Abdelwaheb Dogui

Analysis of a Stackelberg game between a customer and several cooperating suppliers: stability and efficiency

ABSTRACT We analyse the performances of a supply chain where multiple capacitated suppliers are solicited by a customer who offers a new product procurement suggestion. The customer allocates demand volume to suppliers in a way to maximise his own profit. On the other hand, suppliers can cooperate by forming coalitions. We study coalition structures’ stability and show that such cooperation improves the total supply chain performances. We show however that decentralisation of decisions may lead to the loss of the offer even when suppliers cooperate. We show also that total performances can be more improved if suppliers and the customer cooperate together.

Competitive versus cooperative performances of a Stackelberg game between two suppliers

We investigate the competitive and cooperative performances of a supply chain with two capacitated suppliers solicited by a customer who offers a new product procurement suggestion. Suppliers have the option to accept or reject the new product offer according to its profitability. In addition, suppliers have to decide on their base stock levels. We classify suppliers as principal and secondary. The customer usually addresses demand to the principal supplier at first. We consider two schemes: in the first scheme, the principal supplier informs the customer about the demand ratio he wants to be allocated. The customer allocates the remaining quantity to the secondary supplier. In the second scheme, the principal supplier decides to respond to the entire demand and to subcontract a part of it to the secondary supplier. In the competitive situation, we give conditions that allow principal supplier to select the best scheme. We show that the new product offer can be refused while it is accepted when suppliers cooperate. We present a profit allocation policy under which collaboration is beneficial for the two suppliers.

Assessment of intervertebral disc degeneration-related properties using finite element models based on \(\uprho _H\)-weighted MRI data

Quantitative magnetic resonance imaging (MRI) provides useful information about intervertebral disc (IVD) biomechanical properties, especially those in relation to the fluid phase. These properties may improve IVD finite element (FE) models using data closer to physiological reality. The aim of this study is to investigate IVD degeneration-related properties using a coupling between MRI and FE modeling. To this end, proton density (

Prediction of intervertebral disc mechanical response to axial load using isotropic and fiber reinforced FE models

\rho _H

A simplified coupled crankshaft–engine block model

ρH)-weighted MRI sequences of a porcine lumbar IVD were carried out to develop two biphasic swelling models with hyperelastic extracellular matrix behavior. The first model is isotropic, and the second one is anisotropic and takes into account the role of collagen fibers in the mechanical behavior of the IVD. MRI sequences permitted to determine the geometry and the real porosity mapping within the disc. The differentiation between disc components (nucleus pulposus, annulus fibrosus and cartilaginous end plates) was taken into account using spatial continuous distributions of the mechanical properties. The validation of the FE models was performed through two steps: the identification of the model’s mechanical properties using relaxation compressive test and the comparison between the MRI after load porosity distributions and those numerically obtained using the set of identified properties. The results confirmed that the two developed FE models were able to predict the mechanical response of uniaxial time-dependent compressive test and the redistribution of porosity after load. A slight difference between the measured and the numerical local bulges of the disc was found. This study suggests that from the coupling between MRI imaging in different state of load and finite element modeling we can deduce relevant information that can be used in the assessment of the early intervertebral disc degeneration changes.

Rigidité en flexion d’un vilebrequin

Masonry wall is a composite structure formed by units linked vertically and horizontally by mortar. One of the interests in this paper is composed of hollow concrete blocks. Generally, in structural analysis of masonry wall, the determination of the limit strength presents a challenge, due to the complexity and the heterogeneity of his constituent materials. In the present paper, a numerical homogenization is used for the estimation of the strength domain of an in-plane loaded masonry by accounting for the failure of its blocks. The determination of this domain was based on a rigorous definition of the microstructure in three-dimensions, on convex analysis and on the kinematical approach in the frame of limit analysis theory. A three- dimensional periodic basic cell with a nonlinear material behavior is used. Periodic boundary conditions have been imposed on the lateral boundary of the unit cell by matching the degrees of freedom of pairs of nodes.

Decentralized versus cooperative performances in a Nash game between a customer and two suppliers

Collagen fibers play a major role in the determination of the mechanical behavior of soft tissues. In the intervertebral disc (IVD), it was shown that they contribute in both tissue tensile and compressive stiffness (Römgens et al. 2012). IVD collagen network is progressively organized from the nucleus pulposus (NP) to the annulus fibrosus (AF). In the NP, the collagen density is low and the fibers are randomly disposed. However, they are oriented in two directions in the outer lamellae of the AF (about ±30° to the transverse plane). The organization of the collagen fiber network provides an anisotropic mechanical behavior to the AF. Several finite element (FE) models taking into account the anisotropy of the AF have been proposed and validated for several cases of load such as compression, twist and bending of the whole IVD (Jacobs et al. 2014; Reutlinger et al. 2014) or compression, tension and shear of the AF sample (Mengoni et al. 2015; Hollingsworth and Wagner 2011). In order to develop a new method of assessment of degeneration based on the coupling of Magnetic resonance imaging (MRI) and FE modeling, two models of IVD were developed. The first model is isotropic and the second one incorporates an anisotropic behavior of the AF. Through a comparison of these two models using an experimental compressive test, the purpose of this study is to determine the more suitable formulation to assess IVD mechanical properties using a new coupled (MRI-FE modeling) approach to investigate degeneration.

Biomechanical behavior of porcine intervertebral disc in finite deformation

Intervertebral discs (IVDs), usually classified as fibrocartilages, are situated between vertebraes. They ensure the spine motion and play a central role in the transmission and the absorption of loads through the vertebral column. These last properties are in relation with the high disc water content that represents more than 70% of its total volume. The disc being avascular, the water content is also at the heart of the transport process that allows nutrients to diffuse from the vertebral endplates to the disc’s cells. Thereby the regulation of the disc hydration, especially under non-physiological mechanical load, is a key factor of the disc long viability. Based on previous linear model of Etienne et al. (2011), a new development is proposed to take into account finite deformation formulation to model IVD mechanical behaviour during large deformations. The purpose of the present study is therefore to determine the effect of these large deformations on the nutrient processes comparing with the older linear model. The mechanical model and its coupling with the nutrient one are first described. Then, taking into account large deformations, this work highlights that linear model overestimates water waste and nutrient concentration variations within the IVD.