Companies are no longer judged on financial performance alone, but rather on their “Triple-Bottom Line”, which accounts for social and environmental measures as well. This leads companies to investigate the sustainability of their operations and their products. Between the increasing cost of virgin raw materials and customers demanding post-consumer product content, manufacturers have begun looking at recycled material options. This paper addresses a procurement issue facing a polystyrene packaging manufacturer considering its optimal purchasing strategies between two suppliers – one providing virgin material, the other offering recycled material. A single-period scenario is modeled where each supplier sells product with a known yield distribution at market pricing. The manufacturer must choose whether to sole-source or dual-source, as well as determine how much material to purchase from each supplier to meet deterministic demand. Our results indicate that there is a range of prices from the recycled material supplier where dual-sourcing will lead to higher manufacturer profits compared to sole-sourcing. We show, based on the procurement strategy, the optimal quantities to purchase to maximize manufacturer’s expected profit. We then investigate the area of supplier development and how the manufacturer can improve their expected profit by investing in their supplier’s quality improvement effort. The questions addressed are how much the manufacturer would be willing to invest and how they ensure the proper return on their investment. This paper determines the expected increase in profit for the manufacturer from yield improvement projects at a supplier, which therefore becomes the upper threshold for investment. We also find that a company can err in their project acceptance criteria if they have an approval process that views project acceptance myopically rather than holistically. Lastly, we develop a systematic and comprehensive approach to the supplier selection process. We utilize the fundamental concepts behind W. Edwards Deming’s Plan-Do-Study-Act improvement cycle and apply them to the supplier selection process. We also present analytic and numerical study results that can be used in conjunction with contractual mechanisms to not only overcome issues such as free riding, but to also incentivize suppliers to engage in supplier development projects they may not have otherwise undertaken.

Durant les trois années de la thèse, j’ai eu le plaisir de travailler en collaboration avec à la fois des volcanologues, des physiciens de laboratoire et des mathématiciens. Ce mémoire est l’occasion de présenter la démarche et les résultats de mes recherches dans le domaine de la modélisation d’écoulements granulaires denses fluidisés. Ces derniers consistent à développer un nouveau modèle mathématique et son étude théorique et numérique. Sur la base d’observations faites lors d’expériences de laboratoire, nous proposons une façon de modéliser le changement comportemental d’un écoulement granulaire initialement fluidisé au travers de la définition de sa rhéologie viscoplastique à seuil variable. Plus précisément, le seuil de plasticité est défini par la différence entre la pression lithostatique et la pression du fluide interstitiel. La nouveauté apportée par ce modèle ouvre de nouvelles perspectives à la fois pour le champ de recherche en mathématiques et pour la compréhension des lits granulaires fluidisés et leur application à la volcanologie. Du point de vue mathématique, une étude théorique du modèle a été menée. En proposant une preuve de l’existence de solutions faibles à un problème lié à la version homogène du modèle, nous apportons une extension au champ de connaissances autour des écoulements des fluides non-newtoniens. D’autre part, dans le but de reproduire numériquement des expériences de laboratoire de chute de colonne granulaire fluidisée, nous avons développé un code de simulation numérique incluant une nouvelle méthode de résolution des équations d’écoulement de fluides à seuil. Dans ce manuscrit, je décris et justifie les différents choix stratégiques pour le développement de ce code. Par ailleurs, je présente quelques tests académiques permettant de valider le code. Enfin, je donne les résultats de simulation de chute de colonne granulaire, qu’elle soit fluidisée ou non. Une comparaison avec les données de laboratoire est effectuée afin d’évaluer les points forts et les défauts du modèle par rapport à la réalité des expériences. En conclusion, dans la continuité du travail mené dans ce projet, des perspectives d’amélioration sont proposées. / During these three years, I enjoyed to work with collaborators from volcanology, laboratory physics and mathematics. This document presents the steps and results of my research in the field of modelling of fluidised granular flows. The last consists in the development of a new mathematical model and its theoretical and numerical study. Based on observations made on experimental studies, the model focuses on the change in the behaviour of an initially fluidised granular flow through the definition of its viscoplastic rheology with variable threshold. More precisely, the threshold (aslo called yield stress) is defined via the difference between the lithostatic pressure and the pressure of the interstitial fluid. The innovation of this model opens perspectives for the mathematical research as well as for the study of fluidised granular flows and their application to volcanology. From a mathematical point of view, a theoretical study has been conducted. Proving the existence of weak solution for the homogeneous version of the model, we offer an extension in the field of knowledges of non-newtonian fluid flows. Also, we have developped a numerical code to simulate dambreak experiments with fluidised granular media. This one includes a new method to solve the flow equations of viscoplastic fluids. In this thesis, I describe and justify the numerical strategy chosen. Moreover, I present some academic tests to validate the code. At the end, I give the numerical results in the case of the dambreak simulation for dry and fluidised fluids. By comparing with experimental data, we evaluate the validity of the model and its resolution, and highlight the advantages and inconvenients. To conclude the project, I propose some perspectives of improvement for later work.