50%) in the flexible zone. In order to make this acceptable, they decided that if the ordered quantities decreased in this flexible zone, they would anyway buy the cancelled parts in the year.

Fig. 2. Cycle time and firm horizon

The same company was sending the level of its inventories together with each order, in order to show his supplier what could be the consequence of a late order.

Many other problems were listed by the visited SMEs. Many of them for instance claimed that the parts described in an RFQ were in some cases impossible to manufacture because of overestimated tolerances. As a consequence, the suppliers had to commit themselves on delays and costs whereas they were sometimes conscious that they would not meet either of them in the future.

Many SMEs try to group orders in order to decrease their setup times, and so increase their productivity and decrease their prices, as requested by their contracts with their customers. A problem is that many of them were unable to do it using their production management systems, which are often quite simple systems, often dedicated to SMEs1. As a consequence, most of them solved the problem by exporting their production plan to Excel or Access, macros or dedicated programs being then used to group the similar parts. In several cases, the due dates were not exported, so not used as constraints in the grouping process, with the result of both late and early orders. Of course, the SMEs were conscious that they were not supposed to do this, so their customers were not informed and the SMEs tried to negotiate each tardiness when occurring.

Another SME, who have a strong position because of the scarcity of his competence (surface treatment), had a quite original approach to cycle times: he managed to impose to his customers that only three cycle times were possible (10 days, 15 days, 20 days), with decreasing prices. The consequence was the immediate decrease of the urgent orders... Even if the generality of these practices cannot be demonstrated on few examples, we have verified through many talks with consultants of the aeronautic sector that they were rather common. Therefore, we suggest in next section some ideas which are the base of an ongoing study aiming at formalizing these practices into a "collaborative MRP" approach.

III. TOWARDS A "COLLABORATIVE MRP" APPROACH

A. Candidate practices for a "collaborative MRP"

We have seen in section II that the exchanges of information between partners are mainly based on the MRP technique: lead times are discussed when the contract is established, then forecasts are sent and the orders are fulfilled at the short term level. We have also seen during the interviews that many practices are added to these basic principles, in an open way when they come from the customers, but in a more hidden way when they come from the suppliers.

On the customer's side, these practices can be summarized as:

• The use of the firm and flexible periods of the forecasts for protecting, or on the contrary, for putting some pressure on the suppliers. Sending a firm period longer than the received one means to protect the suppliers. Sending the same firm period than the received one means transmitting the pressure on the suppliers. Sending a firm period longer than the one received would mean to try to gain some slack time by urging the suppliers more than needed. • The communication to the supplier of elements of information allowing him to assess the priority of the orders included in the forecasts, in addition to their due dates (e.g. the inventory level as seen above). On the supplier's side, the main practices that we have considered are:

• The grouping of some orders, in order to decrease the set-up times by increasing of the lot-sizes. • The use of an internal priority when all the orders cannot be fulfilled in time. • The pre-order of some raw materials if the firm period of the forecasts is insufficient. • The anticipation of the release of some orders, for smoothing the load. • The possibility to link price and lead time, for instance in order to avoid losing money while processing urgent orders.

B. Suggested collaborative process

On this base, the collaborative process we suggest is summarized (see Figure 3); its main objective is to create loops of negotiation at different levels, in order to better address industrial practices which are nowadays not clearly formulated and may result into increased problems. As it will be seen, the main objective of this collaborative process is to negotiate periodically the parameters of each MRP system (at the customer's and at the supplier's) instead of choosing these parameters only when the contracts are concluded. This collaborative process aims at generalizing and making explicit some constraints which have to be fulfilled either on the customer or on the supplier side, the idea being that their fulfillment should be the result of a negotiation process, and not anymore the result of hidden practices, or the consequence of the power that a company has on his partner. The basic input of this "negotiation space" is the respective situation of the customer and supplier in terms vulnerability, the idea being that the stronger partner should protect the weakest one, for their mutual interest. It may appear as paradoxical that the stronger partner is the one who accepts to decrease the satisfaction of his local objectives. Many research works have emphasized the importance of power on the relationships along the supply chain [START_REF] Thakkar | Supply Chain Management in SMEs: development of constructs and propositions[END_REF][START_REF] Vaaland | Can the SME survive the supply chain challenges[END_REF]. The power of a company over its partners makes it possible to impose his own objectives as the ones of the supply chain, but many studies emphasize that the exercise of power provokes a decreased trust, whereas trust is usually considered as bringing an increased performance [START_REF] Möllering | A typology of supplier relations: from determinism to pluralism in inter-firm empirical research[END_REF]. In several cases, the interviews have shown that a strong partner taking care of a weaker one is a situation that may appear (even if seldom). For the four areas of negotiation considered here, the balance between the conflicting objectives of the partners should depend on their respective situation.

At level 1, the firm and flexible periods of the forecasts are adjusted for each supplier, together with the accepted possible variations within the flexible period. This will allow the customer to protect the weakest suppliers, and to take a part of their risks if the market forces the suppliers to send firm orders

! " # $ %
on the base of the flexible period of their forecasts (see the case of the aeronautical alloys here above). At level 2, the bearable load variation of the supplier will be taken into account by the customer in order to define a supply plan which does not destabilize the supplier. Like in the previous case, the result will inevitably be an increase of the inventories at the supplier's size. The cost of these increased inventories has so to be compared to the costs induced by the present erratic answer of many weak suppliers (especially SMEs) subject to a variable demand. Of course, taking into account the difficulty of the supplier to adjust his capacity is a short term issue, whereas middle/long term issues will allow to help him to better use the means to increase its capacity. In that case, it is also clear that an increased flexibility may have a cost that the customer should be ready to pay when the supplier answers an RFQ.

Negotiation at level 3 is based on the idea that the cycle time required by an order is not anymore fixed but may vary according to the situation. Processing an order quicker than defined in the contract could be acceptable, under condition that the over costs are paid by the customer. This is only the inverse situation of the universally accepted (even if seldom applied) practice of penalties for tardy deliveries.

Level 4 deals with problems which may impact the supplier's schedule (and not anymore the load planning like in the previous case). Especially, urgent orders coming from the customer can be negotiated. Two conditions seem to be necessary to process these orders without destabilizing the supplier:

• Scheduling urgent orders requires that the supplier has access to the real priority of the orders sent by his customers. Most of the time, the supplier guesses that his customer has kept some temporal margin (or security inventory, see interviews) but does not know on which orders and to what extent. If the customer accepts to share the information allowing his supplier to assess the real urgency of each order, the supplier reaction in case or urgency should possibly be less disturbing than when the supplier processes urgent orders by pushing blindly the work in progress. • Of course, the customer should also accept to pay for the over cost generated by urgent orders.

C. Assessment and implementation of the negotiation processes

Studies are in progress in order to better identify the possible domains of interest of the previous negotiation areas. As a general statement, it is clear that this identification requires to identify:

• On one hand, the over cost induced by the negotiation,

• On the other hand, the cost of the present processes where the stronger partner imposes his solution, and where the weaker partner tries to satisfy his local objectives in a hidden way. Four negotiation areas have been suggested as examples but others may be considered. Anyway, a modular implementation of such a collaborative process is in our opinion possible, since it does not concern the internal processes of MRP2 but only the way some of the parameters of MRP are calculated (lot sizes, lead times, etc.). Therefore, we have begun tests aiming at developing prototypes of these modules using constraint propagation techniques.

IV. CONCLUSION

The literature clearly shows the interest of information sharing for increasing the performance of the supply chain [START_REF] Möllering | A typology of supplier relations: from determinism to pluralism in inter-firm empirical research[END_REF][START_REF] Johnston | Effects of supplier trust on performance of cooperative supplier relationship[END_REF]. On the base of interviews in large and small companies of aeronautical supply chains, we have seen that the real practices in these supply chains may set into question the efficiency of the planning process. In order to prevent the drawbacks of both power exertion from the mighty partners and hidden practices from the weak ones, we suggest to calculate dynamically some of the parameters of the MRP method on the base of a negotiation process. An ongoing study aims now at defining more precisely the conditions of negotiation and the prototyping of negotiation support systems using constraint propagation. Of course, sharing the information in order to allow negotiation increases the risk that the partner may have an opportunistic behavior, which is a known drawback of information sharing [START_REF] Liu | Control mechanisms across a buyersupplier relationship quality matrix[END_REF]. Trust is so a pre-requisite for such information sharing [START_REF] Ming | Coordination in Supply Chains: from case studies to reference models[END_REF].

Accepting to take into account new constraints, mainly coming from the suppliers is uneasy for the large companies. Instead of considering that their practices are prohibited, it is in our opinion important to formalize them as a first step in a consistent collaborative process, even if improving the flexibility and reactivity of the suppliers may at long term provide another solution.

Fig. 3 .

 3 Fig. 3. Negotiation between two partners in a "Collaborative" MRP

For instance, some of them are strictly based on a MTO (Make-to-Order) logic, and do not allow to take into account forecasts. In that case, some SMEs were entering the whole forecasts as firm orders, making it impossible to distinguish between firm and flexible periods in the supply plans they were sending to their own suppliers


Yue Ming
email: yue.ming@enit.fr

Raymond Houé
email: raymond.houe@enit.fr

Bernard Grabot
email: bernard.grabot@enit.fr

MRP-based negotiation in customer-supplier relationship

Keywords: MRP, supply-chain, negotiation, cooperation, planning

In the present uncertain context, increasing the performance of the supply chains requires to define cooperative processes between partners aiming at providing a better answer to the final customer, with a risk shared between partners. Based on an analysis of real practices, we suggest in this communication to take the MRP process as a basis for defining what could be such a cooperative process.

INTRODUCTION

Since the manufacturing companies are nowadays more and more focusing on their core processes, supply chains become larger and more complex structures which management has motivated a huge literature. Indeed, it is much more difficult to coordinate distant partners, who can have very different size and culture, than workshops belonging to the same plant. The growing uncertainty on the customers' demand makes this coordination still harder, and it is usually considered that an increased cooperation is a good way to mitigate the risks linked to this uncertainty (Hallikaset al., 2005). We suggest in this communication to use the MRP method as a basis for supporting a cooperative process aiming at a better synchronization of the partners, in a context of risk sharing.

A short state of the art on collaborative processes in supply chains is given in section 2, whereas the main findings of a project aiming at analyzing real practices in supply chains of the aeronautic sector are summarized in section 3. In section 4 are described some points on which a negotiation could be of mutual benefit for the partners, within a collaborative process. One of these negotiation processes is described with more details in section 5.

COLLABORATION IN SUPPLY CHAINS

Coordination, cooperation and collaboration are defined by several authors as increasing degrees of relationships between supply chain partners (see for instance [START_REF] Camarinha-Matos | Collaborative networked organizations-concepts and practice in manufacturing enterprise[END_REF]). Coordination of supply chain partners, which is the first condition for working together, may be achieved in a centralized or distributed way. In the first case, a dedicated software (Advanced Planning System -APS) is used to gather the information coming from each partner and suggest a planning including both manufacturing and transportation activities [START_REF] Stadtler | Supply chain management and advanced planning: concepts, models, software, and case studies[END_REF]. This solution may allow an optimization of the global planning, but is poorly consistent with the autonomy of partners, who are usually independent companies. Therefore, supply chain planning is mainly achieved through local communication between a customer and his suppliers, as suggested in industrial reference models for supply chain management like SCOR (SCOR, 2008). In that case, planning is achieved using a cascade of MRP2 (Manufacturing Resource Planning) modules [START_REF] Orlicky | Orlicky's Material Requirements Planning[END_REF], as denoted in Fig. 1, taken from [START_REF] Grabot | SME and Planning in Supply Chains: a Socio-technical View[END_REF]: the final assembler collects forecasts, then defines a Sales and Operation Plan, usually referring to groups of products. He then builds a Master Production Schedule by product, and determines which components are required, by running the Material Requirement Planning module. The MRP step results in a production plan, allowing to build an internal load plan, and in a supply plan, sent to the suppliers. This supply plan, including a firm period (in which the orders cannot be modified) and a flexible period (in which changes may arise within given limits), is considered as forecasts by the suppliers.

Fig. 1. Supply chain planning using a cascade of MRP processes [START_REF] Grabot | SME and Planning in Supply Chains: a Socio-technical View[END_REF] Many parameters used in the MRP calculations, like the lead times, production and transportation lot sizes, etc., are defined in the contracts that link customer and supplier.

In order to be more reactive, new ways to collaborate on some specific aspects of the planning process have been defined in the last ten years, like Collaborative Planning, Forecasting and Replenishment (CPFR) [START_REF] Vics | CPFR: An Overview of the Model[END_REF] or Vendor Managed Inventories (VMI) [START_REF] Disney | The effect of vendor managed inventory (VMI) dynamics on the Bullwhip Effect in supply chains[END_REF]. Nevertheless, these methods do not address the whole process described in Fig. 1.

For academics, cooperation in supply chains is often considered as suppliers and buyers becoming strategic partners, sharing risks and benefits, exchanging operating and financial information, making joint investments in facilities and systems, jointly involved in continuous improvement and new product development programs, and making their success interdependent [START_REF] Albino | Supply Chain operation in industrial districts: a simulation analysis[END_REF]. Such cooperation is based on a "strategic partnership" sometimes called "cooperative SC relationship" [START_REF] Ellram | A managerial guidelines for the development and implementation of purchasing partnerships[END_REF]. In such business relationship, cooperation should start with joint planning and end with joint control activities to evaluate the performance of the supply chain members as well as the supply chain as a whole [START_REF] Cooper | Supply chain management: more than a new name for logistics[END_REF][START_REF] Tyndall | Supercharging Supply Chains: New Ways to Increase Value Through Global Operational Excellence[END_REF]. Nevertheless, the reality of nowadays supply chains usually still shows more basic relationships: an intense upstream information flow can be noticed, in order to propagate the final customer's demand through the supply chain (see Fig. 1), but the downstream information flow is usually limited, each supplier having to answer to his local customer's demand by every mean.

We have had the opportunity to analyse the behaviours resulting from such relationship in aeronautical supply chains of the south-west of France. Some findings of the study are summarized in next section.

CASE STUDIES

During the last few years, we have been involved in several projects aiming at analyzing or improving cooperation in supply chains, among which one performed with funding from an association of companies of the aeronautic sector and from a public body interested in SMEs (Small and Medium Enterprises) development. The objective of the project was to analyze the problems linked to the cooperation between partners of aeronautical supply chains, especially when SMEs were involved. Twenty companies were visited in that purpose: 7 large ones and 13 of middle (around 200 employees) or low (less than 100 employees) size. If the relatively low number of the visited companies does not allow to fully guaranteeing the generality of the identified problems and situations, it is consistent with the results of previous projects on the same domain [START_REF] Marcotte | Cooperation models for Supply Chain Management[END_REF] and shows that some problems are not yet fully taken into account by present practices.

Many problems linked to the real implementation of the previously described processes were identified during the interviews. We shall not give here an exhaustive list, but focus on some of them, which have influenced the rest of our study.

Problems linked to the firm period of the forecasts

The first issue identified during the interviews is that the size of the freezed period of the forecasts may be inconsistent with the supply lead times. As an example, a relative scarcity of some aeronautical alloys together with a lack of capacity of companies providing casting parts made that the supply time of some raw materials increased up to 12 months in some cases. In spite of this, the firm period of the forecasts sent by the customers to their suppliers remained constant, around 3 months, compelling the suppliers to take the risk to order materials on the base of flexible forecasts, or to take the risk to be late if they would wait for the corresponding orders to be confirmed.

Example:

A company manufacturing small (and highly customized) aircrafts has a firm horizon of 12 months, whereas its supply time for the motors is 14 months, the variant of the motor being chosen by the customer.

Protection or pressure using the periods of the forecasts

Some (rare) companies use the difference between the firm period received from their customers and the one they send to their suppliers as a way to protect their smallest partners, who may have difficulties for dealing with large variation of the demand.

Example: A large tier 1 company mentioned that the importance of one his customers obliged him to accept that all orders could be cancelled until reception. However, the company did not set into question the firm horizon sent to his own suppliers, but introduced high flexibility ratios (±50%) in the flexible zone. In order to make this acceptable, they decided that if the ordered quantities decreased too much in this flexible period, they would commit to buy the parts by the end of the current year.

Load smoothing at supplier's

Load smoothing may be an important issue for SMEs, which have a limited capacity. During the periods when the load is important, some orders may have to be delayed while when the load is low, SMEs are looking for work in order to get minimum incomes.

Example: A supplier explained that during a difficult period, he decided to work on orders belonging to the flexible period of the forecasts sent by his customer, even if he was not sure that these orders would be finally confirmed. For him, the risk was limited and the over cost linked to the late payment and increased inventories was lower than the cost required to temporarily decrease his capacity.

Protection against variations of load

Load smoothing can also be performed by the customer: some cases have been seen where this problem was formally taken into account by customers willing to protect their smallest suppliers.

Example: A customer wanted to protect its smallest suppliers from load variations. As a consequence, a maximum variation between two consecutive periods was considered as a constraint for building his supply plan. The consequence was that the customer had to anticipate any variation and to increase his inventory level in order to cope with the demand of his own customers, varying more dynamically.

Link between price and cycle time

Satisfying urgent orders is part of the daily work in aeronautical supply chains; it usually means to spend extra money (due to extra hours, etc.) or to postpone other orders considered as less urgent, creating perturbations in the planning. In some very specific cases, we have seen that the principle of a negotiation of the price and cycle time was considered in order to address the problem of these urgencies.

Example: A company, who has a strong position because of the scarcity of his competence (surface treatment), managed to impose to its customers that only three cycle times were possible (10 days, 15 days, 20 days), with decreasing prices. Urgencies were only considered under condition that the customer was ready to pay for shorter cycle times.

Information sharing

As already stated, many SMEs are facing a variable demand, which they can hardly satisfy at low cost. Even if some orders are not as urgent as others, this information is often not communicated by the customer. As a consequence, the SMEs have to make their decisions, on the priority of orders, grouping of similar orders, adjustment of lot sizes etc., on the only base of internal considerations. In the case studies, we have nevertheless seen that some customers share information with their suppliers in order to allow them to make their decisions to the benefit of both partners.

Example: A large company was sending the level of its present inventory together with each order, for showing his suppliers what could be the consequence of a tardy order. Sharing information on the inventory level gives to the supplier information on the customer's priorities when it is necessary for him to postpone orders, and increases his flexibility when constraints occur locally.

Lot sizes

Lot sizes are an important item, negotiated in the contracts. Nevertheless, SMEs have to decrease their costs through time, and have so to find solutions for constantly increasing the efficiency of their production system. In order to do this, some of them may need to provisionally increase their lot sizes. Therefore, many suppliers tried to group several orders from their customers in order to decrease their set-ups.

Example: An SME specialized in turning was exporting the planned orders to an Access® application aiming at grouping them according to the diameter of the parts, since this was not possible using their production management system. Since their application was not taking into account the due dates, the result was both early and late orders that were then negotiated individually with the customer.

Conclusions of the study

Nearly all the large companies consider that the process described in Fig. 1 is the only possible to efficiently manage a supply chain. Therefore, suppliers' behaviours that are not consistent with this framework are considered as a sign of poor maturity, with the result of many projects aiming at the so-called "supplier development" [START_REF] Wen-Li | Predicting purchasing performance: the role of supplier development programs[END_REF]. We suggest to have a different attitude, and to consider that the practices of the suppliers, even if they lead to problems, are the symptoms of real concerns. Therefore, we suggest to turn these "hidden" practices into public ones, subject to negotiation with the partner. In order to illustrate this, we have focussed on four points, which are detailed in next section.

NEGOTIATION WITHIN THE MRP FRAMEWORK

Period of forecast

As mentioned previously, the forecasts in the aeronautical industry usually consist of firm, flexible and free periods. As seen during the interviews, practical issues concerning the periods of the forecasts are for instance the link between the firm period and the cycle time of the orders, or the link between the lengths of the periods received by the customer, and those he sends to his supplier. Therefore, we propose to put the periods of forecast into a middle term negotiation process, being defined on the base of the real requirements and actual necessities of both the customer and supplier. The same problem is detected by comparing the load planning and the forecasts sent by their customer on the supplier's side (left part of the figure). Based on the results of risk assessment, negotiation of the periods of forecast may be performed if the supplier or the customer considers the current risks as unacceptable.

Load variation

In case of load variation, instead of considering that the supplier HAS to answer to an overload if it is consistent with the contract, or CANNOT answer to an overload, we suggest that overloads (or lacks of loads) could also be negotiated, including setting into question the price paid by the customer.

Fig. 3. Negotiation on the load variation

Therefore, we suggest to negotiate load variation problems, either resulting from constraints at the supplier's or customer's side, with a direct link with the price (increase if the problem comes from the customer, decrease if the problem comes from the supplier). Fig. 3 presents the information flow during the negotiation on the load variation. On the customer's side, information concerning the load variation is estimated at the MRP level, while real problems of capacity/load balance are usually detected in the S&OP and load planning level on the supplier's side. According to their situations, the supplier and customer may both request a negotiation on the load variation.

Prices and cycle time

Urgencies are detected at the customer's side, but when facing these urgencies, it is the supplier who is challenged through its flexibility and adjustment of capacity.

We shall consider here that the cycle time of urgent orders is negotiable, as well as the price. When an urgent demand occurs, the customer should pay for the cycle time he expects according to the situation of his supplier; for instance, no increase of price would be required if the supplier is in an under loaded period. In other cases, a negotiation process on the price and cycle time is suggested to cope with the constraints coming from the supplier's capacity.

Fig. 4 presents the information flow during the proposed negotiation on price and cycle time. On the customer's side, the information for assessing the feasibility of an urgency is achieved at the MRP and load planning levels, while operational problems for dealing with such urgency come from the load planning and real-time scheduling level on the supplier's side. The result of the negotiation should be a new price and due date after the negotiation.

Fig. 4. Negotiation on price and cycle time

Orders priority and Lot sizes

The final item we suggest to put into the negotiation process is the orders priority and lot sizes. From the interviews, we have seen cases where SMEs try to regroup orders having common features, in order to decrease the set-up times by increasing the lot sizes. Without additional information from their customers, the suppliers use an internal priority for scheduling the orders at the operational level, if all the orders cannot be fulfilled in time, as well as when urgent orders are required. As a consequence, tardy orders towards one or several customers may occur. Temporal margins or safety stocks may allow the customer to face delayed delivery on some of the orders, but this information is not always shared with the suppliers.

Fig. 5. Negotiation on priority and lot sizes

We have chosen here to group these two issues in the same point (see Fig. 5), since they both deal with operational planning. We have seen that practices have been detected in our case studies aiming at decreasing this problem: see the large company sharing the information on his inventory, allowing its supplier to have a better vision of the real priority of the orders. This allows the supplier to make better decisions when it is necessary to postpone orders. We have also seen that minimum lot sizes can be agreed when the contract is established. In order to go one step further, we suggest to include these points in a negotiation process, at middle term (lot sizes) then short term (priorities). Again, extra payment would be an element of the negotiation.

Fig. 5 shows the information flow concerning the negotiation on priority and lot size. On the supplier's side, lot sizes problems are detected at the MRP level, while the problems linked to priorities are detected at the load planning and realtime scheduling levels. On the customer's side, problems linked to the lot size considered as acceptable for their supplier ("estimated lot size" in Fig. 5) can be detected at the MPS level, according to the information produced in the MRP level. If the negotiation is performed, the customer could provide information about its internal priorities, which is usually to the supplier, in order to reach mutual agreement.

EXAMPLE OF NEGOTIATION PROCESS

After having globally defined the modalities of negotiation, we have defined precise negotiation processes aiming at allowing a simulation, which would help us to identify the possible context of interest of such collaborative process. In that purpose, each negotiation process has been modeled using first the Business Process Diagram [START_REF] Bpmn | Business Process Model and Notation (BPMN) Version 2[END_REF].

All the processes cannot be detailed here, but in Fig. 6 is shown the Business Process describing negotiation on periods of forecasts with more details. Normally, forecasts coming from customer's customer are inputs of the S&OP plan, then used to generate the MPS (Master Production Schedule) (point !"#$"%#&'"(). The MPS sends more detailed requirements on material and production to the MRP (Material Requirement Planning) module (point )). The supply plan, an output of MRP, is generated based on the BOM (Bill Of Material), supply lead time, material inventory level, etc., according to the contractual time fences, including the firm, flexible and free periods (point *).

The supply plan is received by the supplier and considered as forecasts (point +). The supplier makes his own MRP calculation (point ,), resulting in his supply plan and load plan (point -). Since he has taken into account his cycle time and the cycle time of his suppliers, the supplier is able to see whether this load plan is consistent or not, or in other terms whether he takes too much risks (for instance by ordering parts on the base of the flexible period of forecasts, point .). Depending on the additional information on his customers and suppliers (such as: can they be urged or not, do they have financial stability or not), he decides whether these risks are acceptable or not (point /). If he considers that he takes more risks than his partners (customers and suppliers), he may ask for negotiation (point 0).

The customer makes his own assessment of both internal risks and risks on supplier's side (point 1). This assessment of course considers the horizon of the firm period received from his customer, the horizon of the firm period he sends to his suppliers, his internal cycle time, supplier's cycle time, etc. It should also include his opinion on additional external information like cycle time from supplier's suppliers, the real costs of his suppliers, etc. It is clear that this information is usually not provided by the supplier, who would not accept to communicate his real costs to his customer.

The risk taken by the customer is in some way proportional to the difference between the horizon he receives and the horizon he sends. It can be different for each of his suppliers, since two different suppliers do not need the same protection, or in other words do not deserve that the customer takes the same risk. It is for instance acceptable to take risks for protecting a critical supplier, but not for a common one. Such assessment will provide a customer's vision on the allocation of risks between the customer itself and his suppliers. The next step is to balance the customer's and supplier's strength, aiming at identifying whether it could compensate the risks, and then assessing the acceptability of the risks taken by the customer (point 2). For instance, the customer may consider that he should take lower risks if his supplier has more "strength" than him. If, from customer's vision, risks are not acceptable, he will request for negotiation (point 3). Otherwise, the customer will accept the current plans (point 4).

CONCLUSIONS

Even if local cooperative processes are already in use in supply chains, we do think that collaboration should be extended in order to increase the global performance of the supply chains. In that purpose, we suggest here to turn hidden practices, often creating more problems than they solve, into official ones, performed through negotiation. The goal is to finally obtain a real win-win relationship. Of course, negotiation processes like the ones suggested here are only possible in a climate of trust between partners, which is not always observed in reality. An analysis of this point can be found in [START_REF] Ming | A taxonomy of the situations of cooperation in supply chains, submitted to Production Planning and Control[END_REF]. A second point is to demonstrate that these negotiation processes can really result in win-win situations. In order to validate this hypothesis, we have developed a simplified cost model which is the base of tests which are now in progress, aiming at better indentifying in which case negotiation on the suggested items can be of mutual benefit. As a third perspective, we would like to formalize with more details the notion of "risk" as considered here, which remains very subjective. In that purpose, we would like to better quantify the financial risks taken. This will require to use the cost model which is under development, but it will also necessitate to formalize more global issues allowing to assess the financial "health" of a company.

Finally, we have begun to present this study to industrial partners in order to get their first comments. Indeed, this reaction has been more positive than expected: nearly all the companies consider that there is a real source of improvement in such methodologies, but all of them also agree on the difficulty to reach the situation of trust which is a prerequisite for it.

Fig. 2 .

 2 Fig. 2. Negotiation on the periods of forecast Fig. 2 presents the information flow between the different MRP steps and the negotiation activities concerning the periods of forecast. The information required for risks assessment is obtained, on the customer's side, from a comparison between the results of the MRP calculation and the horizon from their own customer (right part of the figure). The same problem is detected by comparing the load planning and the forecasts sent by their customer on the supplier's side (left part of the figure). Based on the results of risk assessment, negotiation of the periods of forecast may be

Fig. 6 .

 6 Fig. 6. Business Process Diagram of period of forecast negotiation