Mastering chance has, for a long time, been a preoccupation of mathematical research. Today, we possess a predictive approach to the evolution of systems based on the theory of probabilities. Even so, uncovering this subject is sometimes complex, because it necessitates a good knowledge of the underlying mathematics. This book offers an introduction to the processes linked to the fluctuations in chance and the use of numerical methods to approach solutions that are difficult to obtain through an analytical approach. It takes classic examples of inventory and queueing management, and addresses more diverse subjects such as equipment reliability, genetics, population dynamics, physics and even market finance. It is addressed to those at Master's level, at university, engineering school or management school, but also to an audience of those in continuing education, in order that they may discover the vast field of decision support.
Table of Contents:
Preface ix
Part 1. Basic Mathematical Concepts 1
Chapter 1. Basic Reminders of Probability 3
Chapter 2. Probabilistic Models 25
Chapter 3. Inventory Management 45
Part 2. Stochastic Processes 69
Chapter 4. Markov Chains 71
Chapter 5. Markov Processes 95
Chapter 6. Queueing Systems 113
Chapter 7. Various Applications 131
Part 3. Simulation 181
Chapter 8. Generator Programs 183
Chapter 9. Principles of Simulation 203
Chapter 10. Simulation of Inventory Management 233
Chapter 11. Simulation of a Queueing Process 245
Chapter 12. Optimization and Simulation 257
References 285
Index 287
