Goddard / Sneddon / Ulam Mathematical Techniques of Operational Research

1. Auflage 2014
ISBN: 978-1-4831-8060-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 38, 240 Seiten, Web PDF

Reihe: International Series in Pure and Applied Mathematics

Mathematical Techniques of Operational Research is a seven-chapter text that covers the principles and applications of various mathematical tools and models to for operational research. Chapter I provides the basic mathematical ideas used in later chapters. Chapters II and III deal with linear programming, including the special cases of transportation and assignment, as well as their applications such as the Trim Problem. Chapters IV and V discuss the theory of queues and describe the general stationary properties of the single-channel queue, and of simple queues in series and in parallel. These chapters also examine some transient properties of queues. Chapter VI focuses on machine interference, which is an aspect of queueing theory, while Chapter VII deals with the important and mathematically subject of Stock Control or Inventory Theory. This book is intended primarily to graduate mathematicians, business manages, and industrial leaders.

Autoren/Hrsg.

Goddard, L. S.

Sneddon, I. N.

Ulam, S.

Stark, M.

Inhaltsverzeichnis

1;Front Cover;1
2;Mathematical Techniques of Operational Research;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;10
6;CHAPTER I. MATHEMATICAL INTRODUCTION;12
6.1;ALGEBRA;12
6.1.1;1. Matrices and vectors;12
6.1.2;2. Systems of linear equations;14
6.1.3;3. Introduction;16
6.1.4;4. The Stieltjes' integral;18
6.1.5;5. The Dirac delta function;18
6.1.6;6. Bessel functions;19
6.1.7;8. Integral equations;21
6.1.8;9. The Laplace transform;22
6.2;PROBABILITY;22
6.2.1;10. Introduction;22
6.2.2;11. Conditional probability;24
6.2.3;12. Random variables and probability distributions;26
6.2.4;13. Probability generating functions;29
6.2.5;14. The addition of random variables: convolutions;30
6.2.6;15. The Laplace transform of a probability distribution;34
6.2.7;16. The Poisson process;36
6.2.8;17. Some problems of waiting time;38
6.2.9;18. The solution of a type of partial differential equation;41
6.2.10;REFERENCES;43
7;CHAPTER II. LINEAR PROGRAMMING;44
7.1;1. Introduction;44
7.2;2. The problem of Linear Programming;46
7.3;3. The Simplex Method;47
7.4;4. Remarks on the Simplex Method;53
7.5;5. Example of the use of the Simplex Method;56
7.6;6. The Caterer Problem;60
7.7;7. The Trim Problem;65
7.8;REFERENCES;73
8;CHAPTER .II. TRANSPORTATION AND ASSIGNMENT;75
8.1;1. Introduction;75
8.2;THE PROBLEM OF TRANSPORTATION;76
8.2.1;2. The initial solution;76
8.2.2;3. Testing a solution;78
8.2.3;4. Improvement of a solution;80
8.2.4;5. Degenerate solutions;81
8.2.5;6. Alternative optimal solutions;83
8.2.6;7. Basic and derived solutions;85
8.3;THE PROBLEM OF ASSIGNMENT;86
8.3.1;8. The theorem of König;86
8.3.2;9. Solutions to the problem of assignment;88
8.3.3;10. The algorithm of Munkres;90
8.3.4;11. The complete solution in a particular case;94
8.3.5;12. General remarks;96
8.4;REFERENCES;98
9;CHAPTER IV. QUEUEING THEORY: THE SINGLE CHANNEL QUEUE;99
9.1;1. Introduction;99
9.2;2. General concepts and definitions;100
9.3;3. Types of distributions and a notation for queues;102
9.4;4. The problems of queueing theory;104
9.5;5. The queue M/G/1: formulae for E(n) and E(w);106
9.6;6. The queue M/M/1: differential-difference equations for the queue length;109
9.7;7. Use of the Laplace transform and probability generating function;113
9.8;8. Use of integral equations;118
9.9;9. Analysis of transient behaviour;124
9.10;10. Queue disciplines: random selection, bulk service and priority;132
9.11;REFERENCES;148
10;CHAPTER V. QUEUEING THEORY: CHANNELS IN SERIES OR PARALLEL;152
10.1;1. Introduction;152
10.2;2. Channels in parallel with random input;153
10.3;3. Parallel channels with general input: the queue G/M/c;161
10.4;4. Channels in series;165
10.5;5. Channels in series: various restricted cases;169
10.6;REFERENCES;176
11;CHAPTER VI. MACHINE INTERFERENCE;177
11.1;1. Introduction;177
11.2;2. The case of one operator (r = 1);177
11.3;3. Determination of the average length (xm) of a repair period;180
11.4;4. System characteristics;184
11.5;5. The case of r operators (r > 1);189
11.6;6. System characteristics in the case of several operators;192
11.7;7. The case of an arbitrary distribution of repair periods;193
11.8;8. General remarks;195
11.9;REFERENCES;196
12;CHAPTER VII. PROBLEMS OF STOCK CONTROL;198
12.1;1. Introduction;198
12.2;2. Some elementary problems of optimization;199
12.3;3. Operating characteristics of a simple stockpile;206
12.4;4. The problem of Hammersley;208
12.5;5. The problem of Finch;212
12.6;6. Types of replenishment policies;220
12.7;7. A variant of the problem of Hammersley;224
12.8;8. Problems involving a lead time;229
12.9;9. Problem 1;230
12.10;10. Problem 2;233
12.11;REFERENCES;238
13;INDEX;239