In the first two chapters of this thesis, we address the One-Warehouse Multi-Store (OWMS) problem, a critical inventory control challenge in supply chain management. Motivated by our collaboration with a leading fast-fashion retailer in Europe, we investigate this problem in two scenarios: when the demand is uncensored and when it is censored. For the uncensored demand case, we propose an algorithm based on sample average approximation and the empirical distribution function, enabling continuous learning of the demand and real-time inventory control decisions. This approach delivers significant theoretical and empirical performance improvements. In the censored demand scenario, we develop a primal-dual algorithm to effectively handle incomplete demand information and make optimal inventory control decisions. Again we show the performance of the algorithm in both theoretical analysis and empirical experiments. Furthermore, in the third chapter, we shift our focus to the fulfillment and inventory control problem in the context of the rise of omnichannel retail. Introducing a deterministic approximation algorithm with inventory buffers, we enable efficient inventory control and fulfillment decisions. Through extensive analysis, our work provides valuable insights and optimization techniques for managing inventory with different customer types, as well as practical solutions for fulfillment in the complex landscape of omnichannel retail. Overall, this thesis makes notable contributions to advancing inventory control and learning techniques, benefiting decision-makers in the supply chain and retail sectors.