- 1. Optimization Models, Techniques, and Algorithms
- 1.1 Linear Programming (LP)
- 1.1.1 Fundamental Techniques
- 1.1.2 Large-scale Optimization
- 1.1.3 Non-simplex Algorithms for LP
- 1.2 Nonlinear Programming (NLP) and Global Optimization (GO)
- 1.2.1 Foundations
- 1.2.2 Unconstrained NLP Algorithms
- 1.2.3 Classical Constrained Optimization Methods
- 1.2.4 Emerging Global Optimization Techniques
- 1.2.5 Specially Structured Problem Analysis
- 1.3 Network and Graph Optimization
- 1.3.1 Graph Theoretical Problems
- 1.3.2 Graph Characterizations
- 1.3.3 Network Flows
- 1.3.4 NP-hard Network Flow Problems
- 1.3.5 Equilibrium / Game Theory Problems
- 1.4 Combinatorial Optimization/Integer Programming
- 1.4.1 Models
- 1.4.2 Branch-and-Bound
- 1.4.3 Implicit Enumeration and Constraint Programming
- 1.4.4 Cutting Plane/Valid Inequality Theory, Polyhedral Combinatorics
- 1.4.5 Automatic Convexification Techniques
- 1.4.6 Group Theory in Integer Programming
- 1.5 Optimization under Uncertainty
- 1.5.1 Models
- 1.5.2 Two-stage Stochastic Programming
- 1.5.3 Multi-stage Stochastic Programming
- 1.5.4 Scenario Generation and Sampling
- 1.5.5 Stochastic Integer Programming
- 1.5.6 Probabilistically Constrained Programming
- 1.5.7 Robust Optimization
- 1.5.8 Interdiction Problems
- 1.5.9 Extensions of Stochastic Programming
- 1.6 Dynamic Programming
- 1.6.1 Fundamentals
- 1.6.2 Advanced Concepts
- 1.7 Heuristics and Meta-heuristics
- Single Search Based Meta-heuristics
- 1.7.1 Population Based Heuristics
- 1.7.2 Constructive Heuristics
- 1.7.3 Heuristics for Multiple Objectives
- 1.7.4 Meta-heuristics for Stochastic Problems
- 1.7.5 Emerging and Combined Approaches
- 1.8 Optimization Software
- 1.8.1 Decision Support Systems
- 1.8.2 Optimization Solvers
- 2. Stochastic Models
- 2.1 Stochastic Processes
- 2.1.1 Discrete-time Markov Chains (DTMCs)
- 2.1.2 Continuous-time Markov Chains (CTMCs)
- 2.1.3 Point Processes
- 2.1.4 Renewal and Regenerative Processes
- 2.1.5 Markov Renewal and Markov Regenerative Processes
- 2.1.6 Diffusion Processes and Random Walks
- 2.1.7 Branching Processes
- 2.1.8 Martingales
- 2.1.9 Stochastic Orders for Stochastic Processes
- 2.1.10 Large Deviations Principles
- 2.2 Queueing Theory and Queueing Networks
- 2.2.1 General Description of Queueing Models
- 2.2.2 Single-Station Queues CTMC Models
- 2.2.3 Single-Station Queues: Non-CTMC Models
- 2.2.4 Single-Station Queues: Other Models
- 2.2.5 Approximations for Queueing Systems
- 2.2.6 Matrix-Analytic Methods
- 2.2.7 Product-Form Queueing Networks
- 2.2.8 General Queueing Networks
- 2.2.9 Scheduling and Controlling Queueing Networks
- 2.3 Reliability and Maintainability
- 2.3.1 Failure-based Reliability
- 2.3.2 System Reliability
- 2.3.3 State-dependent Systems
- 2.3.4 Reliability Estimation and Testing
- 2.3.5 Reliability Optimization
- 2.3.6 Maintainability
- 2.3.7 Availability
- 2.3.8 Computer and Network Reliability
- 2.3.9 Condition-Based Maintenance and Reliability
- 2.4 Simulation Modeling and Analysis
- 2.4.1 Simulation Model Building
- 2.4.2 Simulation Input Analysis
- 2.4.3 Simulation Output Analysis
- 2.4.4 Verification, Validation, and Testing
- 2.4.5 Variance Reduction Techniques
- 2.4.6 Random Number Generation
- 2.4.7 Monte-Carlo Method
- 2.4.8 Markov-chain Monte-Carlo
- 2.4.9 Simulation Optimization
- 2.4.10 Simulation of Rare Events
- 2.5 Markov Decision Processes (MDPs)
- 2.5.1 Introduction to MDPs
- 2.5.2 Finite-horizon MDPs
- 2.5.3 Total Expected Discounted Reward Criterion
- 2.5.4 Total Expected Reward Criterion
- 2.5.5 Average Reward Criterion
- 2.5.6 Continuous-time MDPs
- 2.5.7 Partially Observable MDPs (POMDPs)
- 2.5.8 Large-Scale MDPs
- 2.5.9 Structured MDP Policies
- 2.5.10 Linear Programming Formulations of MDPs
- 2.6 Stochastic Optimization
- 2.6.1 Stochastic Approximation Methods
- 2.6.2 Optimization of Empirical Processes
- 2.6.3 Stochastic Heuristic Search Methods
- 2.7 Data Mining and Forecasting
- 2.7.1 Data Mining: Foundations and Applications
- 2.7.2 Forecasting Techniques
- 3. Decision and Risk Analysis and Game Theory
- 3.1 Decision Analysis
- 3.1.1 Foundations and Principles of Decision Analysis
- 3.1.2 Psychological Basis of Decision-making under Uncertainty and Risk
- 3.1.3 Normative Structuring of Decision Problems
- 3.1.4 Modeling a Decision Makers Preferences for Outcomes
- 3.1.5 Modeling a Decision Makers Risk Attitude
- 3.1.6 Modeling a Decision Makers Beliefs about Actions and Outcomes
- 3.1.7 Quantifying a Decision Analysis Model
- 3.1.8 Representing and Modeling Decision Problems
- 3.1.9 Solving Decision Analysis Models
- 3.1.10 Communicating, Interpreting, and Understanding Decision Analysis Results
- 3.1.11 Value of Information and Option Values
- 3.1.12 Decision Aids for Improving Individual Decisions
- 3.1.13 Decision-making without Explicit Models of Decision Problems
- 3.1.14 Decision Aids for Improving Group Decisions
- 3.1.15 Collective Choice and Social Utility Theory
- 3.1.16 Aggregating Individual Knowledge, Beliefs, and Preferences
- 3.1.17 Team Theory, Club Theory, Syndicate Theory
- 3.2 Risk Analysis
- 3.2.1 Risk Perception
- 3.2.2 Risk Measurement
- 3.2.3 Risk Assessment
- 3.2.4 Risk Management
- 3.2.5 Risk Communication
- 3.2.6 Risk Analysis Applications
- 3.3 Game Theory
- 3.3.1 Foundations and Principles of Game Theory
- 3.3.2 Solution Concepts and Algorithms for Two-person Zero-sum Games with Perfect Information
- 3.3.3 Computational Game Theory
- 3.3.4 Solution Concepts and Algorithms for Noncooperative Games and Games with Imperfect Information
- 3.3.5 Differential Games and Applications
- 3.3.6 Principal-Agent Games and Applications
- 3.3.7 Spatial Games
- 3.3.8 Cooperative Games and Applications
- 3.3.11 Solution Concepts and Applications for N-person Games
- 3.4 Problems with Large Numbers of Decision Makers
- 3.4.1 Market Games with Many Players
- 3.4.2 Bilateral Matching Games and Applications
- 3.4.3 Self-organizing Systems of interacting decision-makers
- 3.5 Bidding and Auctions
- 3.5.1 Bidding and Auctions
- 3.6 Toward More Realistic Models of Games
- 3.6.1 Toward More Realistic Models of Games
- 4. Applications and History
- 4.1 Manufacturing Applications
- 4.1.1 Manufacturing Facility Design and Layout
- 4.1.2 Product Design and Life Cycle Management
- 4.1.3 Manufacturing Flexibility
- 4.1.4 Production Scheduling
- 4.1.5 Manufacturing Operations Management
- 4.2 Retail and Service Applications
- 4.2.1 Retail Applications
- 4.2.2 Service Facility Design and Layout
- 4.2.3 Sports and Entertainment
- 4.2.4 Telecommunications
- 4.3 Medicine and Health Care
- 4.3.1 Medicine and Health Care
- 4.4 Transportation and Warehousing Systems
- 4.4.1 Freight Transportation
- 4.4.2 Passenger Transportation
- 4.4.3 Warehousing and Cross-Docking
- 4.4.4 Vehicle Routing and Scheduling
- 4.4.5 Location Analysis
- 4.4.6 Urban Transportation
- 4.5 Supply Chain Management
- 4.5.1 Supply Chain Design
- 4.5.2 Product Design
- 4.5.3 Inventory Management and Control
- 4.5.4 Supply Chain Scheduling
- 4.5.5 Contracts in Supply Chains
- 4.5.6 Supply Chain Collaboration
- 4.5.7 Sales Optimization Models
- 4.5.8 Marketing/Operations Interface
- 4.5.9 Closed Loop Supply Chains
- 4.5.10 Behavioral/Experimental Operations
- 4.6 Applications with Societal Impact
- 4.6.1 Military Applications
- 4.6.2 Anti-Terrorism and Homeland Security
- 4.6.3 Humanitarian and Public Service Applications
- 4.6.4 Environmental Planning and Energy
- 4.6.5 Operations Research in Politics
- 4.7 Financial Applications
- 4.7.1 Auctions
- 4.7.2 Pricing and Revenue Management
- 4.7.3 Financial Engineering
- 4.8 Industrial
- 4.8.1 High-Tech Industries
- 4.8.2 Telecommunications
- 4.8.3 Natural Resources
- 4.8.4 Consumer Packaged Goods
- 4.8.5 Transportation and Logistics
- 4.8.6 Travel and Entertainment
- 4.8.7 Military Applications

