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BL
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| Record Number
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755108
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| Doc. No
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b575070
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| Main Entry
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L S Goddard
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| Title & Author
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Mathematical Techniques of Operational Research : : International Series of Monographs on Pure and Applied Mathematics.\ L S Goddard
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| Publication Statement
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London : Elsevier Science, 2015
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| Series Statement
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International series in pure and applied mathematics.
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| Page. NO
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(241 pages).
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| ISBN
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1483180603
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: 9781483180601
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| Notes
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7. A variant of the problem of Hammersley.
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| Contents
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Front Cover; Mathematical Techniques of Operational Research; Copyright Page; Table of Contents; PREFACE; CHAPTER I. MATHEMATICAL INTRODUCTION; ALGEBRA; 1. Matrices and vectors; 2. Systems of linear equations; 3. Introduction; 4. The Stieltjes' integral; 5. The Dirac delta function; 6. Bessel functions; 8. Integral equations; 9. The Laplace transform; PROBABILITY; 10. Introduction; 11. Conditional probability; 12. Random variables and probability distributions; 13. Probability generating functions; 14. The addition of random variables: convolutions. 15. The Laplace transform of a probability distribution16. The Poisson process; 17. Some problems of waiting time; 18. The solution of a type of partial differential equation; REFERENCES; CHAPTER II. LINEAR PROGRAMMING; 1. Introduction; 2. The problem of Linear Programming; 3. The Simplex Method; 4. Remarks on the Simplex Method; 5. Example of the use of the Simplex Method; 6. The Caterer Problem; 7. The Trim Problem; REFERENCES; CHAPTER < U+004c> II. TRANSPORTATION AND ASSIGNMENT; 1. Introduction; THE PROBLEM OF TRANSPORTATION; 2. The initial solution; 3. Testing a solution. 4. Improvement of a solution5. Degenerate solutions; 6. Alternative optimal solutions; 7. Basic and derived solutions; THE PROBLEM OF ASSIGNMENT; 8. The theorem of König; 9. Solutions to the problem of assignment; 10. The algorithm of Munkres; 11. The complete solution in a particular case; 12. General remarks; REFERENCES; CHAPTER IV. QUEUEING THEORY: THE SINGLE CHANNEL QUEUE; 1. Introduction; 2. General concepts and definitions; 3. Types of distributions and a notation for queues; 4. The problems of queueing theory; 5. The queue M/G/1: formulae for E(n) and E(w). 6. The queue M/M/1: differential-difference equations for the queue length7. Use of the Laplace transform and probability generating function; 8. Use of integral equations; 9. Analysis of transient behaviour; 10. Queue disciplines: random selection, bulk service and priority; REFERENCES; CHAPTER V. QUEUEING THEORY: CHANNELS IN SERIES OR PARALLEL; 1. Introduction; 2. Channels in parallel with random input; 3. Parallel channels with general input: the queue G/M/c; 4. Channels in series; 5. Channels in series: various restricted cases; REFERENCES; CHAPTER VI. MACHINE INTERFERENCE. 1. Introduction2. The case of one operator (r = 1); 3. Determination of the average length (xm) of a repair period; 4. System characteristics; 5. The case of r operators (r> 1); 6. System characteristics in the case of several operators; 7. The case of an arbitrary distribution of repair periods; 8. General remarks; REFERENCES; CHAPTER VII. PROBLEMS OF STOCK CONTROL; 1. Introduction; 2. Some elementary problems of optimization; 3. Operating characteristics of a simple stockpile; 4. The problem of Hammersley; 5. The problem of Finch; 6. Types of replenishment policies.
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| Abstract
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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 parall.
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| Subject
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Mathematical models.
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| Subject
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Operations research.
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| LC Classification
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QA37.L746 2015
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| Added Entry
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I N Sneddon
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L S Goddard
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M Stark
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S Ulam
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