Operations Research

Description

Operations research, which is concerned with the efficient allocation of scarce resources, is both an art and a science. The art lies in the ability to reflect the concepts efficient and scarce in a well-defined mathematical model of a given situation; the science consists in the derivation of computational methods for solving such models. This book is meant to introduce readers to both aspects of the field. Each chapter is divided into three sections. The first deals mainly with methodology; the exception is Chapter 1, which is-concerned exclusively with the modeling aspects of mathematical programming. The second section consists of completely worked out problems. Besides clarifying the techniques presented in the first section, these problems may expand them and may also provide prototype situations for understanding the art of modeling. Finally, there is a section of problems with answers through which readers can test their mastery of the material. The book itself is divided into two parts: mathematical programming and probabilistic methods. The first part, Chapters 1 through 15, is comprised solely of deterministic methods in linear, nonlinear, integer, and dynamic programming, along with a chapter on network analysis. A background in matrix algebra is sufficient for most of this material, although some differential calculus is required for the nonlinear search techniques. The second part, Chapters 16 through 24, includes material on stochastic dynamic programming, graph theory, decision theory, Markov chains, and queueing. As its title suggests, this part of the book has a first course in probability as a prerequisite. Since the optimal allocation of money, manpower, energy, or a host of other scarce factors, is of importance to decision makers in many traditional disciplines, the material in this book will be useful to individuals from a variety of backgrounds. Therefore, this outline has been designed both as a textbook for students wanting an introduction to operations research and as a reference manual from which practitioners can obtain specific procedures.