Operations Research

  1. Linear Programming
    1. Introduction to Linear Optimization
      1. Definition and Structure of LP Problems
        1. Real-World Applications of LP
          1. Advantages and Limitations
          2. Formulation of LP Models
            1. Identifying Decision Variables
              1. Constructing the Objective Function
                1. Defining Constraints
                  1. Equality Constraints
                    1. Inequality Constraints
                      1. Non-negativity Constraints
                      2. Standard Form
                        1. Canonical Form
                          1. Converting to Standard Form
                          2. Assumptions of Linear Programming
                            1. Proportionality
                              1. Additivity
                                1. Divisibility
                                  1. Certainty
                                    1. Non-negativity
                                      1. Implications of Violations
                                      2. Graphical Solution Method
                                        1. Two-Variable Problem Setup
                                          1. Feasible Region Identification
                                            1. Corner Point Method
                                              1. Iso-profit and Iso-cost Lines
                                                1. Optimal Solution Identification
                                                  1. Special Cases in Graphical Method
                                                  2. The Simplex Algorithm
                                                    1. Standard Form Conversion
                                                      1. Basic and Non-basic Variables
                                                        1. Basic Feasible Solutions
                                                          1. The Simplex Tableau
                                                            1. Initial Tableau Setup
                                                              1. Pivot Operations
                                                                1. Entering and Leaving Variables
                                                                  1. Iterative Improvement Process
                                                                  2. Optimality Conditions
                                                                    1. Feasibility Conditions
                                                                      1. Special Cases in Simplex
                                                                        1. Unbounded Solutions
                                                                          1. Infeasible Problems
                                                                            1. Alternative Optimal Solutions
                                                                              1. Degeneracy and Cycling Prevention
                                                                            2. Duality Theory
                                                                              1. Formulation of the Dual Problem
                                                                                1. Primal-Dual Relationships
                                                                                  1. Weak Duality Theorem
                                                                                    1. Strong Duality Theorem
                                                                                      1. Complementary Slackness Conditions
                                                                                        1. Economic Interpretation of the Dual
                                                                                          1. Dual Simplex Method
                                                                                          2. Sensitivity Analysis
                                                                                            1. Changes in Objective Function Coefficients
                                                                                              1. Changes in Right-Hand-Side Values
                                                                                                1. Changes in Constraint Coefficients
                                                                                                  1. Shadow Prices and Reduced Costs
                                                                                                    1. Ranges of Optimality
                                                                                                      1. Ranges of Feasibility
                                                                                                        1. Parametric Programming

                                                                                                      Previous

                                                                                                      2. Mathematical Preliminaries

                                                                                                      Go to top

                                                                                                      Next

                                                                                                      4. Transportation and Assignment Problems