Laurena Masbernat

Sophie Berland

Giana Almeida

Camille Michon
email: camille.michon@agroparistech.fr

Stabilizing highly hydrated wheat flour doughs by adding water in two steps

Keywords: Rheology, microscopy, gluten, network, process, mixing

A major problem in industrial processing of highly hydrated wheat doughs is the stability of the dough over time. Phase separation occurs during storage with a detrimental effect on the viscoelastic properties of the dough. We developed an original production process in which water addition and mixing were done in two steps. The stability of doughs in which water was added in either one step (1S) or two steps (2S) was compared with water contents ranging from 55 to 80% (wb). The 2S process resulted in a significant slowdown of the sedimentation kinetics, hence a higher stability, in doughs with 55 and 70 wt% water. The microstructure and viscoelastic properties of doughs were analyzed by confocal microscopy and rheology.

Protein microstructure helped stabilize the dough. The formation of a gluten network during the first step of the 2S process with only 50 wt% of water is a crucial point.

Introduction

The wide range of currently consumed cereal products comes from the wide range of ingredients used and of incorporation, mixing and cooking processes. Among the ingredients, water appears to contribute particularly to the texture of the end-product. Hence, to prepare 100 g of dough with a T55 wheat flour, about 15 g, 32 g, 43 g and 60 g of water is used to prepare cookie or snack, cake or pasta, bread, crêpes or pancake, respectively [START_REF] Guibert-Martin | Impact of the baking protocol on the structure of French crêpes[END_REF][START_REF] Kiszonas | Effect of aging and ice-structuring proteins on the physical properties of frozen flour-water mixtures[END_REF][START_REF] Monnet | Legume enriched cereal products: A generic approach derived from material science to predict their structuring by the process and their final properties[END_REF].

When mixing wheat flour with water (more than 20 g of water for 100 g of dough), the input of mechanical energy caused by mixing destroys the flour grain particles, which are composed of fragments of albumen cells containing starch and proteins, with cell walls mainly composed of pentosans. The proteins hydrate themselves, go through the glass to rubbery transition and soften. The flour grain particles swell and are mechanically broken apart by mixing, but the starch granules remain embedded in the protein matrix [START_REF] Létang | Characterization of wheat flour-water doughs. Part I: Rheometry and microstructure[END_REF]. In contact with water, proteins and the other components of the flour, hydrate and bind a given amount of water depending on their affinity for water. Depending on the study, in non-limited water conditions, native starch binds from 39% to 87% of water per gram of component, damaged starch from 200% and 430%, pentosanes from 500% to 1500% and proteins from 114% to 215% [START_REF] Berton | Measurement of hydration capacity of wheat flour: influence of composition and physical characteristics[END_REF][START_REF] Feillet | Le grain de blé: Composition et utilisation[END_REF]. Thus, the global maximum capacity of water binding varies depending on the proportion of the different components.

Moreover, when the quantity of water is limited, there is competition for water between the ingredients. The resulting distribution of water between them depends on their proportion but also on the way water is added and enters in contact with flour.

For bread making, specific kneaders are designed to be able to shear, stretch and compress the dough, in turn. When the water is added to the flour during mixing, this results in the swelling of gliadin and glutenin (the insoluble proteins of the wheat flour). These meet and interconnect through covalent (disulfide bonds) and non-covalent bonds. Connected glutenin form big aggregates. Under alternating stretching, shearing and compression, the bonds are broken and new bonds are formed leading to development of a 3D protein-network, called gluten.

The formation of the gluten network depends on mixing time, the water addition kinetics, mixing energy, temperature, flour-to-water ratio and the mechanical stresses applied during mixing [START_REF] Jongen | Analysis of dough kneaders using numerical flow simulations[END_REF]. The protein network provides the viscoelastic properties required for bread products.

A major problem in industrial processing of doughs with high water contents (60% wet basis (wb) and above) concerns the stability of the dough over time. During storage, phase separation can occur leading to the formation of an aqueous upper phase and a sediment bottom phase [START_REF] Kiszonas | Effect of aging and ice-structuring proteins on the physical properties of frozen flour-water mixtures[END_REF][START_REF] Larsson | Phase separation of wheat flour dough studied by ultracentrifugation and stress relaxation. II. Influence of mixing time, ascorbic acid, and lipids[END_REF]. In doughs with 50 wt% water in the total dough (wt% water) and above, using the usual mixing parameters, the gluten network does not form due to the dilution of proteins and insufficient opportunity for them to meet several times to interact and form bonds. However, as described in the work of [START_REF] Auger | A parametric and microstructural study of the formation of gluten network in mixed flour-water batter[END_REF], it is possible to form a fully connected gluten network in doughs containing from 50 to 56 wt% water by optimizing the mixing parameters. This is encouraging, but not sufficient for batter containing even more water, i.e. 60 wt% and above because one of the conditions reported by [START_REF] Auger | A parametric and microstructural study of the formation of gluten network in mixed flour-water batter[END_REF] was a longer mixing time (more than 30 min for a dough containing 56 wt% water) which is not acceptable in terms of input energy but also in industrial processes.

As reducing the water content of the dough enables the development of a tridimensional gluten network, one possible way to produce one even at high water content is to add the water in two steps. The first step would allow the formation of the gluten network in a relatively short time. The second step would dilute the gluten network under further water addition and mechanical kneading.

Our aim in the present work was to explore the interest of adding water in two steps in doughs containing from 55 to 80 wt% water to improve their stability and prevent phase separation.

Doughs were prepared by adding water in two steps and in one step using the same kneader and the same total kneading times. The stability and the rheology of the resulting doughs were evaluated. Results were discussed with the help of the characterization of the protein organization by confocal scanning microscopy.

Material and methods

Dough preparation

Wheat flour was provided by Les Fournils du Val de Loire (Agromousquetaires, France). The composition of the flour was determined using normalized ISO methods. The results were 14.55 ± 0.01 g moisture per 100 g flour (ISO 712:2009), 11.29 ± 0.04 g protein content per 100 g dry flour (ISO 16634-2), and 8.63 ± 0.18 g dry gluten per 100 g flour (21415-4). The flour was stored at -30°C in plastic buckets, then stored at 4°C for one to six days before being brought back to room temperature for an experiment. The calculated water content of the dough, h, also accounted for the water provided by the wheat flour itself, hf (percentage of water in 100g of flour on wet basis). The amount of water to be added (in grams) x, for a weight of wheat flour m, was calculated using equations 1 and 2:

ℎ = ℎ𝑓 * 𝑚+𝑥 𝑚+𝑥 (1) 𝑥 = 𝑚 * ℎ-ℎ𝑓 1-ℎ (2)
The range of water contents, h, was set at 55 wt% to 80 wt% of water of total formula, including the water provided by the flour. Distilled water at a temperature of 25 °C was used in all formulations. All the doughs were prepared using a KSS45 EOB CLASSIC, planetary mixer (KitchenAid, USA) fitted with the leaf device. Two dough production processes were tested to produce wheat flour doughs containing 55, 60, 65, 70 and 80 wt% water. In the first process, the water was added to the flour in one step (1S), and the blend was mixed at speed 4 (corresponding to about 127 rpm) for 12 minutes. In the second process, water was added in two steps (2S). First, sufficient water was added to the flour to obtain a dough with 50 wt% water then mixed at speed 4 for 3 minutes. Second, the remaining water was added and mixing continued for a further 12 min at speed 4. The quantity of water added in the second step depended on the water content targeted, which were 55, 60, 65, 70 and 80 wt% of water of total formula. Each sample of dough was produced in triplicate.

Stability study

The stability of the dough was monitored using a Turbiscan Classic MA 2000V R (Formulaction, France). Dough samples (4 mL) were poured into glass tubes (internal diameter 6.1 mm). Samples were scanned using incident light 880 nm wavelength and a resolution of 40 µm. Light backscattering and light transmission were measured and are expressed as a percentage of incident light. When the transmitted light shows a non-zero value, the sample is translucent and, in that case, the backscattering signal, which is generally about 20%, cannot be interpreted. When the transmission signal is equal to zero, the backscattering scan, whatever the value, can be interpreted and refers to an opaque phase. The average maximum intensity of light backscattering, MBSm (%), is defined as the mean of light backscattering values in the plateau formed in the section of backscattering values when the transmission is equal to zero. The top of the sediment phase (TIP) is detected as the height, H, at which the intensity of backscattering equals the TIP(t) as calculated by equation 3.

TIP(t) = MBSm(t) -2 % *MBSm(t) (3)
Values of H(t) were normalized by H(0) corresponding to the total height of the sample.

Dough samples (4 mL) were poured into glass tubes shortly after production. Scans were carried out at one-minute intervals for 15 min at room temperature. The tubes were then stored at 4 °C and scanned 4 hours, 24 hours, 72 hours and 168 hours (seven days) after the first scan. All the doughs were prepared in triplicate.

Rheological measurements

Rheological measurements were carried out using a dynamic stress rheometer Carri-Med CLS 2 100 (TA Instruments, USA) fitted with a cone-plate geometry of 4 cm of diameter, 4°

angle and 106 µm of truncation. Oscillation frequency sweeps were conducted in the range of 0.1 to 10 Hz, at 20 °C and at 0.2% of maximum strain amplitude chosen in the linear domain (identified by preliminary strain sweeps). The doughs remained in the geometry for only one minute before the beginning of the test to avoid phase separation of the sample during the test.

Values of storage modulus (G') and loss modulus (G'') measured at 1 Hz in the frequency sweep were taken as representative of the G' and G" levels of the frequency sweep. Tan δ, defined as the ratio of G'' over G' indicates the structure of the dough. For a defined frequency, strain and time, the smaller tan δ, the more structured the dough.

Environmental scanning electron microscopy (ESEM)

An ESEM (FEI Quanta 200) was used to observe the structure of the dough. Samples were observed in the following conditions: secondary electron detector, ESEM mode (GBSED: gaseous BSE detector), pressure 893 Pa, voltage 13 kV, and, spot size 4.5 and work distance approximately 6.5 mm. A temperature of 7 °C was set to prevent solvent evaporation using a Peltier stage. Samples were directly placed in cupped aluminum stubs designed specifically for the Peltier stage.

Confocal microscopy observations

The organization of the proteins in doughs at different water contents was observed using a confocal laser scattering microscope (CLSM) (Leica TC SP8 Leica, Germany). Using 250-µm thick spacers, the dough was placed on the lamella and 2 µL of Dylight 488 was poured on the top of the dough to label the proteins. The stain was excited using a laser with a wavelength of 488 nm and the emitted fluorescence was detected in the range of 496 to 576 nm. Photos were taken at magnification: X10.

Results and discussion

Study of dough stability

3.1.1. Effect of the process on the sedimentation kinetics of doughs at 70 wt% of water of total dough

Figure 1 shows the changes in the height of the sediment over time, H(t) in doughs with 70 wt% water made using the 1S and 2S processes. H(t)/H0, the normalized height of sediment phase was initially 0.92 in both samples and remained constant for a period of a few minutes. These H(t)/H0 were lower than 1 because of the presence of some little bubbles, a thin layer of water and/or a small meniscus on the top of the sample. The beginning of the destabilization is the time when H(t)/H0 starts to drop from this value: less than 10 min in the1S process and more than 15 min in the 2S process.

The pictures of the tubes containing doughs are given for different times (15 min, 24 h, 1 week) after production. At 15 min after production, the doughs made using both processes had a thin layer of aqueous phase on the top of the samples. Their height ratio was 0.85 for 1S dough and 0.92 for 2S dough. After 4 h, the dough made using the 1S process separated into three different phases; a foamy phase at the top, an aqueous phase in the middle and a sediment phase at the bottom of the sample. After 24 h, the phases were easy to distinguish in the picture of the sample. The sediment compacted over time as the height ratio decreased from 0.5 after 4 h to 0.4 after one week. This result is in accordance with the hypothesis of [START_REF] Eliasson | Cereals in breadmaking: A molecular colloidal approach[END_REF] who, for a dough with this amount of water, described a suspension of insoluble swollen gluten proteins, starch and fibers in a liquid phase made of water and soluble components. The sedimentation of insoluble components depends on the viscous property of the continuous phase.

In the dough containing 70 wt% water made using the 2S process, the sediment height ratio ranged from 0.92 at t0 to 0.8 after 4 h, pointing to slower phase separation kinetics than in 1S dough (Figure 1). Only two phases were visible: one sediment phase overtopped by an aqueous phase. The distinct kinetics of phase separation and the number of phases obtained using two processes of water addition confirmed the potential interest of adding water in two steps and underlined the probability of a different organization of components in the doughs.

The 2S process includes a step during which a gluten network starts to form during mixing of the flour and water at 50 wt% of water (of total dough) for 3 min. This network is probably diluted by the second addition of water and may be broken down by further mixing in the second step.

Effect of water content and the process on the dough sedimentation kinetics

To investigate the interest of the 2S process in slowing down the phase separation kinetics in more detail, doughs were tested at water contents ranging from 55 to 80% (wb) water. Figure 2 compares the differences in H(t)/H0 in 1S and 2S doughs. Based on repeatability equivalent to the dough including 70 wt% water shown in figure 1 and to simplify the reading, only one result per water content and process is reported in figures 2a (1S) and 2b (2S). Two phase separation kinetics were identified in both processes. Doughs containing 55 wt%, 60 wt% and 65 wt% water showed almost no sedimentation for at least 4 h after production. Doughs containing 70 wt% and 80 wt% water sedimented rapidly, and a bottom phase formed within a few minutes and compacted between 15 min and 4 h. However, differences in sedimentation kinetics were also observed depending on the water addition process. The dough containing 55 wt% water made using the 2S process appeared to be the most stable of all (Figure 2b). Its H(t)/H0 value was equal to 1 at t0 and remained equal to or greater than 0.97 for at least 1 week. The dough containing 55 wt% water but produced using the 1S process had a slightly lower H(t)/H0 ratio (0.93) which started to decrease after only 24h (Figure 2a).

According to [START_REF] Auger | A parametric and microstructural study of the formation of gluten network in mixed flour-water batter[END_REF], more than 30 min is required to form a gluten network when water is added in one step. Thus, considering the mixing time of the present work (1S process, 12 min) it is most likely that gliadin and glutenin could only swell and contribute to an increasein the viscosity of the continuous phase. On the other hand, in the 2S process, a gluten network could have formed after 3 min of kneading with 50 wt% of water (of total dough).

The addition of only 5 wt% more water and the additional 12 min of mixing only resulted in a small dilution and/or disruption of the gluten network, which could consequently considerably stabilize the dough upon sedimentation over a full week. Yet, the stability of the dough over time was improved possibly thanks to the formation of the gluten network during the first step of the process.

The changes in the sediment height in samples produced with the 1S process and containing 60 wt% and 65 wt% water were very similar to those that occurred in the samples containing 55 wt% water (Figure 2a). A slightly steeper decrease in sediment height after a week was even observed with an increase in water content. This could be due to reduced viscosity of the continuous phase. Indeed, the higher the water content, the lower the probability of collision between swollen flour particles during kneading and formation of gluten aggregates. Using the 2S process, increasing the water content from 55 to 65 % (wb) enhanced the sedimentation kinetics of the doughs (Figure 2b). However, the 60 wt% water and 2S process dough appeared to be at an earlier stage of sedimentation compared to 1S dough with the same water content (Figure 2a andb). Both 1S dough and 2S dough with 65% of water content (wb) showed the same H(t)/H0 after a week despite the fact the two kinetics differed, i.e. an earlier beginning but more progressive decrease in the 2S dough (Figure 2a andb). All these observations are compatible with the hypothesis of the formation of a gluten network stabilizing the dough structure in the 2S process. The addition of the complementary water is hypothesized to dilute and/or disrupt the network. The greater the quantity of water added in the second step, the less efficient the organization of the continuous phase around starch granules to prevent their sedimentation.

Interestingly, the sedimentation kinetics observed in the 70 wt% water 2S dough was in good accordance with the kinetics observed in the 55 wt% to 65 wt% water doughs even if it was even more rapid (Figure 2b). The organization of the continuous phase obtained thanks to kneading in the first step with only 50 wt% of water was still in place, even if less efficient.

However, in the 80 wt% water 2S dough, sedimentation was drastic and started in the first minutes after production (Figure 2b). The very same evolution was observed in the 80 wt% water 1S dough (Figure 2a). In both cases, it appears that the continuous phases failed to slow down sedimentation. Finally, the dough with 70 wt% water produced with 1S process also involved rapid kinetics and almost complete sedimentation, even if this occurred a little more slowly than in the 80 wt% water doughs. This behavior could be due to a slightly more concentrated continuous phase which could result in higher resulting viscosity than in the doughs containing 80 wt% water.

Rheological properties and microstructure of the doughs

To check the hypothesis of differences in continuous phase microstructure, doughs containing 55 wt%, 65 wt% and 70 wt% water were analyzed using CLSM. To better understand the changes that take place in the proteins, the doughs were observed at different times in the mixing process. Figure 3 shows the organization of starches and proteins at the end the dough mixing process (1S dough with 55% wt water) and after the end of the first step of the 2S process: 3 min of mixing after addition of only the first part of the water, i.e. 50 wt%.

Figure 3.A shows the sizes of the two populations of wheat starch granules (2 and 20 µm in diameter) embedded in a protein matrix which appeared as a homogeneous soft phase connecting starch granules with each other. These observations are in good agreement with those reported by [START_REF] Létang | Characterization of wheat flour-water doughs. Part I: Rheometry and microstructure[END_REF] in doughs with similar water contents but less mixing time. At this scale, the proteins might play a role in the cohesion and friction between starch granules. Depending on water content and mixing parameters, the proteins are hypothesized to form a complex structure, (the gluten network) that is apparent at a larger scale. Figure 3.B shows large green interconnected strands corresponding to a gluten network as observed by [START_REF] Boitte | Observation of wheat flour doughs under mechanical treatment using confocal microscopy and classification of their microstructures[END_REF]. In the case of dough with 50 wt% of water content, three minutes of mixing is sufficient to enable the formation of a rather well developed protein network. The strands are oriented in the same oblique direction, probably due to slight shearing when the dough was placed between the two microscope slides [START_REF] Boitte | Observation of wheat flour doughs under mechanical treatment using confocal microscopy and classification of their microstructures[END_REF]. The small pale green spots on the strands may be starch particles embedded in the gluten strands. The paler green color of the spots could be caused by partial swelling or solvation of the proteins around the starch granules after only three minutes of mixing, leading to a slight overconcentration around the starch granules. Thus, at the end of the first step of the 2S process, the structure of the dough is rather close to that of bread dough [START_REF] Hackenberg | Mechanical wheat flour modification and its effect on protein network structure and dough rheology[END_REF], which is known to remain stable over time with no phase separation.

Pictures of doughs containing 55 wt%, 65 wt% and 70 wt% water made using the 1S and 2S

processes were taken after 12 min and 15 min of total mixing time (Figure 4). After 12 min of mixing, dough with 55 wt% water made using the 1S process contained large elongated strands of gluten proteins. However, the strands were poorly connected to each other thereby failing to form a real gluten network even if it looked as though one had started to develop.

Indeed, three minutes later, after a total mixing time of 15 min, a gluten network is clearly visible. These two images are very similar to those observed by [START_REF] Auger | A parametric and microstructural study of the formation of gluten network in mixed flour-water batter[END_REF] during the formation of a gluten network in diluted conditions (51 wt% of total dough water) and mixing for a long time. In comparison, the dough made using the 2S process displayed a welldeveloped gluten network, formed by stretched and interconnected strands of gluten after both 12 min and 15 min of mixing. Despite shearing applied for 9 min and even 12 min during the complementary mixing after the second addition of water, the gluten network remained visible. After 9 min of additional mixing (i.e. 12 min total mixing time, 55 wt% water, 2S process, Figure 4), it showed larger and apparently less connected strands compared to those formed after 3 min of mixing with 50 wt% water (Figure 3). However, after 15 min of total mixing time, the strands were again fully interconnected, even if they appeared to be thinner.

The two gluten networks obtained after 15 min of total mixing time had different structures, underlining the importance of the order in which the water is incorporated and of the amount.

Moreover, after 12 min of mixing in presence of the total amount of water (images squared in red in figure 5 for 55 wt% water), the 1S process appeared to produce no gluten network, whereas the 2S process did produce one. This certainly explains the difference in stability upon sedimentation observed in Figure 2.

No gluten network was observed in 65 wt% and 70 wt% water doughs, whatever the 1S or 2S process and the mixing time used (Figure 4). Proteins appeared in the form of particles of different sizes ranging from 10 to 500 µm depending on the process and on the water content.

In the dough with 65 wt% water produced using the 1S process, small protein particles were dispersed evenly throughout the matrix after 12 min of total mixing time. These particles may correspond to the only slightly swollen grains in the flours described by [START_REF] Auger | A parametric and microstructural study of the formation of gluten network in mixed flour-water batter[END_REF].

After 15 min of total mixing time, bigger particles were observed probably due to the further swelling and/or the aggregation of the swollen grains [START_REF] Auger | A parametric and microstructural study of the formation of gluten network in mixed flour-water batter[END_REF]. Larger protein particles were observed in the dough with 70 wt% water using the 1S process, after 12 min of total mixing with no significant change upon further mixing (i.e. 15 min total mixing time). It seemed that after 12 min, flour grains had swollen to a greater extent than in dough with 65 wt% water. However, the dilution prevented the occurrence of sufficient collisions between proteins to start formation of a the gluten network during the 15 min of total mixing time both with the dough with 65 wt% and 70 wt% water in the 1S process. The differences in stability apparent in figure 2 were most probably only due to differences in the viscosity of the continuous phase. Large particles of about 200 µm were observed in dough with 65 wt% water produced with the 2S process. The particles were obtained by adding 15 wt% of water to a dough containing a fully structured gluten network (3 min of mixing with 50 wt% of water, Figure 3.B). These large particles thus corresponded to fragments of the gluten network, which were very similar after 12 or 15 min of total mixing time. Even larger gluten network fragments were observed in dough with 70 wt% water after 12 min of total mixing time using the 2S process. Moreover, small cloudy green particles can also be seen in the bottom part of the image. They probably correspond to thin gluten network afterglows. After 15 min of total mixing time, these thin gluten network afterglows seemed to spread throughout the pictures, embedding the big and lighter gluten network fragments. Their presence may explain the improved stability of the dough with 70 wt% water produced using the 2S process compared to the stability produced using the 1S process. The viscoelastic properties of the doughs were measured to quantify the impact of the production processes on structure of the dough. The results obtained for doughs containing 55 to 70 wt% water are shown in figure 5. It was not possible to characterize doughs containing 80 wt% water because they were not sufficiently stable and sedimented during the test.

In both processes, G' decreased with an increase in the water content. This result is in agreement with the literature, even if the corresponding results were obtained with doughs containing less water (between 35 to 49 wt% of total formula) [START_REF] Hibberd | Dynamic viscoelastic behaviour of wheat flour doughs[END_REF][START_REF] Navickis | Viscoelastic properties of wheat flour doughs : variation of dynamic moduli with water and protein content1[END_REF]. This is logical because of the generally observed softening effect of water. In the range 55% to 65% of water contents (wb), G' values were very similar in the two processes, whereas G' was significantly higher in dough with 70 wt% water doughs produced with the 1S process. However, at 55 wt% of water, the dough produced using the 2S process showed a G' slightly higher and a lower tan δ. Thus, the network observed in Figure 4 provided the dough with increased elastic properties, which is more structured (lower tan δ) than the dough produced with the 1S process, in which large and poorly connected strands are observed.

These results are in agreement with a system that becomes more stable upon sedimentation.

Dough with 65 wt% of water produced using the 1S process had a slightly higher G' but also a much lower tan δ. The many small gluten particles present in the dough produced with the 1S process (Figure 4) seemed to provide a more elastic and structured system with a slower sedimentation kinetics than the 2S process (Figure 2). Finally, the G' obtained for the dough with 70 wt% water produced using the 1S process was significantly higher and the tan δ significantly lower compared to the doughs produced with the 2S process. However, sedimentation occurred very rapidly in the 1S dough while it was much more progressive in the 2S dough (Figures 1 and2). The large, swollen but irregularly shaped particles shown in Figure 4 (1S process), probably rubbed against each other affording this dough more elasticity than in the 2S process. In the latter case, fragments of the broken gluten network were embedded in the very soft and cloudy gluten network afterglows (Figure 4) that contributed less to the elastic behavior of the dough and increased tan δ.

Conclusions

This study investigated the effect of the addition of water and of the mixing processes on the phase separation and microstructure of highly hydrated doughs (55 wt% to 80 wt%) of total dough water). This range of water range has rarely been studied in the literature although several applications exist. An original production process, in which water was added and the dough mixed in two steps (2S), was developed to produce dough with targeted water contents and was systematically compared with the process in which water was added in only one step (1S). Different protein microstructures were obtained, some of which resulted in different rheological properties. The sedimentation kinetics of the dough was shown to be directly linked to the protein microstructure. The schematic representations of the microstructure and induced doughs behavior at macroscopic scale over time in figure 6 to summarize the main findings of this work. With the 1S process, the dough containing 55 wt% of water was made up of large poorly connected gluten strands, whereas in doughs containing 65 wt% of water, the gluten appeared as dense particles, and in doughs containing 70 wt% of water as swollen diluted particles. Adding water in two steps led to the formation of an even more complex protein structure. The first step consisted in adding only 50 wt% water in order to allow the rapid formation of a well-connected gluten network. This gluten network broke up after the second addition of water and further mixing, resulting in fragments of gluten of different sizes for water contents above 65% (wb). In dough with 55 wt% water, the limited dilution of the dough results in a fully connected gluten network made of thin strands after further mixing.

What is more, the same process results in the formation of a diffuse gluten network made of thin connected strands in doughs containing from 55 wt% to 70 wt% water. On average, between 55 wt% and 70 wt% water, stability upon sedimentation was the same or improved with the 2S process. The biggest difference in phase separation kinetics was observed in doughs containing 70 wt% water, when in the 2S process, only two phases separated in 24 hours instead of the three phases in the 1S process. The formation of a gluten network at 50 wt% water before the addition of any more water and further mixing was found to improve the stability of highly hydrated doughs for more than 24 hours. 12.

List of Figure captions

Figure 1 :

 1 Figure 1: Changes in sediment height over time in dough with 70 wt% of water of total dough

Figure 2 :

 2 Figure 2: Temporal changes in the height of sediment in refrigerated doughs containing 55

Figure 3 :

 3 Figure 3: Dough microstructure observed by MEBE (1S dough with 55 wt% water) and

Figure 4 :

 4 Figure 4: Observations of stained proteins (in green) using CSLM in doughs containing 55

Figure 5 :

 5 Figure 5: Effect of water content on the viscoelastic properties of doughs just after the end of

Figure 6 :

 6 Figure 6: Macroscopic and microscopic representation of dough structure immediately after

Figure 2 :

 2 Temporal changes in the height of sediment in refrigerated doughs containing 55 wt% (triangles), 60 wt% (squares), 65 wt% (diamonds), 70 wt% (empty circles and dotted line) and 80 wt% (black dots) water: (a) 1S process, (b) Dough microstructure observed by MEBE (1S dough with 55 wt% water) and CLSM (50 wt% water, 3 min of mixing after the first addition of water during the 2S process). Stained proteins are green in panel B. Effect of water content on the viscoelastic properties of doughs just after the end of mixing. (a) Storage modulus (G'), (b) tan δ (=G"/G'). Empty symbols show the 1S process, Black symbols show the 2S process. 20°C, 1 Hz, 0.2% maximum strain amplitude. 29 24.

Figure 6 :

 6 Figure 6: Macroscopic and microscopic representation of dough structure immediately after production (t0) and after 24 h for doughs containing

Acknowledgments

The authors thank Gabrielle Moulin (AgroParisTech, France) for her contribution to the CLSM experiments. This work was supported by Single Interministry Fund (France) and regionals cofincancing (Hauts de France and Auvergne Rhône Alpes, France) through a collaborative R&D project certified by Vitagora, Euramaterials and Cimes competitiveness clusters.

19.

20.

Figure 4: Observations of stained proteins (in green) using CSLM in doughs containing 55 wt%, 65 wt% and 70 wt% water obtained using 1S and 2S processes with different mixing times (the initial time, ti, indicates the beginning of mixing).

The images of doughs investigated in the stability study are framed in red. The 462 scale bar is 200 µm.

463


Mouad Benbouja
email: mouad.benbouja@gmail.com

Achraf Touil
email: ac.touil@uhp.ac.ma

Abdelwahed Echchatbi
email: echchatbi@gmail.com

Abdelkabir Charkaoui
email: charkaoui.a@gmail.com

-Morocco "New advances and challenges for sustainable and smart industries" MIXED INTEGER LINEAR PROGRAMMING FORMULATION FOR A MULTI-ECHELON INTEGRATED SUPPLY CHAIN WITHIN MASS CUSTOMIZATION STRATEGY

Keywords: Multi echelon supply chain, integrated supply chain, mass customization, product variety, mixed integer linear programming (MILP)

Product customization is considered as the widespread strategy for the actual market trend oriented toward customer focus. In this field, mass customization sights mainly to emerge economy of scale and economy of scope in order to integrate mass production principles with customization abilities. This research views the collaborative management approach by developing an integrated procurement, production and distribution mixed integer linear programming (MILP) model for a multi-echelon and multi-site supply chain, the corresponding resolution is performed with an exact method. The studied supply chain consists of leaders and followers relationships as follows, (a) customers: Original Equipment Manufacturers (OEMs) identified as leaders and (b) first-tier suppliers: customized products manufacturers (c) second-tier suppliers: raw material suppliers, identified as followers. Using this MILP, the operations decision-making is focused on the first-tier suppliers, an optimal solution is achieved so as to satisfy the customized demands from the leaders considering the specific characteristics of mass customization environment for the internal and external constraints through the supply chain. The illustration of the model is performed with an example from the automotive industry in addition to a sensitivity analysis to highlight the interdependence between some key parameters and provide managerial insights.

INTRODUCTION

The market environment change toward customer focus boasts firms to enhance product customization abilities to remain competitive while improving market share. In fact, consumer preferences rise up product variety level so that product features can fit the highlighted requirements. From supply chain standpoint, it could be perceived as a substantial shift from mass production to mass customization (MC) endeavor. While multiple definition of MC are proposed in the literature, the main understanding is the ability to provide customized products for a mass market [START_REF] Coletti | Mass Customization[END_REF][START_REF] Davis | Future Perfect[END_REF][START_REF] Pine | Mass Customization: The New Frontier in Business Competition[END_REF]. [START_REF] Candelo | Mass Customization: Another Marketing Breakthrough[END_REF] provided the new market characteristics that promote the switch from mass production to mass customization argued by three main factors of change, namely, the limits of mass production process which requires stable inputs, reduction of market homogeneity and demand instability, these elements depict the fundamental of the economy of scale. Thereupon, the supply chain as a network should encompass the organizational enablers to successfully establish the interrelated processes of production planning and inventory control as well as logistics and distribution [START_REF] Ballou | Business logistics/supply chain management: planning, organizing, and controlling the supply chain[END_REF]. In fact, mass customization is perceived as an operations management perspective due to its impact on the adopted organizational strategies through the supply chain, for example, the rapid and effective integration to record customer requirements and production launch considering delivery time window in addition to the necessity of building a strong customer relationship with customer-supplier framework for the interactions across supply chain actors [START_REF] Selladurai | Mass customization in operations management: oxymoron or reality?[END_REF]. Basically, the adopted customer involvement level in the supply chain which is well known as the customer order decoupling point (CODP) is the principal trigger of the supply chain design for downstream and upstream processes in order to drive value chain stages, namely, design, fabrication, assembly and distribution. The concept is to delay transformation processes as much as possible until customer orders are known. The increased level of customer integration moves the CODP to upstream positions to dump speculation activities on products manufacturing [START_REF] Budiman | A mixed-integer model for the implementation of postponement strategies in the globalized green supply chain network[END_REF][START_REF] Yang | Implications of postponement for the supply chain[END_REF]. Therefore, the adopted postponement strategy by the supply chain highlights the forecast and order-driven attributes while the main purpose is to ensure cost efficiency and customer service level. Moreover, modularity practices for product development is considered as a core structure design to enhance mass customization strategy [START_REF] Tu | Measuring Modularity-Based Manufacturing Practices and Their Impact on Mass Customization Capability: A Cus-MOSIM'20 -November 12-14, 2020 -Agadir -Morocco tomer-Driven Perspective[END_REF]. It is worth mentioning that postponement and modularization approaches emphasize achieving the desired business process of scale and scope as modularity contributes for postponement implementation [START_REF] Mikkola | Supply-chain integration: implications for mass customization, modularization and postponement strategies[END_REF]. As stated by [START_REF] Blecker | Mass Customization: State-of-the-Art and Challenges[END_REF], mass customization adoption come through the assessment of some critical implementation factors, MOSIM '20 -November 12-14, 2020 -Agadir -Morocco namely, (a) customer demand for customized products (b) market turbulence (c) supply chain readiness (d) knowledge driven organization. The prevailing statement is to ensure firms' capability fulfilment as the implementation necessitates a substantial supply chain actors' alignment to concur the strategic mass customization objectives. Towards that end, supply chain configuration should be addressed with an integrated business process to encompass the generated operations policies. For instance, to cope with manufacturing uncertainties, make to order policy is perceived as a suitable process to preserve the customer value perception on product development. The supply chain planning with pull system reveals a dynamic capability from management perspective where integration abilities enhance information and physical flows across partners according to the required reliability level through upstream and downstream processing capability. As stated by [START_REF] Liu | Linking supply chain management with mass customization capability[END_REF], the literature on mass customization and supply chain management recognized two value creation management competences that should impact the required capability which are customer focused product design and supplier lead-time reduction. It reflects a major fields to sustain the corresponding planning system approach. [START_REF] Xu | A decision support model in mass customization[END_REF] proposed a decision support model to sustain the economy of scale and scope within mass customization context, the constructed quantitative model allows decision makers to drive the balance between customers' preferences and operational cost. The supply chain stakeholders need to adhere within collaboration framework in order to drive the cost performance balance through multiple fields. For instance, resources cost efficiency (e.g. inventory, manufacturing), customer service level and internal operations' flexibility to deal with changing environment. In fact, this necessity arises from the interdependency between actors for different patterns where standalone positions will hinder performance. The resulted coordination mechanism attributes aims to foresee decision-making process to enhance the value chain within a high volatile market environment [START_REF] Jin | Supply chain optimization based on chain management and mass customization[END_REF]. One approach widely adopted is supply chain integration of different planning processes such as production, storage and distribution. [START_REF] Masoud | Integrated cost optimization in a two-stage, automotive supply chain[END_REF] proposed an integrated production and transportation planning problem in the automotive industry for the operational level, the resolution process is formulated with hybrid simulated annealing algorithm employing a constructive heuristic and an effective encoding-decoding strategy. [START_REF] Rafiei | Integrated production-distribution planning problem in a competition-based four-echelon supply chain[END_REF] formulated a four-echelon supply chain for an integrated production-distribution planning problem, two mixed integer linear programming models have been investigated according to no competitive and competitive market, and the elastic constraint method is applied as a resolution approach. [START_REF] Pasandideh | Bi-objective optimization of a multi-product multi-period three-echelon supply chain problem under uncertain environments: NSGA-II and NRGA[END_REF] pointed out the strategic, tactical and planning decision making model for a supply chain network in order to determine, respectively, the number and locations of warehouses, transportation channels assigning in addition to production management. For this field, a bi-objective mixed-integer non-linear mathematical formulation has been proposed and solved with non-dominated sorting genetic algorithm and non-dominated ranking genetic algorithm. [START_REF] Touil | Integrated production and distribution in a milk supply chain under uncertainty with the Hurwicz criterion[END_REF] addressed a mixed integer linear programming model for an integrated production and distribution problem considering different uncertainty sources. The credibility theory is carried out for a constructive framework to cope with uncertainties and the extreme cases of the optimistic and pessimistic criteria are handled with Hurwicz criterion which attempts to drive a balance in order to maximize profit. To the best of our knowledge, there is a lack of mass customization studies with the perspective of an integrated supply chain mathematical modeling through MILP formulation. This paper aims to fill this gap and propose a MILP formulation for modeling a multiechelon, multi-site integrated procurement, production and distribution supply chain within mass customization environment while minimizing the total cost. The tactical decision planning architecture is adopted to draw the root assumptions classes. The motivation of this study arises from first-tier suppliers' interactions with main contractors within demand driven supply chain. The illustration of the empirical application from industrial case is the leader and followers dyadic relationships across the automotive industry. The integration aspect sights to evolve the dynamic capability underpinning for mass customization enablers outlined mainly through product design with modularity concepts as well as postponement and the corresponding CODP in order to address a triggered supply chain according to make to order production policy. The remainder of this paper is organized as follows. Section 2 provides the model formulation and the adopted assumptions. Section 3 presents the case study in addition to the results of the computational experiments. A sensitivity analysis with managerial insights is considered in section 4, followed by the conclusion in section 5.

MODEL FORMULATION

The supply chain being studied in this paper is a multiechelon, multi-site integrated procurement, production and distribution at tactical decision-making level, the automotive industry is considered as an illustration. The multi-echelon supply chain architecture is (a) customers: OEMs (b) first-tier suppliers: wiring harnesses manufacturers (c) second-tier suppliers: raw material suppliers, as stated in figure 1.

Figure 1: Supply chain structure MOSIM '20 -November 12-14, 2020 -Agadir -Morocco The provided demand information with customized orders are transferred from OEMs to the first-tier suppliers as well as the agreed capacity level between different stakeholders. In the studied case, customer involvement (i.e. CODP) occurs at product features definition level with configurator tools as example, the corresponding position of customization degree is known as customized standardization [START_REF] Um | Product variety management and supply chain performance: A capability perspective on their relationships and competitiveness implications[END_REF]. The OEMs propose a set of options for a vehicle model while customers afford the ability to customize their cars to fit their own needs. Whereby, product modularity approach is applied, the assignment is based on basic modules to include common elements and optional modules for preferences as represented in figure 2. In the studied case, the option preferences are addressed through penetration rate shared previously by customers (i.e. OEMS) to assess the percentage of products (i.e. wire harnesses) that will include this option. The postponement level is carried out with make to order mode triggered by confirmed orders reception. As the focus of this supply chain is on the first-tier suppliers operations, the heterogeneous lead times from their different raw material suppliers have an important leverage on production function. Thus, the procurement system is based on the previously shared forecasts from OEMs. Therefore, production and procurement systems are based respectively on confirmed and forecasted demand. The product storage capacity for the first-tier suppliers has a limited behavior, the main storage locations are the advanced warehouses placed generally close to OEMs. Thus, supplier logistic window (i.e. between first-tier suppliers and OEMs) addresses three main timeframe stages as described in figure 3 (i.e. total time in manufacturing sites, total transport time, safety stock).

Figure 3: Mass customization logistic window

The key figure outlines that in spite of disruptions, it is mandatory to preserve just in sequence deliveries (i.e. according to make to order), which led to highly cost expected solutions (e.g. premium freight). The mentioned finish good safety stock provides a restricted buffer level. The adopted model assumptions are presented as follows: Model assumptions:

• Customer demands are handled by confirmed and forecasted demands • Customized demands approach is ensured by serial numbers for each product. Each serial number represents the product content in terms of the chosen modules by the customer (figure 2). The total number of the series depend on the received demand for each product at each period • Products inventory holding cost are set independently of their content in terms of modules • The manufacturing sites have a limited production and storage capacities • Production shortage in manufacturing sites can happen with backorders form, lost sales are not allowed • The advanced warehouses charge an inventory holding cost to manufacturing sites • Product storage capacity at the advanced warehouses is limited for each sites. However, an overstock can be adopted with penalty cost • Raw material inventory management is performed with (s,S) policy • Transportation is outsourced, there is not limit for vehicles availability between nodes while vehicles' capacity is considered • Uncertainty on the received raw material quantity and the delivered products is not considered

The following list presents the model notation including indexes, parameters and decision variables. Objective function:

Indexes and sets

The main objective of the proposed model is to minimize the total cost of the supply chain simultaneously. It includes various cost elements as shown in the objective function (1), each component is defined from (2) to (10) to highlight the cost of production, raw material holding cost, product inventory holding cost in the manufacturing sites, product inventory holding cost at the advanced warehouses, the penalty cost of the overstock at the advanced warehouses, procurement cost of raw materials, transportation cost consisting of vehicles utilization and backorder cost.

(1)

(2)

(3) (4) (5) (6) (7) (8) (9)
(10)

Production

In order to fulfill customers' demand on each manufacturing site, constraint 11 represents the total production which is performed by two parts. denotes production to cover the real demands (i.e. confirmed demand), while represents the fulfillment of the previously generated backorders, in the period t=1 it is equal to 0 as stated by constraint 12:

(12) Constraint 13 defines the backordered products and those to produce. This definition is established from the received demand which is expressed by serial numbers for each product family (i.e. define the serial numbers to produce or to backorder for an upcoming production): MOSIM '20 -November 12-14, 2020 -Agadir -Morocco In order to handle the production of backorders, constraint 16 aims to settle it during two periods. Thus, the backordered serial numbers could be produced at either t+1 or t+2. Constraint 17 defines the maximum threshold of backorders production. Constraint 18 and 19 aim to define the backorder treatment during the last period, it has been set to 0 while ensuring the complete production of the generated backorders at the period T-1. At last, as stated by constraint 20, the total generated backorders over the horizon have to be produced completely. Constraint 24 conserves the flow at the advanced warehouses. It indicates the available inventory of product families in each period, which is the reported inventory from the previous period plus the received quantity from manufacturing sites minus the shipped quantity to customers:

Constraint 25 outlines the restricted minimum quantity to be delivered to customers for each period. Moreover, constraint 26 describes the number of vehicle trips from the advanced warehouses to customers at every time period based on vehicles' capacity:

Constraint 27 shows that there is a safety stock (i.e. buffer) level to maintain at the advanced warehouses, it is established according to a percentage from the confirmed demand presented here by β:

(27)
As discussed previously, to express the inventory level agreement between manufacturing sites and the advanced warehouses, the overstock from the contracted limit is accepted. Though, a penalty cost is applied for the additional volume. Constraint 28 highlights the difference between the inventory level and the maximum contracted capacity: The raw material supply capacity is represented by constraint 41:

(41) Furthermore, the inventory control is performed considering a safety stock level for each raw material. In fact, [START_REF] Hernandez-Ruiz | Optimizing Safety Stock Levels in Modular Production Systems Using Component Commonality and Group Technology Philosophy: A Study Based on Simulation[END_REF] proposed an evaluation development to cope with demand variability for modular product structure based on normal distribution of demand in addition to their independency. Constraint 42 represents the adopted expression for the studied case where K reflects a safety factor, t is the inverse cumula-tive normal distribution coefficient for a target service level highlighting the decision makers' willingness to cope with demand variability:

NUMERICAL RESULTS

In this section, a numerical experiment is conducted to validate the proposed model and illustrate its application. The considered example consists of 3 customers, 3 manufacturing sites, 3 advanced warehouses and 6 product families with a cluster of 102 modules. The bill of material structure of all modules includes a set of 670 raw material. The stakeholders' linkage in addition to products and modules assignment are presented in table 1. Real and forecasted demands are computed according to the normal distribution while optional module preferences are generated with the uniform distribution. After a defined level of customer demand for each product and each period, a corresponding number of series is generated accordingly which is a substantial contribution for mass customization context in order to ensure the traceability of the customized demand. The optional modules affectation to these series depends on their penetration rate. The model planning horizon is assumed to be 10 periods. Due to different possible configurations, the product inventory holding cost at different locations has been set to an average cost. The initial level of backorders and product inventory is set to zero. Besides, the transportation cost between the partners is considered as a fixed one. According to the raw material safety stock to ensure at the first-tier suppliers, the corresponding customer service level in this study has been set to 95% which gives K=1,65. Furthermore, the raw material purchase costs have been generated randomly between 0,05 and 12. Subsequently, they are used to define the modules' costs according to their bill of materials. Table 2 provides a summary of numerical input data. The resolution is performed with exact approach. The model is programmed and solved with GAMS 22.5/CPLEX 12.2 optimization software and all numerical experiments are processed with a Core i5 2.49 GHz computer with 8 GB RAM. The presented data set provides feasible solution after a runtime of 2,29 min. Table 3 presents the generated real demand. The total of the backordered serial numbers for each product is presented in table 4. Table 5 presents a detailed example of the backordered serial numbers for product p4 in the period t=7 for the site e =2. The tables 6,7,8 provide a summary of the numerical results for the production quantity for each product, the product inventory level at the advanced warehouses and the corresponding excess perceived during each period. The cost structure of the resolution status is presented in figure 4. As a global analysis of the results, for instance, the final product flow, it could be perceived that in spite of adopting a maximum hurdle inventory at the plants, the model tends to ensure the buffer at the advanced warehouses. MOSIM '20 -November 12-14, 2020 -Agadir -Morocco This status is also triggered by the applied inventory holding costs' parameters, where the cost at the plants (

) is greater than the one at the advanced warehouses (

). Moreover, we can recognize that products inventory cost at the plants is nil which represents the model orientation to foster deliveries to the advanced warehouses with just in sequence.

Customer

SENSITIVITY ANALYSIS AND MANAGERIAL INSIGHTS

In order to explore the quality of the proposed solutions, a sensitivity analysis is performed for some key parameters from the initial nominal value. The improvement of the given right-hand side (RHS) input data highlights a deep correlation with decision-making process, for instance, those related to capital investment or manpower decisions for the capacity allocation provided in the model by . Therefore, a local sensitivity analysis according to the one-at-a-time method (OAT) is carried out through 3 scenarios while decreasing the upper bound region in order to analyze the optimality resolution behavior of the model [START_REF] Borgonovo | Sensitivity analysis: A review of recent advances[END_REF]. In fact, 3 instances have been launched with the same demand range while decreasing the capacity level. Table 9 describes the shifting percentage from the base case to the sensitivity case with the corresponding optimality resolution status. Figure 5 presents the resulted influence for each instance on the objective function MOSIM'20 -November 12-14, 2020 -Agadir -Morocco which is kept slightly at the same level while decreasing maximum capacity allocation. Likewise, a combined variability of the input parameters related to raw material inventory management is implemented. It is triggered by the resulted main level of the objective function presented previously. The considered parameters are the initial inventory level at each site, the minimum order quantity represented by the minimum supplier capacity as well as the contracted maximum capacity. The parameters' sensitivity is measured in terms of their simultaneous impact on the optimality solution, the related parameter stability region would represent the suitable upper and lower bounds to be considered for the model. It is worth noting that there is dependency between parameters, for example, customer demand impacts directly the adopted maximum and minimum capacities. Thus, as stated by (Yi Chaojue & Lu Ming, 2019), the sensitivity analysis is outlined with how a set of parameters called probe class can vary while another one known as control class is kept unchanged. In this case, the probe class includes the chosen parameters (i.e. initial inventory level, minimum order quantity & maximum capacity), while the control class is defined by the forecasted demand and the maximum production capacity for each site . From managerial standpoint, improving the bounds quality illustrates the related capacity threshold definition with raw material suppliers which is a considerable asset. Thus, 3 scenarios have been launched while improving the discussed bounds as and in addition to the initial level as presented in table 10. As shown in figure 6, the objective function curve has been decreased to -16% for the second scenario, it is mainly related to the corresponding decrease behavior of raw material inventory (i.e. raw material purchased value and the inventory holding cost).

The implementation of real world constraints coming from mass customization context into the quantitative modeling contributes to construct a deep understanding of the supply chain contracts across partners. While including the dynamic behavior of the bill of materials coming from the customized products and the CODP positioning close to customers, the related capacity allocation for different partners can be well defined considering the input demand level and the optimization leverage of the MILP formulation. Therefore, the resulted interrelation with maximum and minimum capacities to ensure can be well clarified. This status improves the win-win coordination for the overall actors with a close understanding of markets' requirements. In addition, the numerical results highlight the global formulation as a system which can be adopted by managers to take planning decisions emanate from an appropriate framework, for instance, the inclusion of the continuous raw material assessment for an optimal stock planning considering modular product structure to accommodate replenishment trigger and the overall review policy.

CONCLUSION

The increasing importance of supply chain management has been recognized during time from practitioners and academics. Though, dealings with mass customization strategy according to value chain management perspective has not been sufficiently reported. In this paper, the supply chain fundamental framework has been drawn asserting mass customization enablers. The study devel-DRo,e,p,t ̴ N(300;50) -10% -20% -30% Solving status Solved Solved Infeasible MOSIM'20 -November 12-14, 2020 -Agadir -Morocco oped a MILP model for a multi-echelon, multi-site supply chain in order to catch up on the assumptions details of the problem depicted from an industrial application to outline stakeholders' interactions and the related aspects. Accordingly, the model formulation is defined through a tactical decision level while integrating production, procurement and distribution systems. In fact, a three echelon supply chain has been illustrated from the automotive industry according to leaders and followers partnership. Furthermore, the demand driven process inferred from customization products highlights the corresponding decoupling point while production activities are established with make to order policies. Thus, to develop further the presented work towards application potential, testing the model with bigger sizes from real industrial cases is an interesting attempt to assess its resolution status according to exact methods. While approaching the extreme boundaries, a benchmark between metaheuristics would support to define the best performing algorithm according to solution quality and the related computational time.

Figure 2 :

 2 Figure 2: Modular product

  Set of time period Set of customers (OEM) Set of manufacturing sites Set of advanced warehouses (AW) Set of product families Set of serial numbers Set of modules Set of raw material Set of raw material suppliers Parameters  Sales Real demand of product p received from customer o to the site e in period t Forecasted demand of product p received from customer o to the site e in period t Minimum demand quantity contracted MOSIM'20 -November 12-14, 2020 -Agadir -Morocco with customer o and the site e of product p in period t Penetration rate of the module m Auxiliary parameter = 1 to activate the serial number s of the forecasted demand of product p of the customer o for the site e at period t Auxiliary parameter = 1 to activate the module m that belongs to the serial number s of the forecasted demand of product p of the customer o for the site e at period t Auxiliary parameter = 1 to activate the serial number s of the real demand of product p of the customer o for the site e at period t Auxiliary parameter = 1 to activate the module m that belongs to the serial number s of the real demand of product p of the customer o for the site e at period t  Production Initial backorder level at the site e of product p with serial number s of the customer o Backorder cost at the site e of the product p with serial number s of the customer o at the period t Inventory holding cost at the site e of product p of the customer o in period t Initial inventory level in the site e of product p of the customer o Maximum storage capacity at the site e of product p of the customer o in the period t Maximum production capacity at the site e of product p of the customer o in the period t Minimum production capacity at the site e of product p of the customer o in the period t The cost of module m  Procurement Purchase price of component c Initial inventory level of raw material c in the site e Minimum contracted demand between supplier f and the site e for raw material c Maximum contracted demand between supplier f and the site e for raw material c Parameter = 1, if replenishment from supplier f to the site e of raw material c in period t is allowed and 0 otherwise The needed quantity of raw material c in module m (Bill of material) Lead time for the raw material c  Distribution Inventory holding cost at the advanced warehouse v of product p of the customer o in period t Initial inventory level at the advanced warehouse v of product p of the customer o Penalty cost of excess inventory at the advanced warehouse v of product p of customer o in period t Vehicle load capacity from the site e to the advanced warehouse v Maximum contracted capacity at the advanced warehouse v for the product p of the customer o at period t Vehicle load capacity from the advanced warehouse v to the customer o Vehicle trip cost from the site e to the advanced warehouse v in period t Vehicle trip cost from the advanced warehouse v to the customer o in period t Big M Decision variables  Production Total produced quantity in the site e of product p with serial number s for the customer o in period t Binary variable, =1 if the serial number s of the product p of the customer o is produced in the site e at the period t to fulfill the real demand, 0 otherwise Binary variable, =1 if the serial number s of the product p of the customer o is produced in the site e at the period t to fulfill the generated backorder, 0 otherwise Binary variable, =1 if the serial number s of the product p of customer o is backordered in the site e at the period t, 0 otherwise Inventory level in the site e of product p of the customer o in period t Consumption level of the raw material c in the site e at period t from the produced quantity to satisfy demand Consumption level of the raw material c in the site e at period t from the produced quantity to satisfy backorders Total consumption level of the raw material c in the site e at period t  Procurement Inventory level in the site e of component c at the period t Purchased quantity by the site e of raw material c from supplier f in period t Required quantity assessment of raw material c for the site e in period t MOSIM'20 -November 12-14, 2020 -Agadir -Morocco Net required quantity to purchase of raw material c by the site e in period t  Distribution Inventory level of product p of the customer o in period t at the advanced warehouse v Shipping quantity of product p from the advanced warehouse v to the customer o in period t Shipping quantity of product p of the customer o from the site e to the advanced warehouse v in period t Number of vehicle trips from the site e to the advanced warehouse v in period t Number of vehicle trips from the advanced warehouse v to the customer o in period t The exceeded storage level at the advanced warehouse v of product p of the customer o in period t Binary variable, =1 if there is no storage excess at the advanced warehouse v of product p of the customer o in period t, 0 otherwise Auxiliary variable for maximum function linearization Using the previously notation, the MILP model is presented as follows:

  the backorder hurdle that should be less than a defined percentage δ from the confirmed demand during each period:

  production and distribution decisions of the manufactured products for each site through the inventory balance flow. It is given by the inventory from the last period plus the realized production minus the shipped quantity to the advanced warehouses: (21) Constraint 22 shows that product's storage capacity in the manufacturing sites has a limited threshold: Distribution Constraint 23 calculates the number of vehicle trips from each manufacturing site to the advanced warehouses at every time period based on vehicles' capacity:

  cope with the nonlinearity generated by the previous maximum function, constraints 29, 30, and 31 are added to the mathematical model: the balance equation of raw material inventory in manufacturing sites. It is equal to the inventory level from the previous period plus the received quantity from raw material suppliers in period t minus the consumed quantity in the sites:(32)In order to assess the raw material consumption, constraints 33 and 34 aim to determine the consumed level depicted from production structure (i.e. demand and backorders fulfilment) using the consumption coefficient of each module. Constraint 35 comes to add up the total consumption: the required quantity for each raw material based on the forecasted demand. Afterwards, constraint 37 aims to define the net required quantity by subtracting the inventory level of the previous period:(37) Constraints 38 and 39 control the purchased quantity based on the net required quantity assessment or the minimum contracted level contracted with raw material suppliers. The policy of the replenishment frequency contracted with suppliers is controlled by the parameter . It is outlined by a binary matrix while the purchased quantity variable is activated when it has a true value (i.e. =1). Constraint 40 enforces the activation of the purchased quantity variable according to the matrix value

Figure 4 :

 4 Figure 4: Objective function-Cost summary

Figure 5 :

 5 Figure 5: Maximum capacity cost impact

  DRo,e,p,t ̴ N(300;50)

Figure 6 :

 6 Figure 6: Objective function cost split

Table 1 :

 1 Affectations of OEMs

		Manufacturing site	Advanced warehouse	Product Range of Modules Basic Module
	o1	e1	v1	p1 p2	M01 -> M17 M18 -> M35	M01 M18
	o2	e2	v2	p3 p4	M36 -> M53 M54 -> M71	M36 M54
	o3	e3	v3	p5 p6	M72 -> M89 M90 -> M102	M72 M90
			Parameters
		Parameter	Value range	Parameter	Value range
			N(300;50)		500
			N(300;50)		U(150;180)
			U(1000;1100)		150
			U(0,05;12)		U(0,05;0,9)
			U (500;700)		U (45000;55000)
			5		1
			4		200
			10		0
			100		0
			0		50
			50		500
			150		50
			50		150
			[1,2,3]	-	-

Table 2 :

 2 Model parameters

	t1	t2	t3	t4	t5	t6	t7	t8	t9	t10
	o1 e1 p1 303,55 293,86 211,97 299,94 284,23 285,27 243,37 238,78 297,18 307,34
	o1 e1 p2 269,76 364,70 290,28 338,88 271,65 317,55 268,37 305,43 175,92 324,97
	o2 e2 p3 330,10 235,95 264,66 223,80 288,81 247,15 230,03 223,01 254,25 270,22
	o2 e2 p4 264,17 291,69 258,53 287,91 270,92 249,10 254,03 311,45 300,77 269,33
	o3 e3 p5 374,51 382,91 213,48 359,20 401,02 303,70 251,31 322,42 303,38 246,81
	o3 e3 p6 334,82 354,86 268,70 253,28 236,67 336,57 310,81 280,92 242,67 289,21

Table 3 : Confirmed demand t7 o2 e2 p4 s35 1 o2 e2 p4 s41 1 o2 e2 p4 s42 1 o2 e2 p4 s43 1 o2 e2 p4 s44 1 o2 e2 p4 s45 1 o2 e2 p4 s46 1Table 4 :

 34 Total backorders for each product from

Table 5 :

 5 Example of backordered serial numbers

	t2 t4 t6 t7 t8
	o1 e1 p1 28		14 24
	o1 e1 p2	30	26 30
	o2 e2 p3		5 22
	o2 e2 p4		7 31
	o3 e3 p5 30		30 3 20
	o3 e3 p6		30 10 14

Table 6 :

 6 Total produced quantity to satisfy demand from

	t1	t2	t3	t4	t5	t6	t7	t8	t9	t10
	o1 v1 p1 60,71 58,77 42,39 59,99 56,85 57,05 48,67 47,76 59,44 61,47
	o1 v1 p2 53,95 72,94 58,06 67,78 54,33 63,51 53,67 61,09 35,18 64,99
	o2 v2 p3 66,02 47,19 52,93 44,76 57,76 49,43 46,01 44,60 50,85 54,04
	o2 v2 p4 52,83 58,34 51,71 57,58 54,18 49,82 50,81 62,29 60,15 53,87
	o3 v3 p5 74,90 76,58 42,70 71,84 80,20 60,74 50,26 64,48 60,68 49,36
	o3 v3 p6 66,96 70,97 53,74 50,66 47,33 67,31 62,16 56,18 48,53 57,84

Table 7 :

 7 Inventory level at the advanced warehouse

	t1	t2	t3	t4	t5	t6	t7	t8	t9	t10
	o1 v1 p1 10,71 8,77		9,99	6,85	7,05			9,44 11,47
	o1 v1 p2 3,95 22,94 8,06 17,78 4,33 13,51 3,67 11,09		14,99
	o2 v2 p3 16,02		2,93		7,76				0,85	4,04
	o2 v2 p4 2,83	8,34 1,71 7,58	4,18		0,81 12,29 10,15 3,87
	o3 v3 p5 24,90 26,58		21,84 30,20 10,74 0,26 14,48 10,68
	o3 v3 p6 16,96 20,97 3,74 0,66		17,31 12,16 6,18		7,84

Table 8 :

 8 Excess inventory at the advanced warehouse

Table 9 :

 9 Resolution status