Cathérine Audin

Jean-Claude Daran

Eric Deydier
email: eric.deydier@iut-tlse3.fr

Eric Manoury
email: eric.manoury@lcc-toulouse.fr

Rinaldo Poli

New ferrocenyl P,O ligands with polar substituents

Keywords: Ferrocene, Phosphine, PEG, Bisphosphonate, Imidazolium, Catalysis, Suzuki coupling. Résumé Ferrocène, Phosphine, PEG, Bisphosphonate, Imidazolium, Catalyse, Couplage de Suzuki

A new ferrocenyl P,O ligand has been synthesized and successfully used in the Suzuki-Miyaura coupling reaction of phenylboronic acid with bromobenzene. Some analogues carrying charged (imidazolium) or neutral (monomethylether PEG 750, tetraethylbisphosphonate) polar substituents have been prepared by functionalization of a common synthetic intermediate easily obtained using bromoalcohol p-HOCH2(C6H4)CH2Br as bifunctional linker.

Introduction

Over the last few decades, homogenous asymmetric catalysis by transition metals has received considerable attention and numerous chiral ligands and complexes allowing high efficiency reactions have been reported [1]. However, only few examples have been transferred to industrial processes [2], in many cases because of the expenses associated to catalyst loss. The efficient separation of expensive catalysts and ligands to enable reuse in subsequent cycles is a main challenge that meets both industrial economical needs and new stricter environmental regulations.

Three major strategies have been reported for immobilizing homogeneous catalyst [3,4]. The first one consists of immobilization on solid supports such as polymers [5,6] or inorganic materials [7] (silica, metal oxides, metal phosphates….). At the end of the reaction, the catalyst is easily recovered by filtration, but its activity and selectivity are often lower relative to the corresponding homogeneous catalyst. As a second approach, in order to combine the advantages of heterogeneous and homogeneous catalysis, soluble polymers [8] or dendrimers [9] have been used as catalyst support. The reaction occurs then in homogeneous media and the catalyst is finally recovered by precipitation or by filtration through membranes. However, longer synthetic procedures are involved because of the functionalization needed to link the catalyst to the support.

The third strategy, involving non conventional liquid media and multiphasic systems with immobilization of the homogeneous catalyst on a "liquid carrier" has attracted increasing interest [10,11]. The functionalized catalyst, with a specifically designed ligand, is isolated in one phase at the end of the reaction, while the product remains in the other phase allowing easy product isolation and catalyst reuse. Among these "liquid carriers", supercritical carbon dioxide [12], perfluorinated solvents [13], ionic liquids [14,15], water [16,17] and polyethylene glycols (PEG) [18] have emerged as interesting candidates.

We have long been interested in the design and the synthesis of new chiral catalysts for exploring new asymmetric catalytic reactions or for improving existing ones [19,20,21,22,23,24,25,26,27]. In this area, chiral phosphines have played a significant role. The possibility to easily modify their electronic and steric properties by a judicious choice of their substituents has proven extremely useful to successfully optimized catalytic reactions. Among the numerous phosphine ligands reported to date, ferrocenyl phosphines functionalized by an oxygen atom (PO ferrocenyl phosphines) constitute a distinct class of hemilabile ligands attracting increasing interest [28,29,30,31,32]. We have recently developed promising PO ferrocenyl ligands in an enantiomerically pure form (planar chirality) and started investigating their efficiency in asymmetric catalysis (allylic substitution) [23]. In addition, we recently took interest in improving catalyst recycling using ionic liquid, water or PEG as catalyst "liquid carriers" and in investigating the influence of these media on both the catalytic reaction and the recycling efficiency. As a first part of our project, we have decided to develop simple chiral phosphine-ethers as new ligands for catalysis in unusual solvents. In this manuscript, we will describe the synthesis of the first members of this new family of phosphine-ethers, their use in Suzuki-Miyura reaction and the synthesis of new PO ferrocenyl ligands bearing charged (imidazolium) or neutral (monomethylether PEG 750, tetraethylbisphosphonate) polar tags [33] for future catalytic application in non conventional media.

Results and discussion

As an entry to new PO ferrocenyl ligands, we have chosen 2thiodiphenylphosphino(hydroxymethyl)ferrocene, 1 (Scheme 1). This compound can be prepared in multigram quantities and isolated as a racemic mixture or in a pure enantiomeric form, opening direct access to chiral ligands [23]. The phosphino function is protected from oxidation by a sulphur atom allowing working in air. Its functionalization can be performed in a one pot process by successive addition of a strong acid (HBF4), generating probably a ferrocenyl carbocation, and then the nucleophile of choice (alcohol, thiol…) usually leading to the expected substitution product in high yields [21]. In order to obtain a large variety of tagged ligands, we needed a synthetic intermediate which bears both a PO ferrocenyl framework and a function (Y) easily transformed into R' tags (Scheme 1). For this purpose, we have designed a bifunctional linker (HO-linker-Y). The bromoalcohol p-HOCH2(C6H4)CH2Br appears to be an interesting first candidate to achieve this task. The benzylic bromide may be easily substituted by various R' substrates which will increase PO ferrocenyl ligand affinity for "liquids carriers" such as water, ionic liquids or PEG. Moreover, the relative para arrangement of the CH2-OH and CH2-Br groups allows the R' tag to be located remotely from the ligand coordinating atoms (P,O). However, before embarking in this functionalization work, we first wished to establish the ligand efficiency in the Suzuki-Miyaura reaction with the simplest member (compound 2b) of this new family of phosphine-ethers (Scheme 2).

Synthesis of ligand 2b

Compound 2b was readily prepared in good yields by addition of an excess of paramethylbenzylalcohol p-HOCH2(C6H4)CH3 to racemic 1 in the presence of tetrafluoroboric acid in dichloromethane, according to the reaction conditions previously optimized for the synthesis of ferrocenyl phosphine thioethers [21]. After purification by flash chromatography on silicagel, compound 2a was obtained as a yellow powder in 45% yield. Desulfurization was achieved with high efficiency using tris(dimethylamino)phosphine in refluxing toluene for twelve hours under an argon atmosphere. 2b was recovered as yellow oil after flash chromatography (70% yield). Both compounds have been fully characterized by mass spectrometry and multinuclear NMR. Selected NMR values are reported in Table 1.

Preliminary evaluation of PO ferrocenyl ligand efficiency in a Suzuki catalytic reaction.

Ligand 2b was tested in the coupling reaction of phenylboronic acid with bromobenzene in the presence of Pd2(dba)3 (1.0% molar of Pd) as catalyst and Cs2CO3 as base (see Scheme 3). A control experiment was also carried out under the same conditions but without ligand 2b.

Figure 1 reports the phenyl bromide consumption (%) and the biphenyl formation (%) versus time for both runs. Whereas the reaction is complete within two hours when using ligand 2b at 70°C, the conversion remained very low (less than 10%) for the control experiment without ligand 2b, even after seven hours. Comparisons to recently published P,O ferrocenyl ligands underline the efficiency of ligand 2b in the Suzuki-Miyaura reaction [29,32]. For example, Shi et al. [32] obtained a 96% isolated yield of biphenyl in 6 hours at 110°C using a polymersupported PO ferrocenyl ligand (cf. with a 98% conversion after only two hours at 70°C using 2b). Using a similar molar ratio, Hor et al. [29] reported isolated yields of 80-90% at 60°C in THF but only after 5 hours of reaction. These results, obtained under non optimized conditions, confirm the interest of such P,O ligands in Suzuki-Miyaura reactions.

Synthesis of tagged ligands

Our next goal was to develop recyclable catalytic systems using water, RT ionic liquids or PEG as "liquid carriers", in particular for Suzuki reaction which have already been efficiently carried out in such solvents [34]. Therefore, we synthesized analogues of ligand 2b bearing various substituents in order to increase their solubility in the "liquid carrier". All of these tagged ligands have been prepared from the same synthetic intermediate, compound 3 (Scheme 4).

Preparation of synthetic intermediate 3

Like 2a, compound 3 was readily prepared in good yields by addition of an excess of p-HOCH2(C6H4)CH2Br to 1 in the presence of tetrafluoroboric acid in dichloromethane. After purification by flash chromatography on silicagel, compound 3 was obtained as a yellow powder with an overall yield of 70%. Its structure was confirmed by NMR, mass spectrometry and X-Ray diffraction analyses of the racemic mixture (Table 2). A view of the compound is shown in Figure 2. As observed in related ferrocenyl derivatives [20,22,23,24,26,35], the sulfur is endo with respect to the Cp ring, being away from the ring plane by 0.808(6) Å, whereas the oxygen is exo by 1.352(5) Å. The two Cp rings are nearly parallel (dihedral angle of 2.6(2)°) and roughly eclipsed (twist angle of 7.7(2)°). The C2-C21-O2-C22 atoms are nearly planar with the largest deviations from the mean plane being 0.085(2) Å for C22 and this plane is nearly perpendicular to the phenyl ring, with which it has a dihedral angle of 89.5(1)°. The O2 and Br1 atoms are anti with respect to the C22---C23 axis. All bonds lengths and angles in this structure are within expected range (Table 3). NMR data are in agreement with the expected values. The C23 atom (bonded to bromide) gives a signal around  = 35 ppm in the 13 C NMR (CDCl3), upfield relative to the C atoms of the other CH2 groups ( > 70). This signal is an efficient probe to follow the bromide substitution by the various tags. Selected values are reported in Table 1.

Synthesis of tagged-ligands

The last step of our synthetic work consists in increasing the affinity of the ligands with water, ionic liquid or PEG solvents by introducing carefully chosen R' fragments (Scheme 1). Three different polar tags have been selected to accomplish this task (Scheme 4). The ligand polarity may be increased by introducing the tetraethylbisphosphonate fragment, already used previously to synthesize water soluble phosphine [36], to generate compound 4b.

Bisphosphonate esters are also potential precursors of highly charged bisphosphonate anions, R2C(PO3 2-)2, which may increase water solubility, although they may also compete with the PO donating atoms of the core ligand for metal coordination. Such anionic ligands could be future synthetic targets. We also imagine increasing the ligand solubility by grafting an imidazolium moiety (compound 5b), a cation frequently found in ionic liquids. This cation is specifically designed for use in water or ionic liquid media. The third considered fragment is a monomethylether PEG750 (compound 6b), in order to increase the ligand solubility in water or PEG media.

Ligand 4b was obtained from 3 in a two step synthesis via compound 4a (Scheme 4).

The methodology involved the reactive tetraethyl methylenebisphosphonate carbanion, prepared from the treatment of tetraethyl methylenebisphosphonate with sodium hydride in THF at 0°C, which efficiently replaced the bromide ion in compound 3. The moderate yield of 40% for this step is partially explained by the subsequent formation of the dialkylated compound 4c (Scheme 5). In agreement with published results [37], this reaction gave mainly monoalkylated product 4a with small amount (60 mg) of dialkylated 4c (12% of the consumed 3) and unreacted starting material. The desulfurization of 4a was achieved with high efficiency using tris(dimethylamino)phosphine in refluxing toluene for twelve hours under argon atmosphere. 4b was obtained as an orange oil after flash chromatographic purification (90% overall yield). Compounds 4a, 4b, 4c have been isolated and completely characterized by mass spectrometry and multinuclear NMR. Significant NMR signals are reported in Table 1.

The synthesis of compound 5a was successfully carried out by addition of methylimidazole on compound 3 in refluxing toluene. It was isolated by filtration as a pure yellow powder in a relatively good yield (70%). The same desulfurization procedure used for 4b was not applied because of the high imidazolium affinity to silicagel. Therefore, we turned our attention to a procedure involving heterogeneous conditions [38,26]. Desulfurization was performed by reacting 5a with Raney Ni in acetonitrile under an argon atmosphere at 50°C. Compound 5b was isolated as a yellow solid in quantitative yield after filtration. Significant NMR signals for both 5a and 5b are reported in Table 1.

The third target is a P,O ferrocenyl ligand bearing a polyethyleneglycol chain. We have chosen PEG 750 monomethylether. 1 H NMR integration confirmed the general formula of this PEG: MeO(CH2CH2O)16.3H. Compound 6a was obtained by addition of an excess PEG 750 monomethylether alcoholate, prepared by treatment of PEG 750 monomethylether with sodium hydride, on compound 3 in THF at 0°C. Compound 6a was isolated as a yellow wax in 60% yield. This low value compared to the crude reaction yield is due to the water solubility of 6a leading to partial loss during the extraction and washing to eliminate the PEG 750 excess.

Desulfurization was carried out using tris(dimethylamino)phosphine (Scheme 4) followed by flash chromatographic purification, yielding compound 6b. Compounds 6a and 6b were fully characterised by multinuclear NMR.

Conclusion

Chiral phosphine-ether 2b has been synthesized and successfully used in a Suzuki-Miyaura coupling reaction. In addition, tagged analogues of 2b bearing various polar substituents (bisphosphonate, imidazolium, PEG750 monomethylether groups) have been prepared from the same synthetic intermediate, compound 3. All of these ligands have been obtained as racemic mixtures but may be easily obtained in an enantiomerically pure form starting from the enantiomerically pure alcohol 1, allowing their use in asymmetric catalysis [39]. The use of this new P,O ligands in catalytic reaction (Suzuki reaction,..) in non-classical media and the assessment of their efficiency in catalyst recycling is currently underway.

Experimental

General

All reactions were carried out using conventional Schlenk techniques under an inert atmosphere of argon. Thin layer chromatography and flash chromatography were carried out on Merck Kieselgel 60F254 precoated aluminum plates and Merck Kieselgel 60 respectively. Solvents were dried by conventional methods before use. Commercial samples were used as received without further purification (tetrafluoroboric acid diethylether complex, tetraethylmethylenebisphosphonate, N-methylimidazole, Pd2(dba)3, Raney ® 2800 slurry in H2O and phenylboronic acid from Sigma Aldrich; tris(dimethylamino)phosphine, monomethylether mPEG 750 and diethylene glycol dibutyl ether from Alfa Aesar; bromobenzene from Janssen Chimica). GC analyses were realized with an Agilent 6890 chromatograph equipped with FID detector, automatic sampler and HP5-MS capillary column (30m x 0.25mm x 0.25µm). NMR analyses were performed on Bruker AV500, AV300 and DPX200 instruments. The spectra were referenced internally using the signal from the residual solvent for 1 H and 13 C, and externally using 85% H3PO4 for 31

Syntheses

Racemic 2-thiodiphenylphosphino(hydroxymethyl)ferrocene, 1, was synthesized according to published procedure [40].

Synthesis and characterization of compound 2a

In a Schlenk tube, 0.75 g of 1 (1.74 mmol) was dissolved in 8 mL of dry dichloromethane. A 54% solution of tetrafluoroboric acid in ether (0.73 mL, 5.30 mmol) was then added. After 1 min stirring, a solution of 2.5 g of 4-methylbenzylalcohol (20.5 mmol) in 8mL of dry dichloromethane was added. After 1 min of stirring, the crude material was filtered on silica gel with ether as eluent. After evaporation of the solvent, 0.4 g of 2a was obtained as a yellow solid (yield = 43%). 1 Hz: subst Cp); 66.7 (s: CpCH2O); 21.3 (s: CH3). 31

Synthesis and characterization of compound 2b

In a Schlenk tube, 350 mg of 2a (0.22 mmol) were dissolved in 5 mL of dry toluene together with 0.75 mL of tris(dimethylamino)phosphine (3.9 mmol). The solution was kept at reflux overnight under argon. After cooling back to room temperature, the solution was evaporated in vacuo. The crude residue was purified under argon by flash chromatography on silica gel with dichloromethane as eluent. After evaporation of the solvent, 235 mg of 2b were obtained as an orange waxy solid (yield = 70%). 1

Synthesis and characterization of 4-(bromomethyl)benzyl alcohol

At 0°C, in a Schlenk tube, 65 mL of BH3.THF (1M in THF, 65 mmol) were added to 11.6 g of 4-(bromomethyl)benzoic acid (54 mmol) in 20 mL of freshly distilled THF, under argon. After 2 h stirring at room temperature, 20 mL of methanol were added slowly. The clear solution was concentrated. The crude product was solubilized in ether and washed with an aqueous saturated solution of NaHCO3. After concentration, 10.4 g of a white solid were obtained (yield = 96%) without further purification. 1

Synthesis and characterization of compound 3

In a Schlenk tube, 1.5 g of 2-thiodiphenylphosphino(hydroxymethyl)ferrocene 1 (3.47 mmol) was dissolved in 15 mL of dry dichloromethane. Then 1.5 mL of a 54% solution of tetrafluoroboric acid in ether (10.86 mmol) was added. After 1 min stirring, a solution of 5.12 g of 4-(bromomethyl)benzylalcohol in 12 mL of dry dichloromethane was added. After 1 min of stirring, the crude material was filtered on silica gel with ether as an eluent. After evaporation of the solvent, 1.5 g of 3 was obtained as a yellow solid (yield = 70%). 1

Synthesis and characterization of compounds 4a and 4c.

In a Schlenk tube, 250 mg of tetraethylmethylenebisphosphonate (0.87 mmol) were reacted with a suspension of 250 mg of sodium hydride (60% dispersion in mineral oil) in 5 mL of THF. After 1 h at room temperature, the filtered solution was transferred via cannula on 500 mg of compound 3 (0.81 mmol) dissolved in 20 mL of THF. After 1 day, 10 mL of a saturated aqueous solution of ammonium chloride were added and the product was extracted with ethyl acetate. The crude material was purified by flash chromatography on silica gel with ethyl acetate/ethanol (9/1) as eluent. Compounds 3, 4a and 4c were successively recovered. After evaporation of the solvent, 270 mg of 4a was obtained as an orange solid (yield = 40%). 1 Hz: CH3 phosphonates). 31 After evaporation of the solvent, 60 mg of 4c were recovered as a waxy solid. 1

Synthesis and characterization of compound 4b

In a Schlenk tube, 180 mg of 4a (0.22 mmol) were dissolved in 5 mL of dry toluene with 0.24 mL of tris(dimethylamino)phosphine (1.3 mmol). The solution was kept at reflux overnight under argon. After cooling back to room temperature, the solution was evaporated in vacuo.

The crude residue was purified under argon by flash chromatography on silica gel with dichloromethane as eluent. After solvent evaporation, 120 mg of 4b were obtained as an orange waxy solid (yield = 70%). 1 (12H, t of d, J= 6.9 Hz, JPH = 4.9 Hz: CH3 phosphonates). 13 After evaporation of the solvent, 35 mg of 6b were obtained as an orange waxy solid (yield = 45%). 1 3.78 (1H, m: subst Cp); 3.66-3.65 (64H, m, CH2-PEG); 3.39 (3H, s, CH3O-PEG). 13 CpCH2); 59.1 (s: CH3O-PEG). 31 P NMR (81.0 MHz, CDCl3),  (ppm): -22.0.

General procedure for coupling reaction of aryl bromides with boronic acids

In a typical procedure for coupling reaction (Scheme 2), ligand 2b (6 mg, 0.012 mmol, 1.2 mol %), Pd2(dba)3 (5 mg, 0.005 mmol, 1.1 mol %), phenylboronic acid (146 mg, 1.2 mmol) and cesium carbonate (750 mg, 2.030 mmol, 2.3 mol %) were introduced into a Schlenk tube under an argon stream. A solution of bromobenzene (157 mg, 1.00 mmol) in 10 mL of dioxane was added into the Schlenk tube via a syringe. The reaction mixture was stirred at 70°C for 8 h under an Ar atmosphere. Aliquots (0.5 mL) of the solution were taken using a polypropylene syringe. One mL of water was added in each collected samples. After extraction by two portions of 1 mL of diethylether, the organic phase was then filtered on silica and analysed by GPC using diethylene glycol dibutyl ether as internal standard.

X-ray diffraction studies.

A single crystal of compound 3 was mounted under inert perfluoropolyether at the tip of a glass fibre and cooled in the cryostream of a Bruker APEXII CCD diffractometer. Data were collected using the monochromatic MoK radiation (= 0.71073). The structure was solved by direct methods (SIR97 [START_REF] Altomare | SIR97 a program for automatic solution of crystal structures by direct methods[END_REF]) and refined by least-squares procedures on F 2 using SHELXL-97 [42]. All H atoms attached to carbon were introduced in calculation in idealised positions and treated as riding models. There is half of a dichloromethane solvate per asymmetric unit located around a twofold axis. The drawing of the molecules was realized with the help of ORTEP32 [START_REF] Farrugia | ORTEP3 for Windows[END_REF]. Crystal data and refinement parameters are shown in Table 1. Crystallographic data (excluding structure factors) have been deposited with the Cambridge Crystallographic Data Centre as supplementary publication number CCDC 745960. Copies of the data can be obtained free of charge on application to the Director, CCDC, 12 Union Road, Cambridge CB2 1EZ, UK (fax: (+44) 1223-336-033; e-mail: deposit@ccdc.cam.ac.uk).

Figure captions

  P. Chemical shifts and coupling constants are given in ppm and Hertz respectively. The following abbreviations are used: s, singulet; d, doublet; t, triplet; quint, quintuplet; m, multiplet; br, broad. Elemental analyses were realized by "Service d'Analyse du Laboratoire de Chimie de Coordination", Toulouse, France. Mass spectral analyses (FAB + with MNBA matrix; HR MASS) were performed by "Service Commun de Spectrométrie de Masse" of the Université Paul Sabatier, Toulouse (France).

  H NMR (200.1 MHz, CDCl3),  (ppm): 7.90-7.65 (4H, m: PPh2); 7.52-7.34 (6H, m: PPh2); 7.05 (2H, d, J = 7.9 Hz: Ph); 6.95 (2H, d, J = 7.9 Hz: Ph); 4.89 (1H, d, J = 10.9 Hz: CpCH2); 4.66 (1H, m: subst Cp); 4.45 (1H, d, J = 10.9 Hz: CpCH2); 4.35 (1H, m: subst Cp); 4.33 (5H, s: Cp); 4.29 (2H, d: 2.9Hz: PhCH2O); 3.85 (1H, m: subst Cp); 2.33 (3H, m: CH3). 13 C NMR (50.3 MHz, CDCl3),  (ppm): 136.8 (s: quat Ph); 135.4 (s: quat Ph); 134.8 (d, JPC = 87.1 Hz: quat PPh2); 133.6 (d, JPC = 86.1 Hz: quat PPh2); 132.2 (d, JPC = 10.7 Hz: PPh2); 132.1 (d, JPC = 10.7 Hz: PPh2); 131.2 (d, JPC = 2.2 Hz: PPh2); 131.1 (d, JPC = 2.2 Hz: PPh2); 128.8 (s: Ph); 128.1 (d, JPC = 12.3 Hz: PPh2); 128.0 (d, JPC = 12.3 Hz: PPh2); 127.7 (s: Ph); 88.3 (d, JPC = 12.1 Hz: quat Cp); 75.2 (d, JPC = 12.5 Hz: subst Cp); 75.6 (d, JPC = 94.7 Hz: quat Cp); 74.5 (d, JPC = 9.4 Hz: subst Cp); 72.4 (s, PhCH2O); 70.7 (s: Cp); 69.4 (d, JPC = 10.4

  P NMR (81.0 MHz, CDCl3) ,  (ppm): 43.1. HR MS (DCI CH4), C31H29OPSFe, calcd. mass [M]: 536.1026; exp. mass [M]: 536.1039.

  H NMR (200.1 MHz, CDCl3),  (ppm): 7.67-7.58 (2H, m: PPh 2 ); 7.48-7.41 (3H, m: PPh 2 ); 7.32-7.29 (5H, m: PPh 2 ); 7.08 (2H, d, J = 8.1 Hz: Ph); 6.97 (2H, d, J = 8.1 Hz: Ph); 4.65 (1H, dd, J = 10.9 Hz, JPH = 2.2 Hz: CpCH2); 4.60 (1H, m: subst Cp); 4.44 (1H, d, J = 10.9 Hz: CpCH2); 4.37 (2H, s: PhCH2O); 4.36 (1H, m: subst Cp); 4.08 (5H, s: Cp); 3.83 (1H, m: subst Cp); 2.37 (3H, m: CH 3 ). 13 C NMR (50.3 MHz, CDCl 3 ),  (ppm): 140.8 (d, JPC = 9.3 Hz: quat PPh2); 138.3 (d, JPC = 8.2 Hz: quat PPh2); 137.6 (s: quat Ph); 136.2 (s: quat Ph); 135.9 (d, JPC = 20.3 Hz: PPh2); 133.2 (d, JPC = 17.9 Hz: PPh2); 129.9 (s : PPh2); 129.6 (s: Ph); 128.9 (d, JPC = 7.5 Hz: PPh2); 128.8 (d, JPC = 5.7 Hz: PPh2); 128.5 (s: PPh2); 128.4 (s: Ph); 90.1 (d, JPC = 24.6 Hz: quat Cp); 77.5 (d, JPC = 8.1 Hz: quat Cp); 73.5 (d, JPC = 3.4 Hz: subst Cp); 72.9 (s, PhCH2O); 72.7 (d, JPC = 3.7 Hz: subst Cp); 70.6 (s: subst Cp); 70.3 (s: Cp); 68.1 (d, JPC = 9.9 Hz: CpCH2); 22.0 (s: CH3). 31 P NMR (81.0 MHz, CDCl3),  (ppm): -22.9 (PPh2). HR MS (DCI CH4), C31H29OPFe, calcd. mass [M+H]: 505.1375; exp. mass [M+H]: 505.1384.

  H NMR (300.1 MHz, CDCl3),  (ppm): 7.87-7.80 (2H, m: PPh2); 7.72-7.65 (2H, m: PPh2); 7.55-7.40 (4H, m: PPh2); 7.39-7.30 (2H, m: PPh2); 7.23 (2H, d, J = 8.0 Hz: Ph); 6.98 (2H, d, J = 8.0 Hz: Ph); 5.01 (1H, d, J = 10.8 Hz: CpCH 2 ); 4.65 (1H, m: subst Cp); 4.48 (2H, s: CH 2 Br); 4.44 (1H, d, J = 10.8 Hz: CpCH2); 4.34 (5H, s: Cp); 4.34 (2H, s: PhCH2O); 4.30 (1H, m: subst Cp); 3.84 (1H, m: subst Cp). 13 C NMR (75.5 MHz, CDCl3),  (ppm): 138.9 (s: quat Ph); 136.6 (s: quat Ph); 134.9 (d, JPC = 87.4 Hz: quat PPh2); 133.6 (d, JPC = 86.5 Hz: quat PPh2); 132.2 (d, JPC = 10.0 Hz: PPh2); 132.0 (d, JPC = 10.0 Hz: PPh2); 131.3 (d, JPC = 2.5 Hz: PPh2); 131.1 (d, JPC = 2.5 Hz: PPh2); 128.9 (s: Ph); 127.9 (s: Ph); 128.1 (d, JPC = 12.5 Hz: PPh2); 128.0 (d, JPC = 12.5 Hz: PPh2); 88.0 (d, JPC = 12.0 Hz: quat Cp); 75.3 (d, JPC = 12.6 Hz: subst Cp); 74.7 (d, JPC = 94.9 Hz: quat Cp); 74.6 (d, JPC = 9.3 Hz: subst Cp); 72.0 (s: PhCH2O); 70.7 (s: Cp); 69.5 (d, JPC = 10.0 Hz: subst Cp); 67.1 (s: CpCH2O); 33.6 (s: CH2Br). 31 P NMR (121.5 MHz, CDCl3),  (ppm): 41.8. MS (FAB >0; MNBA), C31H28BrFeOPS, m/z: 616 ([M] + ).

  H NMR (200.1 MHz, CDCl3),  (ppm): 7.87-7.62 (4H, m: PPh2); 7.50-7.16 (6H, m: PPh2); 7.14 (2H, d, J = 8.1 Hz: Ph); 6.96 (2H, d, J = 8.1 Hz: Ph); 4.38 (1H, d, J = 11.0 Hz: CpCH2). 4.89 (1H, dd, J = 11.0 Hz: CpCH2); 4.63 (1H, m: subst Cp); 4.31 (2H, s: PhCH2O); 4.31 (5H, s: Cp); 4.27 (1H, m: subst Cp); 4.20-4.00 (8H, m: CH2 phosphonates); 3.82 (1H, m: subst Cp); 3.21 (2H, t of d, J = 6.0 Hz, JPH = 16.7 Hz: PhCH2); 2.62 (1H, t of t, J = 6.2 Hz, JPH = 23.9 Hz: CHP2); 1.28 (12H, t of d, J = 7.1 Hz, JPH = 2.6 Hz: CH3 phosphonates). 13 C NMR (50.3 MHz, CDCl3),  (ppm): 135.7 (d, JPC = 87.6 Hz: quat PPh2); 139.4 (dd, JPC = 7.3 Hz: quat Ph); 134.3 (d, JPC = 86.3 Hz: quat PPh2); 137.5 (s: quat Ph); 132.9 (d, JPC = 10.1 Hz: PPh2); 132.8 (d, JPC = 10.1 Hz: PPh2); 132.0 (d, JPC = 2.4 Hz: PPh2); 131.8 (d, JPC = 2.4 Hz: PPh2); 129.4 (s: Ph); 128.9 (d, JPC = 12.8 Hz: PPh2); 128.8 (d, JPC = 12.4 Hz: PPh2); 128.3 (s: Ph); 89.0 (d, JPC = 11.9 Hz: quat Cp); 75.0 (d, JPC = 11.8 Hz: subst Cp); 75.3 (d, JPC = 95.3 Hz: quat Cp); 75.2 (d, JPC = 9.3 Hz: subst Cp); 72.0 (s: PhCH2O); 71.47 (s: Cp); 70.2 (d, JPC = 10.4 Hz: subst Cp); 67.5 (s: CpCH2O); 63.4 (d, JPC = 7.4 Hz: CH2 phosphonates); 63.2 (d, JPC = 7.7 Hz: CH2 phosphonates); 39.8 (t, JPC = 132.5 Hz: CHP2); 31.6 (t, JPC = 4.3 Hz: PhCH2); 17.1 (d, JPC = 6.4

0 (

 0 P NMR (81.0 MHz, CDCl3),  (ppm): 24.3 (phosphonates); 43.PPh2). MS (FAB >0; MNBA), C40H49FeO7P3S, m/z: 845 ([M+Na] + ), 822 ([M] + ).

  H NMR (200.1 MHz, CDCl3),  (ppm): 7.93-7.68 (8H, m: PPh2); 7.56-7.33 (12H, m: PPh2 ; 4H, d, J = 7.8 Hz: Ph); 7.02 (4H, d, J = 7.8 Hz: Ph); 4.91 (2H, d, J = 11.0 Hz: CpCH2); 4.69 (2H, m: subst Cp); 4.50 (2H, d, J = 11.0 Hz: CpCH2); 4.37-4.34 (4H, s: PhCH2O; 10H, s: Cp; 2H, m: subst Cp); 4.00-4.10 (8H, m: CH2 phosphonates); 3.88 (2H, m: subst Cp), 3.34 (4H, dd, JPH = 16.1 Hz: PhCH2); 1.19 (12H, dd, J = 7.0 Hz: CH3 phosphonates). 13 C NMR (50.3 MHz, CDCl3),  (ppm): 136.7 (s: quat Ph); 135.6 (dd, JPC = 6.1 Hz: quat Ph); 134.9 (d, JPC = 87.8 Hz: quat PPh2); 133.6 (d, JPC = 85.7 Hz: quat PPh2); 132.2 (d, JPC = 10.0 Hz: PPh2); 132.0 (d, JPC = 10.1 Hz: PPh2); 131.5 (s: Ph); 131.3 (d, JPC = 2.2 Hz: PPh2); 131.1 (d, JPC = 2.2 Hz: PPh2); 128.1 (d, JPC = 12.7 Hz: PPh2); 128.0 (d, JPC = 12.2 Hz: PPh2); 126.6 (s: Ph); 88.3 (d, JPC = 12.1 Hz: quat Cp); 75.2 (d, JPC = 12.3 Hz: subst Cp); 75.5 (d, JPC = 94.8 Hz: quat Cp); 74.4 (d, JPC = 9.4 Hz: subst Cp); 72.3 (s, PhCH2O); 70.7 (s: Cp); 69.4 (d, JPC = 10.3 Hz: subst Cp); 66.7 (s: CpCH2O); 62.3 (d, JPC = 4.6 Hz: CH2 phosphonates); 48.7 (t, JPC = 132.7 Hz: CP2); 37.3 (d, JPC = 4.2 Hz: PhCH2); 16.2 (d, JPC = 4.9 Hz: CH3 phosphonates). 31 P NMR (81.0 MHz, CDCl3),  (ppm): 43.1 (PPh2); 25.7 (phosphonates). MS (FAB >0; MNBA), C71H76Fe2O8P4S2, m/z: 1379 ([M+Na] + ), 1356 ([M] + ).

  H NMR (300.1 MHz, CDCl3),  (ppm): 7.60-7.50 (2H, m: PPh2); 7.40-7.38 (3H, m: PPh2); 7.25-7.23 (5H, m: PPh2); 7.13 (2H, d, J = 8.1 Hz: Ph); 6.95 (2H, d, J = 8.1 Hz: Ph); 4.58 (1H, dd, J = 10.8 Hz, JPH = 2.2 Hz: CpCH2); 4.54 (1H, m: subst Cp); 4.38 (1H, d, J = 10.8 Hz: CpCH2); 4.32 (2H, s: PhCH2O); 4.31 (1H, m: subst Cp); 4.11 (8H, quint., JHH= JPH = 6.9 Hz: CH2 phosphonates); 4.02 (5H, s: Cp); 3.79 (1H, m: subst Cp); 3.21 (2H, t of d, J = 16.3 Hz, JPH = 6.2 Hz: PhCH2); 2.62 (1H, t of t, J = 6.2 Hz, JPH = 24.0 Hz: CHP2); 1.28

  C NMR (75.5 MHz, CDCl3),  (ppm): 140.0 (d, J PC = 9.6 Hz: quat PPh 2 ); 138.6 (t, J PC = 7.1 Hz: quat Ph); 137.5 (d, J PC = 8.4 Hz: quat PPh2); 136.7 (s: quat Ph); 135.1 (d, JPC = 21.3 Hz: PPh2); 132.4 (d, JPC = 18.1 Hz: PPh2); 129.2 (s : PPh2); 128.7 (s: Ph); 128.1 (d, JPC = 8 Hz: PPh2); 128.0 (d, JPC = 6.2 Hz: PPh2); 127.7 (s: PPh2); 127.4 (s: Ph); 89.2 (d, JPC = 24.6 Hz: quat Cp); 76.6 (d, JPC = 8.0 Hz: quat Cp); 72.6 (d, JPC = 3.5 Hz: subst Cp); 72.0 (s, PhCH2O); 71.9 (d, JPC = 3 Hz: subst Cp); 69.9 (s: subst Cp); 69.6 (s: Cp); 67.4 (d, J PC = 10.0 Hz: CpCH 2 ); 62.6 (d, J PC = 6.7 Hz: CH 2 phosphonates); 62.5 (d, JPC = 6.7 Hz: CH2 phosphonates); 39.1 (t, JPC = 132.1 Hz: CHP2 ); 30.9 (t, JPC = 4.3 Hz: PhCH2); 16.3 (d, JPC = 6.3 Hz: CH3 phosphonates); 31 P NMR (121.5 MHz, purified under argon by flash chromatography on silica gel with dichloromethane as eluent.

  H NMR (200.1 MHz, CDCl3),  (ppm): 7.62-7.52 (2H, m: PPh2); 7.41-7.36 (3H, m: PPh2); 7.25-7.23 (5H, m: PPh2); 7.18 (2H, d, J = 8.1 Hz: Ph); 6.98 (2H, d, J = 8.1 Hz: Ph). 4.60 (1H, dd, J = 10.9 Hz, J = 2.3 Hz: CpCH2); 4.55 (1H, m: subst Cp); 4.52 (2H, s: PhCH2O); 4.38 (1H, d, J = 10.9 Hz: CpCH2); 4.33 (2H, s: PhCH2O); 4.31 (1H, m: subst Cp); 4.02 (5H, s: Cp);

  C NMR (50.3 MHz, CDCl3),  (ppm): 139.9 (d, JPC = 8.9 Hz: quat PPh2); 137.8 (s: quat Ph); 137.4 (d, JPC = 8.2 Hz: quat PPh2); 137.1 (s: quat Ph); 135.1 (d, JPC = 20.6 Hz: PPh2); 132.4 (d, JPC = 17.9 Hz: PPh2); 129.1 (s: PPh2); 128.1 (d, JPC = 7.4 Hz: PPh2); 128.0 (d, JPC = 5.5 Hz: PPh2); 127.7 (s: PPh2); 127.7 (s: Ph); 127.5 (s: Ph); 89.1 (d, JPC = 25.0 Hz: quat Cp); 76.7 (d, JPC = 8.0 Hz: quat Cp); 73.1 (s: PhCH2-PEG); 72.8 (d, JPC = 3.6 Hz: subst Cp); 72.0 (d, JPC = 3.7 Hz: subst Cp); 72.0 (s: CH2); 70.9 (s: CH2-PEG); 69.8 (s: subst Cp); 69.5 (s: Cp); 67.5 (s, JPC = 9.7 Hz:

Figure 1 -

 1 Figure 1 -Suzuki-Miyaura reaction of PhBr with PhB(OH)2 in the presence of Pd2(dba)3 with and without ligand 2 (Reaction conditions: dioxane, 70°C, PhBr/Pd/ligand/Cs2CO3 = 100:1:1.2:2.3).

Figure 2 -Scheme 2 -Scheme 3 -Scheme 4 -Scheme 5 -

 22345 Figure 2 -An ORTEP view of the structure of compound 3. Ellipsoids are drawn at the 30 % probability level. The dichloromethane solvate and H atoms have been omitted for clarity.

Figure 1 -

 1 Figure 1 -Suzuki-Miyaura reaction of PhBr with PhB(OH)2 in the presence of Pd2(dba)3 with and without ligand 2 (Reaction conditions: dioxane, 70°C, PhBr/Pd/ligand/Cs2CO3 = 100:1:1.2:2.3).

Figure 2 -Scheme 1 -Scheme 2 -Scheme 3 -Scheme 4 -

 21234 Figure 2 -An ORTEP view of the structure of compound 3. Ellipsoids are drawn at the 30 % probability level. The dichloromethane solvate and H atoms have been omitted for clarity.

Table 1 -

 1 31 P and13 C (CH2R') NMR data (CDCl3,  in ppm).

Table 2 -

 2 Crystal data and structure refinement parameters for compound 3.

Table 3 -

 3 Bond distances (Å) and bond angles (°) with e.s.d.s in parentheses for the structure of compound 3.

Table 1 -

 1 31 P and13 C (CH2R') NMR data ( in CDCl3).

	compound	R'	31 P{ 1 H}		13 C{ 1 H}
	2a	H	43.1	21.3	-
	2b	H	-21.9	22.0	-
	3	Br	41.8	33.6	-
	4a	CH[PO(OEt)2]2	43.0	31.6
			24.3	dd	JPC = 4.3Hz
	4b	CH[PO(OEt)2]2	23.1	30.9
			-22.1	dd	JPC = 4.3Hz
	4c	C[PO(OEt)2]2	43.1	37.3
			25.7	dd	JPC = 4.2Hz
	5a	Imidazolium	43.0	53.2	-
	5b	Imidazolium	-22.4	53.4	-
	6a	PEG 750	43.0	73.0	-
	6b	PEG 750	-22.0	73.1	-

Table 2 -

 2 Crystal data and structure refinement parameters for compound 3.

	Identification code

Acknowledgement

The authors thank LCC CNRS for financial support, the Chemistry Department of "IUT A Paul Sabatier" for financial support and for offering accesses to some analytical equipment, and L. Orts and T. Scandella for laboratory assistance.


Mohammad Amin Yazdani

Lyes Benyoucef
email: lyes.benyoucef@lis-lab.fr

Amirhossein Khezri
email: amir_hossein.khezri@ensam.euali.siadat@ensam.eu

Ali Siadat

"New advances and challenges for sustainable and smart industries"

Keywords: Sustainability, Process planning, Production planning, Reconfigurable manufacturing systems, Multi-Objective optimization, augmented ε-constraint method

Nowadays, manufacturing systems should be cost-effective and environmentally friendly to cope with various challenges in today's competitive markets. Furthermore, being cost-effective needs to optimize the behaviour and functionality of the production system and being environmentally friendly requires to reduce the amount of harmful gasses emitted in the working area. In this context, reconfigurable manufacturing systems (RMSs) have emerged to fulfil these requirements. RMS is one of the latest manufacturing paradigms, where machines components, software or material handling units can be added, removed, modified or interchanged as needed and when imposed by the necessity to react and respond rapidly and cost-effectively to changing. In this paper, a multi-objective multi-product process and production planning problem in a sustainable reconfigurable manufacturing environment is considered. The cost function and three pillars of sustainability functions such as social, environmental, and economical are introduced and optimized. Moreover, an augmented ε-constraint method is proposed to solve the problem. Finally, an illustrative numerical example is presented to show the validity of the approach.

CONTEXT AND MOTIVATIONS

In today's world, a manufacturing system has to be costeffective and environmentally harmless to acquire sustainability and compete with other rivals in the market. According to a visionary report of Manufacturing Challenges 2020 conducted in USA, this trend will continue, and one of the six grand challenges of this visionary report is "the ability to reconfigure manufacturing systems rapidly in response to changing needs and opportunities" (Khezri et al., 2019(Khezri et al., , 2020)). Moreover, due to the escalation in fuel prices, higher tariff for electrical use and environmental legislations, the reduction in energy consumption and carbon footprint has become the need of the hour in the manufacturing sector.

Reconfigurable manufacturing system (RMS) is one of the latest manufacturing paradigms. In this paradigm, machine components, machines software's or material handling units can be added, removed, modified or interchanged as needed and when imposed by the necessity to react and respond rapidly and cost-effectively to changing requirements. RMS is recognized as a convenient manufacturing paradigm for variety productions as well as a flexible enabler for this variety. Hence, it is a logical evolution of the two manufacturing systems already used in the industries respectively dedicated manufacturing lines (DML) and flexible manufacturing systems (FMS). According to (Koren, 2010), DMLs are inexpensive but their capacities are not fully utilized in several situations especially under the pressure of global competition, thus they engender losses. On the other hand, FMSs respond to product changes, but they are not designed for structural changes. Hence, in both systems, a sudden market variation cannot be countered, such as demand fluctuation or regulatory requirements. RMS combines the high flexibility of FMS with the high production rate of DML. It comprises the positive features of both systems, thanks to its adjustable structure and design focus. Thus, in situations where both productivity and system responsiveness to uncertainties or to unpredictable scenarios (e.g., machine failure, market change, …) are of a vital importance, RMS ensures a high level of responsiveness to changes with a high performance. This can be achieved through six main principles respectively customization, convertibility, scalability, integrability, modularity, and diagnosability.

Moreover, (Koren, 2010) suggested that in manufacturing systems, the key to responsiveness in markets as well as cope with market changes caused by fluctuating quantities of demand, is to adjust the production system capacity. He stressed that this adjustment is possible thanks to two types of reconfiguration capabilities in manufacturing systems, which are functionality adjustment and production capacity adjustment. These characteristics are achievable because of reconfigurable machine tool (RMT), which is considered as one of the major components of RMS. Regarding reconfigurable structure designed, RMT provides a customized flexibility and offers a variety of alternatives features.

A sustainable future is the most important concern of human beings in today's world. This ability comprises of happiness, health, education, job satisfaction, and so on. It relies on most aspects of human race life such as social, environmental, and economic. Nowadays, numerous restrictions and laws are set pointing companies to lower the level of damage caused to the environment. Furthermore, they have to consider the health condition of their workers and the effects of harmful materials and remnants of the production on their bodies as well (Massimi et al., 2020). RMS is able to meet these challenges due to its flexibility and integrability. Moreover, it is thought to be one of the most suitable paradigms with the requirements of sustainability.

In this paper, a multi-objective multi-unit multi-part process and production planning problem in a sustainable reconfigurable environment is addressed. Two objectives are minimized respectively the total production cost and the total harmful effects of the dangerous liquids and remnants of the production on the workers' bodies. A mathematical formulation is proposed and solved using an adapted version of the augmented ε-constraint method.

The rest of paper is organized as follows. Section 2 brings up some literature review. Section 3 presents the problem description and its mathematical formulation. Section 4 describes the proposed approach. Section 5 shows the applicability of the approach using a simple numerical example. Section 6 concludes the paper and suggests some future works directions.

LITERATURE REVIEW

As one of the newest paradigms, RMS has demonstrated great potential for further researches. In this section, we briefly review some research works in sustainability, process planning and production planning.

Sustainability in manufacturing systems

The most paramount part of sustainable manufacturing is innovative products to achieve a major part of markets share and implement a sustainable environment at the same time (Khezri et al., 2019). It is necessary to shift all the production sites to sustainable product development, which is possible by using reconfigurable manufacturing systems. Besides, RMS has several advantages to impact on manufacturing process and performance as permanent changes due to answer different and situational demands of market zones. Other elements such as cost reduction, improved flexibility, and high quality of final products make RMS a suitable choice for the enabling of economic sustainability in allover the systems. Moreover, it is also plausible to implement social and environmental sustainability by the RMS (Koren et al., 2018).

Considering economic sustainability, (Garbie, 2013) claimed that cost is most widely use criterion for produc-tion environment and the consideration of the final value. In the concept of environmental sustainability, (Aljuneidi and Bulgak, 2016) believed that the implementation of the product and service design on sustainable business development can represent the system sustainability. (Dubey et al., 2017) considered the role of authorities on the final RMS sustainability by the management and organizational culture as sustainable indicator. Furthermore, energy consumption that arose from the usage of the machines in the working environment can be the indicator of the sustainable environment (Choi and Xirouchakis, 2015). In the social environment, the fluctuation of the customer's demand and their satisfaction through the changes can represent the sustainability.

Process planning

One of the essential parts of RMS is process planning. Process planning leads to find the best way of manufacturing according to the shape, properties, surface, and appearance of the final product. Process planning has emerged as an important issue in the manufacturing systems because a part of the massive production can use only one process plan. (Khezri et al., 2020) developed an environmental oriented multi-objective optimization problem in an RMS. Authors considered process plan generation while introducing a sustainability metric value and counting the manufacturing cost and time to obtain optimal process plans.

Production planning

Production planning links several segments in a manufacturing environment such as operations scheduling, capacity of the output, final product quality, etc. Furthermore, quality control and process planning can play a decisive role in the decision making of the quantitative matters (Jacob et al., 2019).

In this context, few research works have considered the implication of multiple production systems to produce a specific amount of the final products. (Liu et al., 2019) presented a mixed integer stochastic programming model for manufacturing systems. They introduced an effective tool for optimizing the production plan rely on the decision maker point of view. (Kaltenbrunner et al., 2019) considered the production planning for a highly automated pallet production. They proposed a heuristic solution approach to solve the cutting stock problem with a constraining open stack problem occurring at the beginning of the production of pallets, the saw and the downstream stacking robots. The objective is to minimize the waste of material and to ensure a continuous production flow at the pallet production site.

From the above literature review, we can conclude that the combination of process and production planning in a sustainable environment is an interesting and new topic in the RMS. Moreover, some new approaches, like the augmented ε-constraint method, can solve the problem more precisely.

PROBLEM DESCRIPTION AND MATHEMATICAL FORMULATION

Problem description

In this paper, multi-unit products are considered to be produced by several reconfigurable machines. Each product requires a set of operations linked by a precedence graph (see Figure 1). The problem aims to find the optimal process plan of each product. In this section, the mathematical formulation of the problem is presented, where two objective functions are minimized:

i) Total production cost includes the cost of operations, machines changing costs, production costs and product costs in each sequences. ii) Total sustainability function includes the environmental sustainability and social sustainability.

Some other assumptions are considered: 1-Workers just check the function of the machines during changes and process. 2-The machines wastes are hazardous for the human beings bodies'. 3-Working area is fulfilled by the hazardous gasses that can affect workers bodies'. 4-The demand is deterministic. 5-Production planning tries to consider the optimum amount of production according to the problem. 6-Process planning tries to find the best sequences and machines.

Figure 1: A simple illustrative precedence graph

Mathematical formulation

In this section, the developed multi-objective mixedinteger linear programming (MINLP) model is presented, where the following notations are used. (1)

Sets

Min 𝑍 2 = 𝑤 𝑆𝑜 𝑠 𝑆𝑜 + 𝑤 𝐸𝑛 𝑠 𝐸𝑛 (2)
Subject to the following constraints:

∑ ∑ 𝑥 𝑖𝑗ℎ 𝑝 𝑃 𝑝=1 𝐼 𝑖=1 = 1 ∀𝑗 = 1 … 𝐽 ∀ℎ = 1 … 𝐻 (3) ∑ ∑ 𝑥 𝑖𝑗ℎ 𝑝 𝑃 𝑝=1 𝐽 𝑗=1 = 1 ∀𝑖 = 1 … 𝐼 ∀ℎ = 1 … 𝐻 (4) ∑ 𝑥 𝑖𝑗ℎ 𝑝 × |𝑃𝑅 𝑖 | ℎ ≤ ∑ ∑ ∑ 𝑥 𝑖 ′ 𝑗 ′ ℎ ′ 𝑝 ℎ ′ 𝐽-1 𝑗 ′ 𝑖 ′ ∀𝑖 = 1 … 𝐼 ∀𝑗 = 1 … 𝐽 ∀𝑝 = 1 … 𝑃 (5) ∑ 𝑦 𝑗ℎ 𝑚𝑝 𝐻 ℎ=1 = 1 ∀𝑗 = 1 … 𝐽 ∀𝑚 = 1 … 𝑀 ∀𝑝 = 1 … 𝑃 (6) 𝑦 𝑗ℎ 𝑚𝑝 ≥ 𝑥 𝑖𝑗ℎ 𝑝 ∀𝑖 = 1 … 𝐼 ∀𝑗 = 1 … 𝐽 ∀𝑚 = 1 … 𝑀 ∀𝑝 = 1 … 𝑃 ∀ℎ = 1 … 𝐻 (7) ∑(𝑥 𝑖𝑗ℎ 𝑝 + 𝑥 𝑖𝑗-1ℎ 𝑝 ) 𝑖 ≤ 𝑣 𝑗𝑗 ′ 𝑚𝑝 + 1 ∀𝑗, 𝑗 ′ = 2 … 𝐽 ∀𝑚 = 1 … 𝑀 ∀𝑝 = 1 … 𝑃 ∀ℎ = 1 … 𝐻 (8) ∑ ∑ 𝑥 𝑖𝑗ℎ 𝑝 𝐽 𝑗=1 𝐼 𝑖=1 × 𝐴𝑆 𝑖𝑝ℎ × 𝐻 = 𝑞 𝑝 ∀𝑝 = 1 … 𝑃 ∀ℎ = 1 … 𝐻 (9) 𝑞 𝑝 ≥ 𝐷 𝑝 ∀𝑝 = 1 … 𝑃 (10) 𝑞 𝑝 × 𝑇 ℎ ≤ 𝐶𝐴𝑃 ℎ ∀𝑝 = 1 … 𝑃 ∀ℎ = 1 … 𝐻 (11) 𝐴𝑆 𝑝ℎ -𝐴𝑆 𝑝ℎ ′ + (1 -𝑣 𝑗𝑗 ′ 𝑚𝑝 ) × BM -1 ≥ 0 ∀𝑗, 𝑗 ′ = 1 … 𝐽 ∀𝑚 = 1 … 𝑀 ∀𝑝 = 1 … 𝑃 ∀ℎ, ℎ ′ = 1 … 𝐻 (12) ∑ 𝑞 𝑝 × 𝑇𝑃 𝑝 ≤ 𝑃𝐶𝐴𝑃 𝑝 (
𝑤 𝑆𝑜 + 𝑤 𝐸𝑛 = 1 (17) 𝑥 𝑖𝑗ℎ 𝑝 Є {0,1} 𝑦 𝑗ℎ 𝑚𝑝 Є {0,1} 𝑣 𝑗𝑗 ′ 𝑚𝑝 Є {0,1} ∀𝑖 = 1 … 𝐼 ∀𝑗 = 1 … 𝐽 ∀𝑚 = 1 … 𝑀 ∀𝑝 = 1 … 𝑃 ∀ℎ = 1 … 𝐻 (18)
Constraint (3) ensures every operation is done according to process plan. Constraint (4) indicates that each operation is processed once for products in each configuration. Constraint (5) states that each operation is processed if all of the predecessors operations are already finished. Constraint (6) illustrates that each configuration contains machines and products. Constraint (7) ensures that if operation i performed at position p, machine m and configuration c are required. Constraint (8) shows that if there is a change in the machines between the positions or not during the production. Constraint (9) claims that the number of final products is equal to the production sides. Constraints (10) indicates that it is crucial to produce more than the customer demands in order to prevent shortage. Constraint (11) introduces the production capacities. Constraint (12) uses to break the loops in the production site of RMS. Constraint (13) indicates that the amount of production time should not exceed the available time. Constraint ( 14) illustrates the environmental impacts of the production. Constraint (15) considers the limitation of total required liquid in during the production process. Constraint ( 16) indicates the social impacts of the production. Constraint ( 17) is the sum of weights.

PROPOSED APPROACH

Several researchers categorized process plan generation as NP-hard problem (Khezri et al., 2020). The proof is simple since process plan generation is aimed to assign suitable machines and configurations to each operation, it can be translated to the well-known travelling salesman problem, which is known as a NP-hard problem. By this translation, operations are taken as nodes and problem is to minimize the objectives given. For the first step, the algorithm calculates the maximum and minimum of each objective function (Mavrotas, 2009). For example, we optimize the kth objective function with consideration of all the constraints. Then, consider the set of achieved solutions for the other functions in the range of each one of them. In this case:

• i= 1 contemplates cost objective function • i=2 contemplates sustainability objective function

The using range is as follows:

𝜀 𝑖 = 𝐹𝑛 𝑖 𝑚𝑎𝑥 - 𝑟 𝑝 𝑘 × 𝑖 𝑤ℎ𝑒𝑟𝑒 𝑖 = 2 ( 19
)
where i is total objective functions interval grids and 𝜀 𝑖 is considered as the upper bound and by varying the kth objective function, the Pareto solutions can achieved. In this regard, the augmented ε-constraint method is implemented to solve the problem. Figure 2 illustrates the flowchart of the algorithm. The decision maker will choose his preference objective function and the other objective will go under the constraint of the problem. It is contemplate as the initial step.

NUMERICAL EXPERIMENTS AND ANALYZES

In this section, an illustrative example is given and the presented mathematical formulation is implemented in GAMS 30.3.0 and test problems are solved by a laptop computer with Intel(R) Core(TM) i7-6700HQ CPU 2.60GHz and 12GB RAM.

Solving a test problem

We have three reconfigurable machines M1, M2 and M3 to produce three different products P1, P2, and P3. The sustainability effects of each one of the sustainability effectors are equal to 0.5, and three different configurations H1, H2 and H3 are available. The best generated process plans achieved by running the algorithm, and the best sequence of each product are shown in Table 1. As an example, product P3 uses machine M3 during Operation Op1 by configuration H3. The most important thing is to avoid irrational changes that increase costs. Furthermore, the pay of table of augmented ε-constraint method is presented in Table 2.

In this test problem, the best amount of cost function is 716.69($) and the amount of harmful effects of liquid and gases is 0.27 sustainability unit (S.u). The less amount of final sustainability function shows lower environmental and social harmful impacts. Hence, we tried to minimize these values as much as possible. Moreover, for the production planning, the optimum amount of the products according to the solved problem is shown in Table 3.

Changes of PT

Changes of the processing time, can be predictable on the sustainability function, and the increase of this parameter will increase the final answer of second objective function. But the increases of this parameter have unpredictable impacts on the cost function. Figure 3 shows the changes of this parameter. In most cases, decision makers prefer to maximize their profits; therefore, they try to minimize the cost and consider the best choice for their business. The silver lining is that by choosing the best cost, they will put their workers' health into a risky position, and it is possible to hurt them more than the usual way. Moreover, they have to obey laws that exist for human rights. In the working area, they have to consider an average point that minimum costs and doesn't cross the rolls line that means having proper sustainability objective function. On the other hand, they can't only focus on the best sustainability function. In this problem, the point with 766 ($) and 0.37 (S.u) can be a suitable choice for a decision-maker.

CONCLUSION

For the first time, in this paper, the process and production planning are considered in the RMS concept. Furthermore, to make the problem more realistic, all the sustainability issues, such as social, environmental, and economic are deemed. The problem has been formulated with two objective functions to minimize and solved using an adapted version of the ε-constraint method. For future works, new meta-heuristic algorithms or other heuristic approaches to solve the problem in a large number can be exciting. Furthermore, considering inventory management and maintenance can be useful extensions for the mathematical formulation.

  i , i' Indices of operations ∈ {1, …, N} j , j' Indices of position in the sequences ∈ {1, …, J} p, p' Indices of products ∈ {1, …, P} m ,m' Indices of machines ∈ {1, …, M}

  𝑃𝐶 𝑖𝑗𝑝Processing cost of operation i on the product p at position j 𝑃𝑅 𝑖 Set of predecessors of operation 𝑄𝐶 𝑝ℎ Production cost of product p in configuration h 𝐸𝐿 𝑖,𝑗 Harmful liquid remnants of the operation i at position j 𝐸𝐺 𝑖,𝑗 Harmful gases emission of the operation i at position j 𝑙 𝑖,𝑗 Required liquid for operation i at the position j L Total available liquid EF The effect of harmful gases on the human body during the working hours Decision variables 𝑥 𝑖𝑗ℎ 𝑝 (𝑥 𝑖𝑗ℎ 𝑝 = 1) if operation i, of product p is processed at position j, using configuration h (𝑥 𝑖𝑗ℎ 𝑝 = 0) otherwise 𝑦 𝑗ℎ 𝑚𝑝 (𝑦 𝑗ℎ 𝑚𝑝 =1) if machine m, is at the position j, to produce product p using configuration h (𝑦 𝑗ℎ 𝑚𝑝 = 0) otherwise 𝑣 𝑗𝑗 ′ 𝑚𝑝 (𝑣 𝑗𝑗 ′ 𝑚𝑝 = 1) if there is a change in machine m between the position 𝑗 and 𝑗 ′ , to produce product p (𝑣 𝑗𝑗 ′ 𝑚𝑝 = 0) otherwise 𝑞 𝑝 Production quantity of product p 𝐴𝑆 𝑝ℎ Assignment matrix of the product p to sequence h 𝑠 𝑆𝑜 Sustainability indicator of the social aspect 𝑠 𝐸𝑛 Sustainability of the environmental aspect 𝑍 1 Cost function 𝑍 2 Sustainability function Objective function (1) details the total cost, where objective function (2) presents the sustainability matters. In this research work, social and environmental aspects are considered as the sustainability matters that can have impacts other than economic factors on the human being lives during production.

Figure 2 :

 2 Figure 2: Flowchart of the developed augmented εconstraint method

FigureFigure 4

 4 Figure 3. Changes of PT 5.3 Pareto frontier solutions Figure 4 illustrates the Pareto frontier solutions that consist 22 different points by the running of the algorithm. As we see in the payoff table and in the chart, the best amount of cost function is 716.69($) when the sustainable function is 0.60 (S.u). The best amount of sustainable function is 0.27 (S.u), while the cost function is 841.22($). The Pareto frontier solutions obtained by

Figure 4 .

 4 Figure 4. Parto frontier solutions

Table 1

 1

	: Optimum sequence of each product
	𝒁 𝟏 ($)	𝒁 𝟐 (S. u)
	716.69	0.60
	841.22	0.27

Table 2 .

 2 Payoff table of objective functions

	Products	q
	1	10
	2	15
	3	15

Table 3 .

 3 Optimum product quantitates

 Aljuneidi, T., & Bulgak, A. A. (2016)


Erica Capawa Fotsoh

Pierre Castagna
email: pierre.castagna@univ-nantes.fr

Nasser Mebarki
email: nasser.mebarki@univ-nantes.fr

Pascal Berruet
email: pascal.berruet@univ-ubs.fr

-Agadir -Morocco "New advances and challenges for sustainable and smart industries" MODULARITY OF RMS: WHAT ABOUT THE AGGREGATION?

Keywords: Modularity, Aggregation methods-functions, simulation model, KPI, RMS, reconfiguration decisionmaking

Modularity of Reconfigurable Manufacturing System (RMS) reduces the system complexity, both in design and evaluation of the system. In this paper we proposed a modular view of the system that considers a module regarding four aspects: physical, control logic, KPI and simulation model. The last two one allows an accurate diagnosis of the system in case of disturbances. Each module is evaluated and studied. Yet, the reconfiguration decision is made regarding the system level, thus, modules have to be aggregated. The lack of aggregation methods for simulation model and control logic, and the lack of aggregation functions for KPIs constitute the issue addressed by this paper. The aim of our study is to investigate the aggregation of these aspects of the modules in order to have accurate data at the system level for reconfiguration decision making. A case study in conducted to show how aggregation could be made. Far from proposing rigid models of aggregation, the aim of the paper is to provide opportunities of thinking about the notion of aggregation of simulation models, KPI and control logic within manufacturing context, especially within modular reconfigurable manufacturing system.

INTRODUCTION

Reconfigurable manufacturing systems (RMSs) are designed to produce "what is needed just when is needed". [START_REF] Mehrabi | Reconfiguration manufacturing systems: Key to future manufacturing[END_REF]. This is possible because the configuration chosen for the system at a given time matches with the needs that arise. A deep diagnosis of the system is often needed to clearly identify the reconfiguration needs and to determine an appropriate reconfiguration strategy [START_REF] Capawa Fotsoh | A Classification for Reconfigurable Manufacturing Systems[END_REF]. This involves a deep knowledge about the manufacturing system and a good analysis of the system performances through KPI [START_REF] Maier-Speredelozzi | Selecting manufacturing system configurations based on performance using AHP[END_REF].

The diagnosis should reveal the level at which the reconfiguration might be carried: machine level or system level for example [START_REF] Capawa Fotsoh | A Classification for Reconfigurable Manufacturing Systems[END_REF]. Herein an analysis of the performances through KPIs at each level is required. This task is often difficult due to the complexity of the systems. One way to overcome this issue is to use modularity. [START_REF] Lameche | Modularity in the design of reconfigurable manufacturing systems[END_REF] states that modularity reduces the system complexity and allows the organization of the system in a set of distinct functional component that can be developed and studied independently. That is, the system is broken into number of subsystems each having its KPIs. As KPIs results from the behavior of the system, the analysis of the KPIs at a given time should take into account the control logic applied at that time.

Once the diagnosis is done and the reconfiguration point identified, a new configuration is chosen. This configuration has to be evaluated before its implementation.

Simulation is widely used to address this issue. [START_REF] Cardin | Handling uncertainty in production activity control using proactive simulation[END_REF], [START_REF] Lateef-Ur-Rehman | Manufacturing configuration selection using multicriteria decision tool[END_REF]). Yet, building a simulation model of a complex system, is difficult. Nevertheless, the use of the system modularity could lead to a modular build of the simulation model. That is, each subsystem is faithfully represented by a simulation model, as it is in real life. This principle of modularity in simulation models has been widely applied during the last decades to easily evaluate manufacturing system [START_REF] Hibino | Manufacturing adapter of distributed simulation systems using HLA[END_REF].

Therefore, modularity is seen as an answer to the system complexity. It helps in a deep knowledge about the system and guide the reconfiguration strategy. As the reconfiguration decision is made regarding the system level, the evaluation of the results of each subsystem have to be considered at the system level. Thereby, arises the need to aggregate subsystem's KPIs, simulation models and even control logic. This issue is the one addressed by this paper. Our target is to investigate the modularity of the system regarding the simulation model, control logic and KPI of the system, and to study the aggregation of the module in order to have accurate data at the system level for reconfiguration decision making. Far from proposing rigid models of aggregation, the aim of the paper is to provide opportunities of thinking about the notion of aggregation of simulation models, KPI and control logic within manufacturing context. Herein, the aim of the paper is to highlight the importance of aggregation, especially within the process of reconfiguration decision making for modular manufacturing systems.

The remainder of this article is as follow: section 2 presents the modular vision of RMS, section 3 states the MOSIM'20 -November 12-14, 2020 -Agadir -Morocco aggregation problem and present the role of aggregation. Section 4 uses an illustrative example to present some ideas about aggregation methods. Finally section 5 discusses and concludes the paper.

A MODULAR VISION OF RMS

Modularity helps in reducing the system complexity. It concerns physical and logical aspect [START_REF] Koren | Design of reconfigurable manufacturing systems[END_REF], but also KPIs and even simulation model used to represent the system. A module is then considered as a system element with four aspects: physical, logical, KPIs and simulation. The aggregation of several modules constitute the system. Hence, choosing a new configuration will be choosing the modules that will be put together (aggregated) and define how the aggregation will be made. The highest module represents the system itself.

The physical aspect of the module (PM) refers to tangible element in the real life. It could be a workstation, operators, storage system, etc. It is managed by a control logic, and has related KPI and simulation model. Before implementing the PM in real life, its simulation model can be used for evaluation.

The control aspect (CM) describes the behavior and manages the PM. It represents the intelligence of the PM. CM is faithfully replicate in the simulation aspect of the module, to ensure the correspondence between the real world and virtual word.

The simulation aspect (SM) is the virtual representation of the module. It allows to evaluate modules as it would be in real life situation. Simulation aspect of the module gives an insight of the system in case of reconfiguration process.

The KPIs measure the performance of the module. Value could either be measured on the real system or simulated. It allows the diagnosis of the module, and triggers the reconfiguration decision.

A representation of this module-based view of RMS is given on (Fig. 5). This module based view of the system allow to reduce the system complexity regarding the design or even the evaluation of the configuration, thus ease the reconfiguration process. The remaining issue concerns the aggregation of the modules

AGGREGATION: PROBLEM STATEMENT AND ROLE

Problem statement

To better understand the issue, let us consider the following example: A manufacturing system made of two workstations M1 and M2. M1 behaves following the FIFO (First in First out) rule and its utilization rate is represented by the curve denoted M1 on Fig. 1. Whereas M2 follows a particular control logic, depending on the product and its utilization curve is denoted M2 on Fig. 1.

In order to study the behavior of the system, the models of M1 and M2 are put together. It is therefore necessary to consider an aggregation function that will allow the system (upper level) to combine the different information from the lower levels (i.e from M1 and M2). For example, what would be the utilization rate to consider? Fig. 2 gives an glimpse of possible answers. At the system level, solution 1 considers the utilization rate as the sum of M1 and M2. Solution 2 considers maximum (Max) between M1 and M2, and solution 3 the average between M1 and M2.

Role of aggregation

Aggregation functions are usually defined and used to combine and resume several values into one, so that the end result of the aggregation takes into account, in a specified way, all the individual values. The notion of aggregation functions is widely used in statistics, economics, finance or even informatics (information retrieval) [START_REF] Moulahi | Définition et évaluation de modèles d'agrégation pour l'estimation de la pertinence multidimensionnelle en recherche d'information[END_REF], where aggregated values are often numerical or strings, as KPIs in manufacturing domain.

The reconfiguration decision at the system level takes into account the KPIs of each the module within a configuration. Even though the module is evaluated individually, it contributes to the system's performance. Therefore, the aggregation function of KPIs is needed and should be chosen carefully. Many mathematical functions are used to address numerical aggregation issue. Depending on the context and the purpose of the study, functions such as quadratic mean, minimum, maximum, standard deviation, etc. could be chosen [START_REF] Bouyssou | Concepts et méthodes pour l'aide à la décision[END_REF]. As modules of the system have an impact on each other and exchange information. Aggregating two modules results in determining what will be KPIs and the behavior of the system. That is to de-MOSIM'20 -November 12-14, 2020 -Agadir -Morocco termine the control logic that will be applied at the system level to manage several aggregated modules. Herein, the aggregation of control logic is required [START_REF] Leitão | An Agile and Adaptive Holonic Architecture for Manufacturing Control[END_REF], as well as the aggregation of simulation model for a relevant evaluation of the system.

For simulation models, High Level Architecture (HLA) is a standard that promotes aggregation, interoperability between simulations, and aid the reuse of models in different context (IEEE 1516(IEEE , 2000)). More often, HLA is used when simulations use different several activities: each activity is represented by a simulation model which is then connected and coordinated with other model. HLA has proposed standards to support the interoperability within simulation of a whole system that involved several manufacturing actives such as materials activity, production activity and even commercialmarketing activity. Each activity often has its simulator, and the drawback that remains when applying the standards in real life is about combining models from different simulators [START_REF] Pedrielli | Simulation of complex manufacturing systems via HLA-based infrastructure[END_REF]. The literature review conducted by [START_REF] Thein | Implementing Data Distribution Management System Using Layer Partition-based Matching Algorithm[END_REF] gives a great overview about previous works carried in this field. So far, the concept of HLA has been implemented for systems with different activities and simulations. The scope of this paper is limited on the production activity, where the simulation models of each sub model is built with the same simulator. Unlike HLA where the system will need a RTI (Run Time Infrastructure) to support information exchange between models, here the models belong to the same simulation software. It is therefore not necessary to transit information through a RTI. However, the different models must be able to communicate in a consistent manner to ensure the consistency of the production system model. Therefore, in addition to KPIs and control logic aggregation, simulation models have to be aggregated (Fig. 3).

Fig. 3: Role of the aggregation functions

ILLUSTRATIVE EXAMPLE

Let us consider a manufacturing line made of three workstations: M1, M2 and M3. The system manufactures two types of product (P1 and P2) that both uses M1 and M2 with different operational time here denoted time unit (tu). M3 is the same as M2. M1 behaves in FIFO, M2 gives priority to product P1 and M3 to product P2. There is a storage zone for M2 and M3. (Fig. 4).

The modular decomposition of the line considers the following modules: Et (entry), M1, M2 M3, Ex (exit). Each has its simulation model, KPI and logical control. The system model is obtained by putting together the module models. The KPI of the system depend on the module's KPI, and the behavior on a system level is added to manage control logic of each workstation. The following details the aggregation methods used for this example. FlexSim© is the simulation software used for this example. Fig. 4: system scheme

Aggregation of simulation models and control logic

For the aggregation of models, we propose to build simulation libraries. For each module, an object and the behavior describing the module are associated. The resulting element is stored in a library, so that whenever the module is needed, it can be easily extracted from the library. Thus, to each module of the system, we will associate a virtual module that describes it. The construction of the simulation model of the system will then import from the library all the modules we need. This saves time in the construction of the model, since the control logic relative to each module will already be associated to the module. For this example, Fig. 6 and Fig. 8 show the elements of the library created and the logic associated with each module.

Yet, the issue remains the communication between the elements of the library. To make them work together, a control logic that will trigger and manage the system is needed. We find here the notion of aggregations for the control logics. To manage the system very often the control logic at the system level is obtained by assigning priority order to the decisions taken by the different modules at specific times [START_REF] Barbosa | Dynamic self-organization in holonic multi-agent manufacturing systems: The ADACOR evolution[END_REF]. These priorities can change over time, or remain fixed. They are very often logics of the type {if, … else}.

In our case, the module models are retrieved from the library and a coordination logic is added. This logic may be stored in a library or not. It can be derived from priority rules as shown in this example. The priority order between M2 and M3 is manage by a system logic that switches between satisfying control logic of M2 and M3 or impose a new rule in order to avoid the system from stuck. In order words the logic at the system level is the following:

When workstations are available (i.e idle or there is a place in the storage), follow the priority of M2 and M3 (i.e send P1 on M2 and P2 on M3). If M2(3) is busy (i.e its storage full) ask for the availa-

MOSIM'20 -November 12-14, 2020 -Agadir -Morocco

bility of M3(2). If M3(2) is available, send products (P1 and P2) on M3 (2), else, stop production on M1, till a workstation become available.

This rule is described by the logic on (Fig. 7). It is important to notice that, the logic both of the modules and the system, is built independently of the "object" representing the physical aspect. Thus we can easily add a new workstation (eg. Workstation type 1) to the system without deep changes. In other words, adding a new workstation means to add an object workstation from the library and associate the appropriate logic (the one describing the type 1 workstations), then add the behavior of the new workstation the system control.

The simulation model aggregation is possible with the use of a library, and the control logic aggregation, by defining an upper control that uses the lower control in addition to a priority rule.

Aggregation of KPI

Many KPI could be used for a system evaluation. (ISO 22400, 2014) described a set of KPI for manufacturing context. [START_REF] Zhu | Key performance indicators for manufacturing operations management in the process industry[END_REF] proposed a framework to organizing KPI regarding three types : measurement, equipment and process. For our example, we choose to study aggregation of one KPI from each section: Work In Progress (WIP) for measurement, utilization rate (U) for equipment and Throughput (T) for process.

Simulated valued for modules are given in Table 2.

Aggregation of WIP

At the system level, the WIP is considered as the sum of the WIP of each workstation. Of course the workstations include possibilities for storing product awaiting production.

(1)

(2)

ɛwip represents the products located on the transportation equipment between two successive work stations. If the two workstations follow each other (without transport agent) then ɛwip is zero. In some applications ɛwip can be neglected. However, for a complete analysis and evaluation at system level, it is better to take it into account. The use of this aggregation function allows us to determine the system WIP, and thus to evaluate the performance of the configuration. A reconfiguration decision could aim at reducing the system WIP.

Aggregation of Utilization rate

The simulation shows that M2 and M3 are almost completely used; whereas, M1 is still available up to 40%. The utilization rate of the system should integrate this two data. More often, the utilization rate at the system level is calculated by using the arithmetic mean of workstation. This could be explained by the fact that workstations are often the most requested in the system. In this study we realize that the result obtained by just considering the workstation gives a glimpse, but not a very representative state of the system. Hence, we propose to considered the utilization rate of other modules such as transportation, storage. The aggregation will be made as follow:

(3) (4)

Aggregation of Throughput

The throughput represents the average number of products that can be manufactured per hour. The simulation for our example shows that, M1 has a higher throughput than M2 and M3. This can be explained by the fact that, the product coming from M1 are split between M2 and M3 for final operations. Thus, at the system level, the throughput will depend both on the throughput of M1 and on the sum of the throughput of the workstations that perform the last operation of the task list (M2 and M3).

The throughput at the system level is then obtained by considering the minimum between these two:

(5)

DISCUSSION AND CONCLUSION

The aggregation method for simulation and control logic models is implemented by using libraries containing representations of each module of the system. The construction of a new configuration consists of importing the necessary objects from the library, associating the necessary control logic to them, and finally, defining the logic to be applied to the whole system, according to the needs and objectives of the configuration. With the modular construction of the simulation model, the proposition of a new configuration can be easily tested and evaluated. This significantly reduces the time required to build the simulation model. Nevertheless, the concept of the simulation library remains a solution that can be adapted to various manufacturing contexts, as long as the system is modular. About KPIs, their analysis allows an in-depth diagnosis of the system and allow to determine the causes of possible disturbances. For our example, we used simulation to obtain KPIs of each module, nevertheless, these valued could be measured on the real system. KPIs can lead to the identification of a bottleneck station in the system and thus lead to a reconfiguration decision. E.g. The system is too much busy because M3 is full (U =99%) and its Storage always full (WIP=10), means that M3 is a bottleneck. A reconfiguration decision could be to duplicate M3. As the system and the KPIs are modular, it is easier to identify the origin of the problems and to provide a targeted solution. However, the KPI aggregation functions proposed here remain MOSIM'20 -November 12-14, 2020 -Agadir -Morocco specific to the example. But, they can be extended to similar systems (i.e. modular), or inspire the definition of aggregation functions for other modular systems.

Aggregation is important for a relevant analysis and evaluation of the system, and the notion of modularity helps by reducing the complexity and guiding to a relevant diagnosis of the system. Yet, modularity could be a source of complexity in the analysis if the relationships between modules are not well defined. As production contexts are very different, it is very difficult to generalize aggregation functions. But the idea of building simulation libraries and control logics already allows a step forward in the application of modularity. The construction of new configurations by module aggregation is similar to the formation of holarchies in holonic systems [START_REF] Chacón | Planification en ligne pour les systèmes de production distribués: une approche par les systèmes holoniques[END_REF] and to the modular construction of digital twins [START_REF] Redelinghuys | A Six-Layer Digital Twin Architecture for a Manufacturing Cell[END_REF]. The notion of aggregation proposed here can thus be used to feed some discussion concerning the issue about aggregating data and models within holonic system or digital twins.

Fig. 1 :

 1 Fig. 1: utilization rate shape per workstations

Fig. 5 :

 5 Fig. 5: A modular vision of the system

Table 1 :

 1 operation time by product by workstation

	Product	Operation 1on	Operation 2 on
		M1	M2 or M3
	P1	2 tu	5 tu
	P2	2 tu	10tu

Table 2 : Modular analysis of KPIs Machine level System level

 2

		ET	M1	M2	M3	Ex	Configuration
							(aggregation)
	U(%)	99.79	53.55	99.86	99.92	99.85	90.6
	T	966	965	507	454	960	960
	WIP	--	9	10	10	--	29

ACKNOLEGDMENT

This research work is supported by funding of the PhD program PERFORM (Fundamental research and development program resourcing on manufacturing) from the IRT Jules Verne ( https://www.irt-jules-verne.fr/).