Optimal Stochastic Scheduling

This book provides a comprehensive and unified coverage of studies in this area. The objective is two-fold: (i) to summarize the elementary models and results in stochastic scheduling, so as to offer an entry-level reading material for students to learn and understand the fundamentals of this area; and (ii) to include in details the latest developments and research topics on stochastic scheduling, so as to provide a useful reference for researchers and practitioners who are performing research and development work in this area. Research interests have been increasingly devoted to stochastic scheduling in recent years, which incorporates the approaches of probability and stochastic processes into scheduling problems to account for uncertainties from different sources. Many interesting and important results on stochastic scheduling problems have been developed, with the aid of probability theory.§Optimal Stochastic Scheduling is organized into two parts: Chapters 1-4 cover more fundamental models and results, whereas Chapters 5-10 elaborates on more advanced topics. Chapter 1, provides the relevant basic theory of probability, and then introduces the basic concepts and notation of stochastic scheduling. In Chapters 2 and 3, the authors review well-established models and scheduling policies, under regular and irregular performance measures, respectively. Chapter 4 describes models with stochastic machine breakdowns. Chapters 5 and 6 introduce, respectively, the optimal stopping problems and the multi-armed bandit processes, which are necessary for studies of more advanced subjects. Chapter 7 is focused on dynamic policies. Chapter 8 describes stochastic scheduling with incomplete information, where the probability distributions of random variables contain also unknown parameters, which can however be estimated progressively according to updated information. Chapter 9 is devoted to the situation where the processing time of a job depends on the time when it is started. Lastly, in Chapter 10 the authors look at several recent models beyond those surveyed in the previous chapters.§