Industrial Engineering & Operations Research
  • Algebra
    • Cheatsheet
    • Logarithms
  • Linear Algebra
    • Cheatsheet
    • Vectors
    • Real Coordinate Spaces
    • Vector Operations
    • Norm
    • Unit Vector
    • Dot Product
    • Inner Product
    • Cauchy–Schwarz Inequality
    • Triangle Inequality
    • Orthogonality
    • Angles Between Vectors
    • Cartesian Coordinates
    • Polar Coordinates
    • Parametric Line
    • Planes
    • Point–Plane Distance
    • Plane–Plane Distance
    • Hyperplane
    • Cross Product
    • Cross Product Magnitude
    • Dot vs Cross Product
    • Vector Space
    • Linear Combination
    • Span
    • Linear Independence
    • Subspace
    • Basis
    • Dimension
    • Coordinate Vector
    • Change of Basis
    • Gram–Schmidt
    • Matrices
    • Matrix–Vector Product
    • Matrix Multiplication
    • Transpose
    • Trace
    • Identity Matrix
    • Zero Matrix
    • Diagonal Matrix
    • Triangular Matrix
    • Symmetric Matrix
    • Orthogonal Matrix
    • Linear Equations
    • Augmented Matrix
    • Row Echelon Form
    • RREF
    • Gaussian Elimination
    • Gauss–Jordan Elimination
    • Substitution
    • Addition / Subtraction
    • Linear System Solutions
    • Linear System Special Cases
    • Homogeneous System
    • Linear Transformation
    • Matrix Representation
    • Domain
    • Codomain
    • Surjective, Injective, Bijective
    • Image
    • Image of Subset
    • Preimage
    • Kernel
    • Column Space
    • Null Space
    • Rank
    • Rank–Nullity Theorem
    • Projection
    • Composition of Linear Transformations
    • Transformation Sum
    • Transformation Scalar Multiplication
    • Rotation Matrix
    • Reflection Matrix
    • Scaling Matrix
    • Shear Matrix
    • Minor
    • Principal Minor
    • Leading Principal Minor
    • Determinant
    • Cramer's Rule
    • Adjugate
    • Unimodularity
    • Matrix Inverse
    • LU Decomposition
    • QR Decomposition
    • Cholesky Decomposition
    • SVD
    • Pseudoinverse
    • Eigenvectors & Eigenvalues
    • Characteristic Polynomial
    • Diagonalization
    • Spectral Theorem
    • Jordan Canonical Form
    • Quadratic Form
  • Real Analysis
    • Sets
  • Calculus
    • Calculus I
      • Cheatsheet
      • Limits
      • Derivatives
      • Higher-Order Derivatives
      • Power Rule
      • Product Rule
      • Quotient Rule
      • Chain Rule
      • Implicit Differentiation
      • Derivatives of Inverse Functions
      • Inverse Functions
      • L'Hôpital's Rule
      • Mean Value Theorem
      • Extreme Value Theorem
      • Critical Points
      • Derivative Test
      • Arc Length
      • Series
      • Taylor Series
    • Calculus II
      • Cheatsheet
      • Chain Rule
      • Double Integrals
      • Gradient
      • Hessian Matrix
      • Jacobian
      • Semi-Definiteness
    • Calculus III
      • Vector-Valued Functions
    • Integration
      • Rules
      • Leibniz's Rule
    • Differential Equations
  • Geometry
    • Cheatsheet
  • Probability Theory
    • Cheatsheet
    • Sample Space
    • Sets
    • Axioms
    • De Morgan's Laws
    • Sequences
    • Series
    • Countability
    • Bonferroni Inequality
    • Conditional Probability
    • Multiplication Rule
    • Total Probability Theorem
    • Bayes' Rule
    • Independence
    • Counting Principle
    • Expected Value
    • Linearity of Expectations
    • Joint, Marginal & Conditional Probability
    • Mixture Distributions
    • Law of Total Expectation
    • Law of Total Variance
    • I.I.D.
    • Moment Generating Function
    • Markov's Inequality
    • Chebyshev's Inequality
  • Statistics
    • Cheatsheet
    • Descriptive Statistics
      • Mean
      • Median
      • Mode
      • Range
      • Variance
      • Standard Deviation
      • Interquartile Range
    • Probability Distributions
      • Bernoulli
      • Gaussian
      • Student's t
      • Binomial
      • Poisson
      • Exponential
      • Differentiating the Normal Distribution
    • Functions
      • PDF
      • PMF
      • CDF
      • PPF
      • SF
      • Standard Normal Loss Function
      • Likelihood
    • Error Metrics
      • MD
      • MAE
      • MSE
      • RMSE
      • MPE
      • MAPE
      • R²
      • MSLE
      • Cross-Entropy Loss
    • Hypothesis Testing
      • Null Hypothesis
      • Alternative Hypothesis
      • Type I Error
      • Type II Error
      • One-Sample Z-Test for Mean
      • One-Sample Two-Tail Z-Test for Mean
      • One-Sample Z-Test for Proportion
      • Two-Sample Z-Test for Mean
      • Two-Sample Z-Test for Proportion
      • One-Sample t-Test
      • One-Sample Two-Tail t-Test for Mean
      • Independent t-Test
      • Paired t-Test
      • Chi-Square Goodness of Fit
      • Chi-Square Independence
      • One-Way ANOVA
      • Two-Way ANOVA
      • A/B Testing
    • Regression Analysis
      • Simple Linear Regression
      • Multiple Linear Regression
      • Logistic Regression
      • Ridge
      • Lasso
      • p-value
      • F-statistic
      • Confidence Intervals
    • Correlation
      • Pearson
      • Spearman Rank
      • Covariance & Correlation
    • Non-Parametric Statistics
      • Mann–Whitney U
      • Wilcoxon Signed-Rank
      • Kolmogorov–Smirnov
      • Kruskal–Wallis
    • Maximum Likelihood Estimation
    • Generalized Linear Models
    • Cross Validation
    • Markov Chains
    • Monte Carlo Simulation
    • Design of Experiments
      • Factorial Designs
      • Response Surface Methodology
      • Analysis of Interaction Effects
    • Principal Component Analysis
    • AIC & BIC
    • Bootstrap & Resampling
    • Types of Statistics
  • Time Series
    • Moving Averages
      • Overview
      • Naive
      • Cumulative
      • Simple Moving Average
      • Weighted Moving Average
    • Decomposition
      • Classical
      • STL
    • Frequency
      • Fourier
      • Periodogram
    • Exponential Smoothing (ETS)
      • Summary
      • A-N-N
      • A-N-A
      • A-N-M
      • A-A-N
      • A-A-A
      • A-A-M
      • A-Ad-N
      • A-Ad-A
      • A-Ad-M
      • A-M-N
      • A-M-A
      • A-M-M
      • A-Md-N
      • A-Md-A
      • A-Md-M
      • M-N-N
      • M-N-A
      • M-N-M
      • M-A-N
      • M-A-A
      • M-A-M
      • M-Ad-N
      • M-Ad-A
      • M-Ad-M
      • M-M-N
      • M-M-A
      • M-M-M
      • M-Md-N
      • M-Md-A
      • M-Md-M
    • ARIMA Family
      • Summary
      • AR
      • MA
      • ARMA
      • ARIMA
      • SARIMA
      • SARIMAX
      • VAR
      • VMA
      • VARMA
      • VARIMA
      • VARIMAX
  • System Dynamics
    • System Dynamics
    • Stocks Flows
    • Causal Loop Diagrams
    • Feedback Loops
    • Delays
    • Second-Order
    • Smoothing
    • Stock Management
    • Bullwhip SD
    • Beer Game
    • Bass Diffusion
    • Logistic Growth
    • SIR SEIR
    • Lotka-Volterra
    • Phase Plane
    • Numerical Integration
    • Validation
  • Operations Research
    • Optimization
      • Cheatsheet
      • MILP Idioms
      • Standard Form
      • Linear Programming
      • Simplex Method
      • Simplex Cheatsheet
      • Input / Output
      • Integer Programming
      • Branch and Bound
      • Mixed Integer Programming
      • Non-Linear Programming
      • Convexity
      • Convex Analysis
      • Gradient Descent
      • Newton's Method
      • Heuristic Algorithms
      • Duality
      • Multi-Commodity Network Flow
      • Sensitivity Analysis
      • Network Flow
      • Ford–Fulkerson
      • Edmonds–Karp
      • Transportation Problem
      • Assignment Problem
      • Hungarian Algorithm
      • Transshipment Problem
      • Min-Cost Flow Algorithms
      • Network Simplex
      • Min Spanning Tree
      • Floyd-Warshall
      • TSP
      • TSP 2opt
      • Christofides
      • VRP
      • VRP Time Windows
      • Clarke-Wright
      • Daganzo Continuous
      • Facility Location
      • UFLP
      • CFLP
      • p-Median
      • p-Center
      • Set Covering
      • Max Covering
      • Center of Gravity
      • Stochastic Programming
      • Two-stage Recourse
      • Scenario Trees
      • Chance Constraints
      • Sample Average Approximation
      • EVPI vs VSS
      • Lagrange Relaxation
      • Lagrangian
      • KKT Conditions
      • Dynamic Programming
      • Bellman Equation
      • Backward Induction
      • Forward Induction
      • Stochastic DP
      • Value Iteration
      • Policy Iteration
      • Regression
      • Support Vector Machine
    • Queuing Theory
      • M/M/1
      • M/M/c
      • Little's Law
      • Kingman VUT
      • Sakasegawa
      • Linking Equation
      • Erlang B
      • Erlang C
      • MMc Abandonment
      • Square-Root Staffing
    • Decision Analysis
      • Decision Analysis
      • Decision Trees
      • EMV
      • EVPI
      • EVSI
      • Decision Criteria
      • Utility Theory
    • Control Charts
      • Cheatsheet
      • C-Chart
      • P-Chart
      • U-Chart
      • NP-Chart
      • X-Chart
    • Process Capability
      • Cheatsheet
      • Cp
      • Cpk
      • Cpm
      • Pp
      • Ppk
    • Causes of Variation
      • Common
      • Special
    • Acceptance Sampling
    • Critical Path Method (CPM)
  • Supply Chain
    • Planning
      • Aggregate Planning
      • MPS
      • MRP
      • DRP
      • RCCP
      • Silver-Meal
      • Least Unit Cost
      • Part-Period Balancing
    • Manufacturing
      • Factory Physics
      • Best Worst PWC
      • Critical WIP
      • CONWIP
      • Kanban Sizing
      • Takt Time
      • Line Balancing
      • Theory of Constraints
      • Learning Curves
      • Heijunka
    • Bullwhip Effect
    • Classification
      • ABC
      • XYZ
      • ABC × XYZ
      • FSN
      • VED
    • Metrics
      • Inventory Turnover
      • Days of Supply
      • Order Cycle Time
      • Perfect Order Rate
      • Stockout Rate
      • GMROI
    • Service Levels
      • Cycle Service Level
      • Fill Rate
      • Ready Rate
    • Stocks
      • Cycle Stock
      • Lead Time
      • Safety Stock
      • Anticipation Stock
      • Decoupling Stock
      • Pipeline Stock
    • Newsvendor
      • Overview
      • Discrete
      • Expected Profit
      • Shortage Penalty
      • Multiplicative
      • Multi-Product
      • Capacity-Constrained
    • Multi-Echelon
      • Multi-Echelon
      • Clark-Scarf
      • Graves-Willems
      • Stochastic-service
      • METRIC
      • VARI-METRIC
    • Risk Pooling
      • Risk Pooling
      • Square-Root Law
      • Correlated Pooling
      • Location Pooling
      • Product Pooling
      • Lead-time Pooling
    • EOQ
      • EOQ
      • EPQ
      • Backorders
      • Lost Sales
      • Quantity Discounts
      • Capacity-Constrained
      • Joint Replenishment
      • Multi-Echelon
      • Perishables
      • Wagner–Whitin
    • Policies
      • Overview
      • Base Stock
      • (s, S)
      • (Q, r)
      • (nQ, r)
      • (R, S)
      • (R, s, S)
      • (R, nQ, s)
  • Graph Theory
    • Overview
  • Machine Learning
    • Bias–Variance Tradeoff
    • Classification
      • Support Vector Machine
      • XGBoost
    • Graphs
      • Graph Neural Network
  • Economics
    • Supply & Demand
    • Utility
    • Production Functions
    • Externality
    • Network Effect
  • Algorithms
    • Dijkstra
  • Organisations
    • Actor Network
    • Bounded Rationality
    • Bureaucracy
    • Cybernetic
    • Embeddedness
    • Functional Theory of Stratification
    • Institutional Theory
    • Network Theories
    • Resource Dependency
    • Scientific Management
    • Transaction Costs
    • Organizational Ecology
  • Certifications
    • CSCP
    • Supply Chain Analytics
    • ACCA F3 — Financial Accounting
      • Cheatsheet
      • Overview
      • Stakeholders
      • Balance Sheet
      • Income Statement
      • Cash Flow Statement
  • Appendix
    • Scheduling Code
  • White Paper
  • References
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