The amount of safety stock to hold at each stage in a supply chain is an important problem for a manufacturing company that faces uncertain demand and needs to provide a high level of service to its customers. The amount of stock held should be small to minimize holding and storage costs while retaining the ability to serve customers on time and satisfy most, if not all, of the demand. This thesis discusses the issue of safety stock placement in a supply chain. This problem is modelled as nonlinear optimization problem. In a first step, the thesis examines possible linearization of this objective function and computes the errors. The work is then extended to the capacitated case. It is organized in five chapters. First of all, there is an introduction explaining the motivations to develop the thesis and to familiarize with inventory placement issue. Second chapter consists in a literature review of research already done and a brief explanation of nomenclature and assumptions. It is important to differentiate between networks without capacity constraints and networks with. Third chapter explains the methods developed by myself. Then, fourth chapter mentions the numerical experiments done, results and a deep analysis. Finally, fifth chapter includes conclusions and achievements obtained with this research.