This course is designed to introduce fundamental models and technical tools of solving real world problems to PhD students, and to train their original thinking skills and prepare them for advanced research. This course aims to provide students a comprehensive understanding of linear programming, convex optimization, dynamic programming and stochastic control. Students are trained to make optimal decisions under deterministic and stochastic environments. Applications in inventory control and pricing strategy are demonstrated. This course is designed to introduce fundamental models and technical tools of solving real world problems to PhD students, and to train their original thinking skills and prepare them for advanced research in the fields of operations research and operation management.