Probability models in operations research, by C. Richard Cassady and Joel A. Nachlas

This is a nice, compact and focused book which is very well written. It can be used as a textbook for single semester courses that introduce probabilistic and stochastic model concepts for operations research (OR). The target readership is industrial engineering students who will be taking more than one operations research course within their curriculum, while this can ideally be the textbook for a second course in OR series. The book may also be used in part within an OR course offered as an elective course to other engineering students. Additionally, it can also be used in introducing the basic concepts of probability and stochastic processes to students starting an industrial engineering master program coming from a different major or programs such as engineering management. The book is composed of eight chapters. In the first three chapters basic concepts of probability are introduced for readers with little background on the subject. After the conceptual definitions of Chapter 1, Chapter 2 introduces the concepts of random variables and the two basic operators defined on them: expected value and variance. Some well known random variables are also explained. Chapter 3 continues with the analysis of multiple random variables and describes how expectation can be defined and calculated for them. Then, special emphasis is given on how the probability distribution or the expectation of a random variable can be calculated by conditioning on another one. The second part of the book is devoted to stochastic processes. A satisfactory general introduction is made in Chapter 4 where counting processes, renewal processes and Bernoulli processes are defined in general. Chapter 5 is reserved for the Poisson process, which is the most famous counting process. The analysis on the interarrival times is also made and some special types of Poisson processes are defined. Chapter 6 continues with the discrete time Markov chains. The classification of states and chains, the limiting and transient behaviours are all explained. Continuous time Markov chains are explained in Chapter 7 with a special emphasis on birth and death processes. Their limiting behaviour and the time dependent behaviour are explained. In the last chapter (Chapter 8) the basic Markovian queueing systems are explained and the formulas for calculating the basic measures are given. These are mainly the single and multiple server systems with Markovian interarrival and service times. The book flows naturally and even the most difficult subjects are explained with a readable narration. Another strength of the book is the application part given at the end of the chapters, where the reader is asked a series of questions and in this way can learn how the concepts explained in that chapter are used in an industrial engineering application. I believe if this part is covered in detail by the lecturer, students will develop a deeper understanding of the subject area.