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'HÃ´pital'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