Operations Research and Optimization

  1. Integer Programming
    1. Introduction to Integer Programming
      1. Differences from Linear Programming
        1. Discrete Decision Variables
          1. Combinatorial Nature
            1. Computational Complexity
            2. Types of Integer Programs
              1. Pure Integer Programming
                1. Mixed-Integer Programming
                  1. Binary Integer Programming
                    1. General Integer Programming
                    2. Applications Overview
                      1. Logical Constraints
                        1. Fixed Costs
                          1. Discrete Choices
                        2. Integer Programming Formulations
                          1. Binary Variable Applications
                            1. Yes-No Decisions
                              1. Logical Relationships
                                1. Set Partitioning
                                2. Fixed-Charge Problems
                                  1. Setup Costs
                                    1. Binary Variable Modeling
                                      1. Piecewise Linear Functions
                                      2. Knapsack Problems
                                        1. 0-1 Knapsack
                                          1. Multiple Knapsack
                                            1. Bounded Knapsack
                                            2. Set Covering Problems
                                              1. Minimum Set Cover
                                                1. Set Partitioning
                                                  1. Set Packing
                                                  2. Facility Location Problems
                                                    1. Uncapacitated Facility Location
                                                      1. Capacitated Facility Location
                                                        1. P-Median Problems
                                                        2. Scheduling Problems
                                                          1. Job Shop Scheduling
                                                            1. Machine Scheduling
                                                              1. Workforce Scheduling
                                                              2. Traveling Salesman Problem
                                                                1. Symmetric TSP
                                                                  1. Asymmetric TSP
                                                                    1. Subtour Elimination Constraints
                                                                  2. Solution Methods for Integer Programming
                                                                    1. Branch and Bound Method
                                                                      1. Branching Strategies
                                                                        1. Bounding Techniques
                                                                          1. Node Selection Rules
                                                                            1. Pruning Conditions
                                                                              1. Tree Search Process
                                                                              2. Cutting Plane Methods
                                                                                1. Gomory Cuts
                                                                                  1. Chvatal-Gomory Cuts
                                                                                    1. Problem-Specific Cuts
                                                                                      1. Cut Generation
                                                                                      2. Branch and Cut Method
                                                                                        1. Integration of Methods
                                                                                          1. Cut Pool Management
                                                                                            1. Preprocessing Techniques
                                                                                            2. Lagrangian Relaxation
                                                                                              1. Dual Problem Formation
                                                                                                1. Subgradient Optimization
                                                                                                  1. Bound Quality
                                                                                                  2. Heuristic Methods
                                                                                                    1. Construction Heuristics
                                                                                                      1. Improvement Heuristics
                                                                                                        1. Metaheuristic Approaches

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                                                                                                    4. Network Optimization

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                                                                                                    6. Nonlinear Programming