Operations Research--Methods and Problems

By Maurice Sasieni; Arthur Yaspan | Go to book overview

CHAPTER TWO
Probability

Some familiarity with the basic notions of probability is essential for an understanding of the remaining chapters of this book. The information on which decisions are to be based is usually in the form of numbers; and these numbers, as well as the conclusions derived therefrom, are usually doubtful to a greater or lesser extent. The theory of probability furnishes a means for expressing the degree of doubt in mathematical terms.

A rigorous development of probability theory involves logical and mathematical difficulties of high order, and will not be attempted here. Instead, we shall present working definitions of such concepts as "random variable" and "probability distribution," and illustrate their application with examples. The chapter is intended to serve as a brief review for those readers who have an understanding of probability theory, and as a guidepost to further study of the subject for those who come to this book with less preparation. Several good references are given at the end of the chapter.


SIMPLE EVENTS

Suppose that within a particular limited environment the possible states of nature are E1, E2, ..., En, and that the environment periodically changes from one state to another in some random fashion. For example, the environment might be a coin lying on the ground with an

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Operations Research--Methods and Problems
Table of contents

Table of contents

  • Title Page ii
  • Preface v
  • Acknowledgments vii
  • Contents ix
  • Chapter One - Introduction 1
  • Chapter Two - Probability 5
  • References 39
  • Chapter Three - Sampling 40
  • References 69
  • Chapter Four - Inventory 70
  • Chapter Five - Replacement 102
  • References 124
  • Chapter Six - Waiting Lines 125
  • References 154
  • Chapter Seven - Competitive Strategies 155
  • References 182
  • Chapter Eight - Allocation 183
  • References 249
  • Chapter Nine - Sequencing 250
  • References 269
  • Chapter Ten - Dynamic Programming 270
  • References 293
  • Appendix One - Finite Differences 294
  • Appendix Two - Differentiation of Integrals 304
  • Index 312
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