Sequencing Theory

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The intent of these notes is to provide an appreciation of sequencing theory, and to develop an awareness of the combinatorial aspects of sequencing problems. An under­ standing of the ideas and concepts presented in these notes will provide the necessary background to enable further study in this rapidly growing subject. These notes have been used as a part of one-semester C0urses in Operations Research for both senior and first-year graduate students. Following the introductory chapter, several classes of scheduling models are discussed in Chapter 2. Chapter 3 is devoted to discussing the characteristics of several types of criteria that have been proposed in the literature. Because of the importance of the combinatorial properties in the analysis of scheduling models, various combinatorial aspects are treated in Chapter 4. The primary objective of such a treatment is to provide the reader with an insight into the nature of the problem. Due to the tremendous number of sequences involved, and the fact that many sequences have the same schedule time, statistical sampling has elicited a great deal of theoretical studies. Two such studies, one of which has evolved from my research, are reported in Chapter 5. Many references to basic sources are cited at the end of each chapter to provide a guide for further readings. I am indebted to Professor Santa Arora of the University of Minnesota who intro­ duced me to the subject during my graduate career.