Este trabalho tem por objetivo propor um método eficiente para avaliar gestão de estoque, aplicando conjuntamente a Teoria de Controle Ótimo (OCT), para obter funções de estocagem dinamicamente ótimas, e Análise Envoltória de Dados (DEA), para calcular as eficiências relativas. Tendo em vista esse objetivo foi desenvolvido um modelo integrado DEA-OCT para calcular a eficiência de custo otimizada ao longo do tempo, quando o sistema possui variáveis relacionadas entre si, como no caso de sistemas de controle de estoque, e para analisar produção e demanda (assim como a variável estoque, oriunda dessa relação), estendendo o modelo variacional. Este trabalho aplica o modelo proposto a 647 empresas das Américas do Sul e do Norte, depois faz uma comparação entre Brasil e Chile (países emergentes economicamente), posteriormente focando no setor de comércio, considerando seus sistemas produção-estoque com dados de variáveis contábeis. Os modelos minimizam os custos de produção e de estoque para calcular a eficiência de custo ao longo do tempo. O output (produto, ou variável de saída) é a demanda; o input (insumo, ou variável de entrada) é a produção, e o intermediate (variável intermediária) é o estoque. Seus custos são considerados na função objetivo. É acrescentada uma restrição variacional da OCT para descrever a relação entre demanda, produção e estoque. Em resumo, o modelo é relevante por calcular eficiência prevenindo a possibilidade de obter uma projeção que ignora a relação entre as variáveis, uma vez que essa relação sempre ocorre, na prática, em sistemas de controle de estoque. As principais contribuições são: possibilitar o uso de OCT como a ferramenta de benchmarking DEA no contexto de eficiência dinâmica, estender o modelo DEA variacional de Sengupta (1995), incluindo restrições de modelos mais recentes e possibilitar o cálculo de eficiência quando há relação entre as variáveis. / This work aims to propose an efficient method to evaluate inventory management, jointly applying optimal control theory (OCT), obtaining dynamically optimal production and inventory functions, and data envelopment analysis (DEA), calculating the relative efficiencies. With this objective in mind, it was developed a DEA-OCT integrated model to calculate allocative efficiency optimized over time, when systems have variable with relationship among themselves, like in the case of inventory control systems, and for analyzing production and demand (as the inventory variable obtained from this relationship), extending the variational model. This paper applies the proposed model to 647 companies from South and North America, after that it was made a comparison between Brazil and Chile (economically emerging countries), then focusing on the commercial sector, considering its production-inventory systems and data from accounting variables. The model minimizes the inventory and production costs to calculate the allocative efficiency over time. The output is demand; the input is production, and the intermediate variable is inventory. Their costs are considered in the objective function. A variational constraint OCT is added to describe the relationship among demand, production, and inventory. In summary, the model is relevant to calculate efficiency by preventing the possibility of finding a projection that ignores the relationship among variables, since this relationship always occur in practice in inventory control systems. The main contributions are: using OCT as the benchmarking tool DEA in the context of dynamic efficiency, extending the Sengupta (1995) variational DEA model, including constraints from recent model and making it possible to calculate efficiency when there is a relationship among variables.

Cette thèse comporte trois essais sur l'existence de cycles endogènes sous efficacité dynamique et compte deux thèmes. Le premier thème est traité dans le chapitre 2 et aborde la relation entre la structure industrielle et l'émergence de fluctuations endogènes. Le deuxième sujet est examiné dans les chapitres 3 et 4, et tente d'améliorer notre compréhension du rôle du commerce international sur l'existence de cycles endogènes.La première contribution analyse dans quelle mesure l'existence de bien durable et non-durable est associée à l'occurrence de cycles endogènes sous efficacité dynamique. Les résultats indiquent que des cycles endogènes existent si la part de la consommation des jeunes allouée au bien non durable est assez petite. Nous démontrons qu'une politique de stabilisation basée sur des taxes et transferts forfaitaires permet dans un même temps d'augmenter le bien-être des agents et de supprimer l'existence des cycles.La seconde contribution considère un modèle à générations imbriquées à deux facteurs, deux biens et deux pays. Cette approche est basée sur l'hypothèse d'immobilité des facteurs de production entre pays. On suppose également que les pays sont identiques en tout point excepté en leur taux d'escompte. Nous établissons à l'aide d'une simulation numérique que des cycles à deux périodes se propagent d'un pays à l'autre.La troisième contribution se situe dans un cadre proche du modèle du chapitre 3 mais se focalise sur des différences technologiques entre pays. Nous mettons en évidence par le biais de simulations numériques que le commerce international peut générer des cycles à deux périodes qui n'existaient pas en économie fermée. / This dissertation consists of three essays on the existence of endogenous cycles under dynamic efficiency and covers two different topics. The first one developed in chapter 2 addresses the relation between the structure of production and the occurrence of endogenous fluctuations. The second topic is developed in chapters 3 and 4, and tries to better understand the role of international trade on the emergence of sunspot cycles. These chapters explain that international trade may have a destabilizing effect.Chapter 2 examines how the existence of durable and non-durable goods are associated with the occurrence of endogenous cycles with dynamic efficiency. Main results indicate that sunspot fluctuations exist if young agents consume less non-durable goods than old agents. In this context, we show that a stabilization policy based on lump-sum taxes and lump-sum transfers allows to increase the welfare of agents and eliminate the existence of endogenous cycles.Chapter 3 analyzes a two-factor, two-good, two-country overlapping generations model. We assume that countries differ only with respect to their discount rate. We suppose that the factor of production are immobile across countries. Using a numerical simulation, we show that period-two cycles spread from one country to another.Chapter 4 considers a framework similar to the model of chapter 3 but with focus on asymmetric technology. We show through numerical simulations that the opening to international trade can create two-period cycles that can exist in the world economy even though the closed-economy equilibrium in each country is saddle-point stable.

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