Operations Research An Introduction

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Operations Research An Introduction

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

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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