Operations Research and Optimization

  1. Simulation Modeling
    1. Principles of Simulation
      1. Simulation Definition
        1. When to Use Simulation
          1. System Complexity
            1. Analytical Intractability
              1. Experimentation Requirements
              2. Advantages of Simulation
                1. Flexibility
                  1. Detailed Analysis
                    1. Risk-Free Experimentation
                    2. Limitations of Simulation
                      1. Time and Cost
                        1. Model Complexity
                          1. Statistical Nature
                          2. Types of Simulation Models
                            1. Static versus Dynamic
                              1. Deterministic versus Stochastic
                                1. Discrete versus Continuous
                              2. Discrete-Event Simulation
                                1. System Concepts
                                  1. Entities
                                    1. Attributes
                                      1. Activities
                                        1. Events
                                          1. State Variables
                                          2. Simulation Clock
                                            1. Event Scheduling
                                              1. Time Advancement
                                                1. Event List Management
                                                2. Event-Driven Simulation
                                                  1. Event Routines
                                                    1. Event Calendar
                                                      1. Simulation Loop
                                                    2. Random Number Generation
                                                      1. Pseudorandom Numbers
                                                        1. Linear Congruential Generators
                                                          1. Multiplicative Generators
                                                            1. Mixed Generators
                                                            2. Tests for Randomness
                                                              1. Frequency Tests
                                                                1. Runs Tests
                                                                  1. Correlation Tests
                                                                    1. Spectral Tests
                                                                    2. Random Variate Generation
                                                                      1. Inverse Transform Method
                                                                        1. Acceptance-Rejection Method
                                                                          1. Composition Method
                                                                            1. Special Techniques
                                                                            2. Common Distributions
                                                                              1. Uniform Distribution
                                                                                1. Exponential Distribution
                                                                                  1. Normal Distribution
                                                                                    1. Poisson Distribution
                                                                                      1. Empirical Distributions
                                                                                    2. Model Development Process
                                                                                      1. Problem Formulation
                                                                                        1. Objectives Definition
                                                                                          1. System Boundaries
                                                                                            1. Performance Measures
                                                                                            2. Conceptual Modeling
                                                                                              1. System Abstraction
                                                                                                1. Model Assumptions
                                                                                                  1. Input-Output Relationships
                                                                                                  2. Model Implementation
                                                                                                    1. Programming Languages
                                                                                                      1. Simulation Software
                                                                                                        1. Code Development
                                                                                                          1. Debugging
                                                                                                          2. Model Verification
                                                                                                            1. Code Verification
                                                                                                              1. Logic Verification
                                                                                                                1. Animation and Visualization
                                                                                                                2. Model Validation
                                                                                                                  1. Face Validity
                                                                                                                    1. Statistical Validation
                                                                                                                      1. Sensitivity Analysis
                                                                                                                        1. Comparison with Real System
                                                                                                                      2. Output Analysis
                                                                                                                        1. Types of Simulations
                                                                                                                          1. Terminating Simulations
                                                                                                                            1. Steady-State Simulations
                                                                                                                              1. Transient Behavior
                                                                                                                              2. Statistical Analysis
                                                                                                                                1. Point Estimation
                                                                                                                                  1. Confidence Intervals
                                                                                                                                    1. Sample Size Determination
                                                                                                                                    2. Variance Reduction Techniques
                                                                                                                                      1. Common Random Numbers
                                                                                                                                        1. Antithetic Variates
                                                                                                                                          1. Control Variates
                                                                                                                                            1. Importance Sampling
                                                                                                                                            2. Comparison of Systems
                                                                                                                                              1. Paired-t Confidence Intervals
                                                                                                                                                1. Independent Sampling
                                                                                                                                                  1. Ranking and Selection
                                                                                                                                                2. Experimental Design
                                                                                                                                                  1. Single-Factor Experiments
                                                                                                                                                    1. Factor Level Selection
                                                                                                                                                      1. Response Analysis
                                                                                                                                                      2. Multi-Factor Experiments
                                                                                                                                                        1. Factorial Designs
                                                                                                                                                          1. Fractional Factorial Designs
                                                                                                                                                            1. Response Surface Methodology
                                                                                                                                                            2. Optimization via Simulation
                                                                                                                                                              1. Response Surface Methods
                                                                                                                                                                1. Gradient-Based Methods
                                                                                                                                                                  1. Metaheuristic Methods