Growing uncertainty in both demand and supply, fast-paced technological developments, and increasingly stringent customer requirements progressively complicate supply chain management across numerous industries. To improve efficiency and foster resilience, companies focus on optimizing their production inventory planning processes, addressing the fundamental trade-off between inventory investments and customer service levels under uncertain conditions. This thesis develops stochastic mathematical models and solution approaches to optimize production-inventory systems with diverse characteristics. It examines centralized and decentralized decision-making structures, single- and multiperiod planning, and various supply chain configurations, including single echelon and capacitated multi-echelon systems. The models address key sources of uncertainty, such as demand, lead times and new product introduction dynamics, while exploring both risk-neutral and risk-averse decision-making perspectives. In collaboration with ASML, a leader in the high-tech sector, the first part of the thesis introduces methods tailored to complex industry-driven settings. These include a rolling horizon decision framework for integrated production and buffer planning, multi-stage stochastic programming models for risk-averse service level management and product rollover planning, and a deep reinforcement learning-based inventory policy for handling non-stationary demand and capacity constraints. The second part emphasizes theoretical contributions, offering insights into decision making under demand correlation, risk aversion and contractual agreements through analytical models. By integrating practical and theoretical advancements, this thesis aims to contribute to the broader field of production inventory planning and supply chain management, providing structural insights to guide and complement the development of general approaches to practical problems.