Operations Research An Introduction

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Operations Research An Introduction

Chapter 1 : What Is Operations Research

=> What Is Operations Research?
=> Operations Research Models
=> Solving The OR Model
=> Queuing and Simulation Models
=> Art of Modeling
=> More than Just Mathematics
=> Phases of an OR Study

Chapter 2 : Modeling with Linear Programming

=> Modeling with Linear Programming
=> Two-Variable LP Model
=> Graphical LP Solution: Solution of a Maximization Model
=> Graphical LP Solution: Solution of a Minimization Model
=> Selected LP Applications: Urban planning
=> Selected LP Applications: Currency Arbitrage
=> Selected LP Applications: Investment
=> Selected LP Applications: Production Planning and Inventory Control
=> Selected LP Applications: Blending and Refining
=> Selected LP Applications: Manpower Planning
=> Selected LP Applications: Additional Applications
=> Computer Solution With Solver and AMPL

Chapter 3 : The Simplex Method and Sensitivity Analysis

=> The Simplex Method and Sensitivity Analysis
=> LP Model in Equation Form
=> Transition from Graphical to Algebraic Solution
=> The Simplex Method
=> Artificial Starting Solution: M-Method and Two-Phase Method
=> Special Cases in the Simplex Method
=> Graphical Sensitivity Analysis
=> Algebraic Sensitivity Analysis-Changes in the Right-Hand Side
=> Algebraic Sensitivity Analysis-objective Function
=> Sensitivity Analysis with TORA, Solver, and AMPL

Chapter 4 : Duality and Post Optimal Analysis

=> Duality and Post-Optimal Analysis
=> Definition of the Dual Problem
=> Primal-Dual Relationships
=> Economic Interpretation of Duality
=> Additional Simplex Algorithms: Dual Simplex Method and Generalized Simplex Algorithm
=> Post-Optimal Analysis

Chapter 5 : Transportation Model and Its Variants

=> Transportation Model and its Variants
=> Definition of the Transportation Model
=> Nontraditional Transportation Models
=> The Transportation Algorithm
=> The Assignment Model and The Hungarian Method
=> Transshipment Model

Chapter 6 : Network Models

=> Network Models
=> Scope and Definition of Network Models
=> Minimal Spanning Tree Algorithm
=> Examples of the Shortest-Route Applications or Problem
=> Shortest-Route Algorithms
=> Linear Programming Formulation of the Shortest-Route Problem
=> Maximal flow model
=> CPM (Critical Path Method) and PERT (Program Evaluation and Review Technique)
=> CPM AND PERT: Network Representation
=> CPM AND PERT: Critical Path (CPM) Computations
=> CPM AND PERT: Construction of the Time Schedule
=> CPM AND PERT: linear Programming Formulation of CPM
=> CPM AND PERT: PERT Networks

Chapter 9 : Integer Linear Programming

=> Integer Linear Programming
=> Capital Budgeting- Integer Linear Programming Illustrative Applications
=> Set Covering Problem- Integer Linear Programming Illustrative Applications
=> Fixed Charge Problem- Integer Linear Programming Illustrative Applications
=> Either Or and If Then Constraints- Integer Linear Programming Illustrative Applications
=> Integer Programming Algorithms
=> Branch-and-Bound (B&B) Algorithm
=> Cutting-Plane Algorithm
=> Computational Considerations in ILP
=> Traveling Salesperson Problem (TSP)
=> Heuristic Algorithms: nearest neighbor and subtour reversal algorithms - Traveling Salesperson Problem (TSP)
=> B&B Solution Algorithm - Traveling Salesperson Problem (TSP)
=> Cutting Plane Algorithm - Traveling Salesperson Problem (TSP)

Chapter 10 : Deterministic Dynamic Programming

=> Deterministic Dynamic Programming
=> Recursive Nature of Computations in DP(Dynamic Programming)
=> Forward and Backward Recursion- Dynamic Programming
=> Selected Dynamic Programming(DP) Applications
=> Knapsack/Fly-Away/Cargo Loading Model- Dynamic Programming(DP) Applications
=> Work Force Size Model- Dynamic Programming(DP) Applications
=> Equipment Replacement Model- Dynamic Programming(DP) Applications
=> Investment Model- Dynamic Programming(DP) Applications
=> Problem of Dimensionality- Dynamic Programming

Chapter 18 : Classical Optimization Theory

=> Classical Optimization Theory
=> Unconstrained Problems -Classical Optimization Theory
=> Necessary and Sufficient Conditions -Unconstrained Problems
=> Newton Raphson Method -Unconstrained Problems
=> Constrained Problems: Equality Constraints
=> Inequality Constraints-Karush-Kuhn-Tucker (KKT) Conditions

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