This thesis focuses on the modelling of supply chains operating under demand uncertainty. Supply chain network design models are an essential tool for companies to manage their supply chain efficiently, and thereby to reduce costs (e.g., facility, inventory, transportation) and to improve customer service. Supply chain network design decisions (i.e., number and location of facilities), which are highly influenced by the current volatile market conditions, have a significant impact on the performance of the company in the long term, and directly affect tactical and operational decisions. In the past recent years, researchers have refined classical supply chain network design models by integrating tactical and operational decisions. The present work provides different integrated location-inventory models, and analyses the impact of demand uncertainty and the trade-offs arising from including tactical and operational decisions in the supply chain design. The ultimately goal of this thesis is to provide insights that may support the decision-making process in the supply chain design, and may allow to mitigate the impact of demand uncertainty. This thesis consists of an introductory chapter that provides a background of the study and outlines the thesis, and of three chapters representing the collection of three scientific publications. Chapter 2 proposes a location-inventory model, including cycle inventory and safety stocks, for the design of large supply chains under uncertain demand. The model is solved using a heuristic algorithm, which obtains close to optimal solutions, and drastically reduces the computational time compared to a state-of-the-art conic quadratic mixed-integer program. This permits the analysis of larger supply chains, and provides interesting managerial insights on how the integration of safety stocks at retailers offsets risk pooling benefits, and affects the design of a supply chain. Chapter 3 integrates safety stock placement and delivery strategy decisions in the supply chain network design problem. Safety stock placement decisions are modelled using the guaranteed-service approach, avoiding the use of service time variables. The results capture the interdependencies between safety stock placement and location decisions, and addresses interesting managerial insights related to the location of facilities, demand variability and lead time pooling. Finally, Chapter 4 explores the impact of long-term demand uncertainty, and proposes a stochastic program for the design of robust supply chains. The model integrates several flexibility mechanisms at the operational level (e.g., reallocation, temporary DCs or lost markets), which allow to design cost-effective robust supply chains, and to obtain a more comprehensive uncertainty mitigation framework. Computational results show that the integration of flexibility mechanisms in the design of robust supply chains has a great influence in its configuration, and leads to important cost savings.