Completely revised and updated, this new edition of a bestselling handbook presents analytical results and formulas needed in the science applications of operations research and management. It provides quick calculations and insight into system performance. The material is organized by topic and presented in aconcise format that allows readers ready access to a wide range of results ina single volume. The second edition adds a wealth of information including new chapters on reliability theory results, order statistics, heuristic search methods, and probability relationships. It also offers invaluable information on production systems modeling and priority queuing. INDICE: Introduction Means and Variances Mean (Expectation) and Varianceof a Random Variable Covariance and Correlation Coefficient Mean and Varianceof the Sum of Random Variables Mean and Variance of the Product of Two RandomVariables Mean and Variance of the Quotient of Two Random Variables Conditional Mean and Variance for Jointly Distributed Random Variables Conditional Meanof a Constrained Random Variable Mean and Variance of the Sum of a Random Number of Random Variables Mean of a Function of a Random Variable Approximationsfor 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 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 Hyper-Exponential and Hypo-Exponential Distributions Probability Relationships 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 Queueing Theory Results Notation for Queue Types Definitions of Queueing System Variables Little's Law and General Queueing System Relationships Extension of Little's Law Formulas for Average Queue Length, Lq Formulas for Average Time in Queue, Wq References for the Formulas for Average Queue Length and Time in Queue Pollaczek--Khintchine Formula for Average Time in Queue, Wq Additional Formulas for Average Time in Queue, Wq Heavy Traffi c Approximation for Distribution of Time in Queue Queue Departure Process Distribution Results for the Number of Customers in M/M/1 Queue Distribution Results for Time in M/M/1 Queue Other Formulas in Queueing Theory Production Systems Modeling Definitions and Notation for Workstations Basic Relationships between Workstation Parameters Distribution of the Time to Produce a 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 Inventoryin a Production/Distribution System Note on Cumulative Plots Distance Formulas for Logistics Analysis Distance Norms "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 Average Rectangular Grid Distance between Two Random Points in a Circle Great Circle Distance Traffic Flow and Delay Traffic Flow Parameters Traffic Speeds Delay to Vehicle Merging with Traffi c Stream Critical Flow on Minor Road Delay to Traffi c Queue on Minor Road Waiting to Merge Delay to Vehicle at Traffi c Signal Linear Programming Formulations General Formulation Terminology Example of a Feasible Region Alternative Formulations Diet Problem Duality Special Cases of Linear Programming Problems Integer Linear Programming Formulations Solution Methods Heuristic Search Methods Overview of Heuristics Local Search Methods Simulated Annealing Tabu Search Genetic Algorithms Other Heuristics Order Statistics General Distribution Order Statistics Uniform Distribution Order Statistics Exponential Distribution Order Statistics Mathematical Functions Gamma Function Incomplete Gamma Function Beta Function Incomplete 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 MaclaurinSeries L'Hopital's Rule Lagrange Multipliers Differentiation under the Integral Sign (Leibnitz's Rule) Change of a 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 Derivatives of Matrices Combinatorics Summations Finite Sums Infinite Sums InterestFormulas References Index
- ISBN: 978-1-4200-5240-4
- Editorial: CRC PRESS, INC.
- Encuadernacion: Rústica
- Páginas: 256
- Fecha Publicación: 18/12/2009
- Nº Volúmenes: 1
- Idioma: Inglés