Book Introduction:
In many real-world optimization problems, the value of parameters is not known with certainty, and in practice, decisions made withot incorporating uncertainty, may be sub-optimal or even infeasible. This book studies optimization problems under uncertainty with a practical and operational viewpoint. The first four chapters focus on modeling issues of stochastic programming problems, investigation of the value of stochastic solutions, and scenario generation and scenario reduction. In chapter 5, probabilistic programming is described as another approach of incorporating uncertainty. Additionally, due to the importance of the risk conept to managers, different risk measures are introduced and their incorporation into optimization models are described. Further, since stochastic programming models are large-scale, the presentation of efficient methods is of great importance, and the decomposability structure of such models can be utilized to develop efficient methods such as Dantzig-Wolfe decomposition, Benders decomposition, lagrangian relaxation, cross decomposition methods, etc. Decomposition methods and their implementation tips with defferent examples are addressed in chapters 6 and 7.
