Operations Research Calculations Handbook

Series:
Operations Research Series
Published:
June 27, 2001 by CRC Press - 216 Pages
Author(s):
Dennis Blumenfeld, General Motors, Warren, Michigan, USA

Purchasing Options

Hardback
Not available
in your region
ISBN 9780849321276
Cat# 2127
 

Features

  • Provides one-stop resource for more than 300 important results and formulas needed in operations research applications
  • Compiles common results in probability theory, stochastic processes, calculus, queueing and production systems, and a concise listing of the main linear programming formulations
  • Includes a summary of standard results in inventory control
  • Gives references for derivations and additional details on every key result

    • Summary

    The field of Operations Research (OR) covers a wide range of mathematical topics. Because it is so broad, results and formulas relevant to the field are widely scattered in different texts and journals and can be hard to find. As the field continues to grow, OR practitioners and students need a convenient, one-stop source for the results relevant to their work.

    The Operations Research Calculations Handbook meets that need. It contains more than 300 results in a single, concise volume. Organized by topic and listed in a convenient summary format, it allows readers to have frequently used results at their fingertips. Although based on the author's experience in the manufacturing industry, many of the results are basic to system modeling. They carry over easily to applications in other areas of operations research and management science.

    While modern software packages are useful for obtaining numerical results, formulas continue to play a significant role in systems modeling. They allow one to draw general conclusions about system behavior, reveal the underlying system model, and help provide an understanding of system performance. Whether you are a student, professor, or seasoned professional, the Operations Research Calculations Handbook offers not only a handy reference that will save time, but also a tool that will help build the intuitive understanding you need to apply systems models with confidence.

    Table of Contents

    INTRODUCTION
    MEANS AND VARIANCES
    Mean (Expectation) and Variance of a Random Variable
    Covariance and Correlation Coefficient
    Mean and Variance for Sum of Random Variables
    Mean and Variance of a Product of Two Random Variables
    Mean and Variance of a Quotient of Two Random Variables
    Conditional Mean and Variance for Jointly Distributed Random Variables
    Conditional Mean of a Random Variable in a Limited Range
    Mean and Variance for Sum of a Random Number of Random Variables
    Mean of a Function of a Random Variable
    Approximations for the Mean and Variance of a Function of a Random Variable
    Mean and Variance of the Maximum of Exponentially Distributed Random Variables
    Mean and Variance of the Maximum of Normally Distributed Random Variables
    Moments for the Greatest of a Finite Set of Random Variables
    Moment Generating Functions

    DISCRETE PROBABILITY DISTRIBUTIONS
    Bernoulli Distribution
    Binomial Distribution
    Geometric Distribution
    Negative Binomial Distribution
    Poisson Distribution
    Hypergeometric Distribution
    Multinomial Distribution

    CONTINUOUS PROBABILITY DISTRIBUTIONS
    Uniform Distribution
    Exponential Distribution
    Erlang Distribution
    Gamma Distribution
    Beta Distribution
    Normal Distribution
    Lognormal Distribution
    Weibull Distribution
    Logistic Distribution
    Gumbel (Extreme Value) Distribution
    Pareto Distribution
    Triangular Distribution

    PROBABILITY FORMULAS
    Distribution of the Sum of Independent Random Variables
    Distribution of the Maximum and Minimum of Random Variables
    Change of Variable in a Probability Distribution
    Conditional Probability Distribution for a Constrained Random variable
    Combination of Poisson and Gamma Distributions
    Bayes' Formula
    Central Limit Theorem
    Probability Generating Function (z-Transform)
    Moment Generating Function
    Characteristic Function
    Laplace Transform

    STOCHASTIC PROCESSES
    Poisson Process and Exponential Distribution
    Renewal Process Results
    Markov Chain Results

    QUEUING THEORY RESULTS
    Notation for Queue Types
    Definitions of Queuing System Variables
    Little's Law and General Queueing System Relationships
    Extensions of Little's Law
    Formulas for Average Queue Length
    Formulas for Average Time in Queue
    References for Formulas for Average Queue Length and Time in Queue
    Pollaczek-Khintchine Formula for Average Time in Queue
    Additional Formulas for Average Time in Queue
    Other Formulas in Queueing Theory

    PRODUCTION SYSTEMS MODELING
    Definitions and Notation for Workstations
    Basic Relationship Between Workstation Parameters
    Distribution of the Time to Produce Fixed Lot Size at a Workstation
    Throughput of a Serial Production Line with Failures
    Throughput of a Two-Station Serial Production Line with Variable Processing Times
    Throughput of an N-Station Serial Production Line with Variable Processing Times

    INVENTORY CONTROL
    Economic Order Quantity
    Economic Production Quantity
    "Newsboy Problem:" Optimal Inventory to Meet Uncertain Demand in a Single Period
    Inventory Replenishment Policies
    (s,Q) Policy: Estimates of Reorder Point (s) and Order Quantity (Q)
    (s,S) Policy: Estimates of Reorder Point (s) and Order-Up-To Level (S)
    (T,S) Policy: Estimates of Review Period (T) and Order-Up-To Level (S)
    (T,s,S) Policy: Estimates of Review Period (T), Reorder Point (s), and Order-Up-To Level (S)
    Summary of Results for Inventory Policies
    Inventory in a Production/Distribution system
    A Note of Cumulative Plots

    DISTANCE FORMULAS FOR LOGISTICS ANALYSIS
    "Traveling Salesman Problem" Tour Distance: Shortest Path Through a Set of Points in a Region
    Distribution of Distance between Two Random Points in a Circle
    Great Circle Distance

    LINEAR PROGRAMMING FORMULATIONS
    General Formulation
    Terminology
    Example of Feasible Region
    Alternative Formulations
    Diet Problem
    Duality
    Special Cases of Linear Programming Problems
    Integer Linear Programming Formulations
    Solution Methods

    MATHEMATICAL FUNCTIONS
    Gamma Function
    Beta Function
    Unit Impulse Function
    Modified Bessel Functions
    Stirling's Formula

    CALCULUS RESULTS
    Basic Rules for Differentiation
    Integration by Parts
    Fundamental Theorem of Calculus
    Taylor Series
    Maclaurin Series
    L'Hôpital's Rule
    Lagrange Multipliers
    Differentiation Under the Integral Sign
    Change of Variable in an Integral
    Change of Variables in a Double Integral
    Changing the Order of Integration in a Double Integral
    Changing the Order of Summation in a Double Sum
    Numerical Integration

    MATRICES
    Rules for Matrix Calculations
    Inverses of Matrices
    Series of Matrices
    COMBINATORICS
    SUMMATIONS
    Finite Sums
    Infinite Sums
    INTEREST FORMULAS
    REFERENCES

    Editorial Reviews

    "The layout is good and the writing concise … . … I can recommend this book to all those who are looking for a one-stop, handy formulae collection."
    - Journal of the Operational Research Society, Vol. 55, No. 2, 2004


    "[A] useful resource book … ."
    - Zentralblatt MATH, 1042

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