Operations Research, often abbreviated as OR, is a relatively new branch of Applied Mathematics. Its aim is to optimise mathematical models of reality involving probabilistic uncertainty and its results are applied to real life problems. The aim of this book is to cover, in a condensed but rigorous way, the main chapter of the OR probablisitc models based on optimisation. The topics are taken from Game Theory, Decision Theory, Simulation, Reliability, and Queueing Theory. Game Theory deals with how to find the best winning strategies in a confrontation between two players with opposite interest and how to evaluate the value of different possible coalitions in a game involving more than two players. In Decision Theory the main objective is to find the optimum actions of the decision maker for minimising his loss when he has limited information available and faces uncertainty about the future possible events. Simulation is a powerful instrument for obtaining representative examples, of any length, from probability distributions of interest and for approximating multiple definite integrals and the solutions of linear and non-linear equations and programs. In the chapter dealing with Reliability, the main problem is how to evaluate the probability that a system functions properly, or is still alive, during an arbitrary time interval. Finally, Queuing Theory deals with how to assess what may happen in a complex system where the customers arrive randomly, wait in line, and later are served. A main concept is the waiting time in the queuing system, waiting to be served and being served. In each chapter, some representative examples and the mathematical formalism are discussed first, eventually followed by the comments on ramifications, generalisations and applications of the basic results. Computer tips and programs are inserted in each chapter. The text is based on lectures delivered for more than twenty-five years in the Department of Mathematics and Statistics at York University in Toronto. The book is rather a monograph an the probablistic modes in Operations Research which could also be used as a text book in a more advanced OR course. The book is self-contained, compact, and accessible to mathematicians, economists, system analysts, decision makers, and people dealing with computer assisted modelling. It contains also new original topics and proofs not covered in the standard OR textbooks. The chapters are kept to be as independent as possible.
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