The results of discrete optimization structures developed for decision-making with consideration of emerging risks in various decisions are presented in this work. For each of the models discussed in this book, a numerical example is presented to illustrate some of the model's capabilities. The computational procedures used to solve the optimization problems are of polynomial computational complexity. The numbering of the formulae, figures, and tables is for convenience, compiled separately for each of the seven chapters, and consists of two elements – the chapter number and the sequential number of the relevant table, figure, and formula. At the end of each chapter, a summary of the results in that chapter is given, as well as the references used in that chapter. The proposed book also draws on the authors' many years of research in network flows, Markov decision processes, and discrete optimization.