This book introduces readers to the innovative world of Fenchel and disjunctive decomposition for tackling stochastic mixed-integer programming (SMIP) problems. SMIP is a crucial area of stochastic programming that addresses optimization challenges under uncertainty with discrete decision variables, applicable in fields like healthcare, transportation, and energy planning. Key concepts explored include the foundational theories of Fenchel decomposition (FD) and disjunctive decomposition (D2), as well as their integration into FDD. The book provides a comprehensive look at decomposition algorithms and their practical implementation, offering numerical illustrations to guide readers in applying these methods to real-world problems. Chapters delve into topics such as mean-risk SMIP models, risk-neutral and risk-averse settings, and advanced techniques like FDD with integer set reduction (FDD-ISR). Ideal for students, researchers, and practitioners with a background in mathematical programming, this book offers new insights and algorithms for solving complex SMIP problems. It stands out by emphasizing both theoretical foundations and practical applications, making it an essential resource for anyone interested in advancing their understanding of stochastic programming.
