Des stratégies d'approvisionnement pérennes sont nécessaires pour les gestionnaires de la chaîne d'approvisionnement afin de faire face aux incertitudes d’approvisionnement et de demande. La diminution des niveaux de service et l'augmentation simultanée des coûts de stockage sont les impacts les plus importants de ces incertitudes. Les perturbations peuvent être causées par des discontinuités de l’approvisionnement, de l'instabilité politique, des catastrophes naturelles et des grèves des employés. Elles pourraient avoir un effet important sur la performance de la chaîne d'approvisionnement. Pour faire face à de telles perturbations, les modèles d'optimisation des stocks doivent être adaptés pour couvrir une structure de réseau multi-échelons et envisager des stratégies d'approvisionnement alternatives telles que le transport latéral (lateral transshipment) et plusieurs sources d’approvisionnement. Dans ce travail, une approche de modélisation basée sur des scénarios est proposée pour résoudre un problème d'optimisation multi-échelons des stocks. En prenant en compte la demande stochastique et les incertitudes sur les capacités de production, le modèle minimise le coût opérationnel total (coûts de stockage, de transport et de retard) tout en optimisant la gestion des stocks et les flux des marchandises. Afin de faire face aux incertitudes, plusieurs échantillons de scénarios sont générés par Monte Carlo et les exemples correspondants d'approximation (SAA) des programmes sont résolus pour obtenir une politique de réponse adéquate au système d'inventaire en cas de perturbations. De nombreuses expériences numériques sont menées et les résultats permettent d'acquérir des connaissances sur l'impact des perturbations sur le coût total du réseau et le niveau de service. / Supply Chain Management (SCM) is an important part of most companies and applying the appropriate strategy is essential for managers in competitive industries and markets. In this context, Inventory Management plays a crucial role. Different inventory systems are widely used in practice. However, it is fundamentally difficult to optimize, especially in multi-echelon networks. A key challenge in managing inventory is dealing with uncertainties in supply and demand. The simultaneous decrease of customer service and increase of inventory-related costs are the most significant effects of such uncertainties. To deal with this pattern, supply chain managers need to establish more effective and more flexible sourcing and distribution strategies. In this thesis, a “framework to optimize inventory decisions in multi-echelon distribution networks under supply and demand uncertainty” is proposed. In the first part of the research work, multi-echelon distribution systems, subject to demand uncertainty, are studied. Such distribution systems are one of the most challenging inventory network topologies to analyze. The optimal inventory and sourcing policies for these systems are not yet unknown. We consider a basic type of distribution network with a single family product through a periodic review setting. Based on this property, a two-stage mixed integer programming approach is proposed to find the optimal inventory-related decisions considering the non-stationary demand pattern. The model, which is based on a Distribution Requirements Planning (DRP) approach, minimizes the expected total cost composed of the fixed allocation, inventory holding, procurement, transportation, and back-ordering costs. Alternative inventory optimization models, including the lateral transshipment strategy and multiple sourcing, are thus built, and the corresponding stochastic programs are solved using the sample average approximation method. Several problem instances are generated to validate the applicability of the model and to evaluate the benefit of lateral transshipments and multiple sourcing in reducing the expected total costs of the distribution network. An empirical investigation is also conducted to validate the numerical findings by using the case of a major French retailer’s distribution network. The second part of the research work is focused on the structure of the optimal inventory policy which is investigated under supply disruptions. A two-stage stochastic model is proposed to solve a capacitated multi-echelon inventory optimization problem considering a stochastic demand as well as uncertain throughput capacity and possible inventory losses, due to disruptions. The model minimizes the total cost, composed of fixed allocation cost, inventory holding, transportation and backordering costs by optimizing inventory policy and flow decisions. The inventory is controlled according to a reorder point order-up-to-level (s, S) policy. In order to deal with the uncertainties, several scenario samples are generated by Monte Carlo method. Corresponding sample average approximations programs are solved to obtain the adequate response policy to the inventory system under disruptions. In addition, extensive numerical experiments are conducted. The results enable insights to be gained into the impact of disruptions on the network total cost and service level. In both parts of the research, insights are offered which could be valuable for practitioners. Further research possibilities are also provided.

O problema de controle de estoques com demanda não estacionária e lead-time positivo tem se tornado cada vez mais relevante em virtude da crescente tendência de redução do ciclo de vida dos produtos e internacionalização das cadeias de suprimentos. Embora haja uma solução exata para a minimização do custo esperado da política de estoques para este cenário, baseado no método de programação dinâmica, o custo computacional deste método ainda é considerado elevado. Este trabalho detalha e avalia através de simulação o método exato e duas aproximações para a minimização do custo esperado da política de estoques, em termos do desempenho em custo e eficiência computacional. Os resultados experimentais permitem a análise dos métodos disponíveis. Enquanto a abordagem heurística de Bollapragada e Morton, que utiliza o nivelamento da demanda não estacionária, perde desempenho de custo com o aumento do lead-time, a nova heurística proposta, que aproxima os parâmetros da política ótima por valores limitantes, produz resultados sucessivamente melhores com o aumento do lead-time. / The inventory control problem with nonstationary demand and positive lead-time has become increasingly important due to the growing trend of reduction in product life cycle and internationalization of the supply chain. Although there is an exact solution to the minimization of the expected cost of inventory policy on this environment, through the method of dynamic programming, the computational cost of this method is still considered high. This work details and evaluates through simulation the exact method and two heuristic solutions for the minimization of expected cost of inventory policy, in terms of cost performance and computational efficiency. The experimental results allow the analysis of the available methods. While the Bollapragada and Morton heuristic approach, which levels the non-stationary demand, decreases the cost performance when lead-time is increased, the new heuristic proposed, that approximates the optimal policy parameters by limiting values, successively produces better results with increasing lead-times.

O problema de controle de estoques com demanda não estacionária e lead-time positivo tem se tornado cada vez mais relevante em virtude da crescente tendência de redução do ciclo de vida dos produtos e internacionalização das cadeias de suprimentos. Embora haja uma solução exata para a minimização do custo esperado da política de estoques para este cenário, baseado no método de programação dinâmica, o custo computacional deste método ainda é considerado elevado. Este trabalho detalha e avalia através de simulação o método exato e duas aproximações para a minimização do custo esperado da política de estoques, em termos do desempenho em custo e eficiência computacional. Os resultados experimentais permitem a análise dos métodos disponíveis. Enquanto a abordagem heurística de Bollapragada e Morton, que utiliza o nivelamento da demanda não estacionária, perde desempenho de custo com o aumento do lead-time, a nova heurística proposta, que aproxima os parâmetros da política ótima por valores limitantes, produz resultados sucessivamente melhores com o aumento do lead-time. / The inventory control problem with nonstationary demand and positive lead-time has become increasingly important due to the growing trend of reduction in product life cycle and internationalization of the supply chain. Although there is an exact solution to the minimization of the expected cost of inventory policy on this environment, through the method of dynamic programming, the computational cost of this method is still considered high. This work details and evaluates through simulation the exact method and two heuristic solutions for the minimization of expected cost of inventory policy, in terms of cost performance and computational efficiency. The experimental results allow the analysis of the available methods. While the Bollapragada and Morton heuristic approach, which levels the non-stationary demand, decreases the cost performance when lead-time is increased, the new heuristic proposed, that approximates the optimal policy parameters by limiting values, successively produces better results with increasing lead-times.

<p dir="ltr">Employee staffing and scheduling are critical aspects of resource management in labor-intensive, customer-centric service organizations. This thesis investigates the optimal decision-making process for these critical tasks in the presence of non-stationary uncertainty, such as case-mix resident need, recommended staffing hours, and potential staffing turnover, a challenge prevalent in various domains, including healthcare and nursing home management.</p><p dir="ltr">The research begins predicting resident needs accurately. For this purpose, we present a novel Bayesian modeling approach to predict nursing home need-based resident census and staffing time. The resultant time series data of need-based resident census and staffing time are nonstationary with potential correlations between resource utilization groups. We thus propose Bayesian latent variable models with time-varying latent states to capture the dynamic patterns of resident service needs. We demonstrate the superiority of the proposed Bayesian prediction models by comparing their forecasting performance with several popular benchmark models, using historical assessment and aggregate staffing data from representative nursing homes.</p><p dir="ltr">The thesis further incorporates a rolling-horizon scheduling approach that integrates a periodically evolving Bayesian forecasting method into a series of stochastic look-ahead decision actions over multiple periods. To deal with the workforce scheduling with nonstationary demand uncertainty, we introduce a stochastic lookahead optimization framework that executes two-stage stochastic programming periodically along a rolling horizon to address the evolving non-stationary uncertainty. We obtain two-stage stochastic programming models to design effective work schedules, specifically assigning nurses to various shifts while balancing the staff workload and accommodating fluctuating resident needs.</p><p dir="ltr">We finally introduce the SNHSSO framework (stochastic nursing home staffing and scheduling optimizer), encompassing data modeling and addressing multi-period, multi-uncertainty, and multi-objective staffing and scheduling challenges. When the SNHSSO Optimizer is executed with the provided inputs, it generates recommended staffing decisions for longer planning horizons, as well as schedules and contingency plans for shorter planning horizons. These adapted decisions and adjusted parameters are archived for future reference, facilitating subsequent iterations of the process. SNHSSO optimizes caregiver assignments by taking into account probabilistic forecasts of service requirements, resident acuity, and staff turnover, all within two-stage stochastic mixed integer linear programs. Our approach leverages a scenario-based rolling horizon methodology to effectively solve the SNHSSO model.</p><p dir="ltr">The empirical foundation of this work is built on case studies conducted using Minimum Data Set (MDS) data spanning five years from 2014 to 2018 in Indiana nursing homes.</p>