An Introduction to Optimization Techniques

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Acknowledgements
Authors
Chapter 1: Introduction to Optimization Techniques
	1.1 Introduction
	1.2 Need for Optimization
	1.3 Historical Perspective
	1.4 Optimization Terms/Parameters
	1.5 Types of Optimization
		1.5.1 Based on Constraints
		1.5.2 Based on the Physical Configuration
		1.5.3 Based on the Nature of the Variables
		1.5.4 Based on the Number of Objective Functions
		1.5.5 Geometric Programming Problem
		1.5.6 Integer Programming Problem
		1.5.7 Real-Value Programming Problem
		1.5.8 Non-linear Programming (NLP)
	1.6 Advanced Optimization Techniques
	1.7 Optimization by Design of Experiments (DOE) (Experimental Designs)
		1.7.1 Types of Experimental Design
	1.8 Applications of Optimization Techniques
	1.9 Limitations of Optimization Techniques
	1.10 Optimization Method in Engineering and Management Applications
	Questions
Chapter 2: Linear Programming
	2.1 Introduction
	2.2 Examples of LPP
	2.3 Formulation of LPP
	2.4 General Form of LPP
		2.4.1 Important Concepts of LP
		2.4.2 Variables Used in LP
	2.5 Basic Assumptions of the LPP Model
		Examples based on LP formulation
	2.6 Solutions to LPP
		2.6.1 Graphical Method
		2.6.2 Procedure of Graphical Method
		2.6.3 Types of Graphical Methods to Solve LPP
	2.7 Types of Solutions to LPP
		Examples based on the LP graphical solution
	2.8 Simplex Method
		2.8.1 Some Important Terms of the Simplex Technique
		2.8.2 Simplex Method Steps
			Examples based on the LP simplex method
	2.9 Big M Method/Method of Penalty
		Example based on the LP big M method
	2.10 Two-Phase Method
		Example based on the LP two-phase method
	2.11 Duality in LPP
		Example based on duality in LPP
	2.12 Sensitivity Analysis
	2.13 Advantages of the LP Model
	2.14 Limitations of the LP Model
		Questions
Chapter 3: Transportation Problems and Assignment Problem
	3.1 Introduction
	3.2 Mathematical Form of the Transportation Problem
	3.3 Solution of a Transportation Problem
		3.3.1 Methods to Find an Initial Basic Feasible Solution (BFS)
		3.3.2 Unit Cost Penalty Method (Vogel’s Approximation Method)
			Examples based on the initial BFS
		3.3.3 Methods to Find an Optimal Solution
			Examples based on an optimal solution
	3.4 Degeneracy in Transport Problems
		Examples based on degeneracy
	3.5 Unbalanced Transportation Problem
		Examples based on an unbalanced transportation problem
	3.6 Introduction to an Assignment Problem
	3.7 The Nature of an Assignment Problem
	3.8 Mathematical Formulation of an Assignment Problem
		3.8.1 Fundamental Theorems
	3.9 Assignment Algorithm (Hungarian Assignment Method)
		Examples based on an assignment problem
	3.10 The Maximal Assignment Problem
		Examples based on maximization
	3.11 Unbalanced Assignment Problem
		Examples based on an unbalanced assignment problem
		Questions
Chapter 4: Network Models
	4.1 Introduction
		4.1.1 Network
	4.2 Dummy Activity
		Examples based on drawing a network diagram
	4.3 Critical Path Method (CPM)/Program Evaluation and Review Technique (PERT)
		4.3.1 CPM Computations
		4.3.2 Forward Pass and a Backward Pass
			Examples based on CPM
		4.3.3 PERT Computations
		4.3.4 Probability Computations
			Examples based on PERT
		4.3.5 Project Crashing
			Examples based on the crashing of the project
	4.4 Introduction to the Shortest Path Method
		4.4.1 Dijkstra’s Shortest Path Method
		4.4.2 Minimum Spanning Tree Algorithm
			Examples based on the shortest path method
	4.5 The Maximum Flow Problem
		Example based on the maximum flow problem
	4.6 A Travelling Salesman Problem (TSP)
		4.6.1 TSP Solution by Branch and Bound Method
	4.7 Chinese Postman Problem (CPP)
		Examples based on TSP and CPP
		Questions
		Practice Problem
Chapter 5: Sequencing
	5.1 Introduction
		5.1.1 Assumptions Made while Solving Sequencing Problems
		5.1.2 Terms Used in Sequencing
	5.2 Gantt Chart
	5.3 Sequencing of n Jobs through One Machine
		Examples based on sequencing of n jobs through one machine
	5.4 Sequencing of n Jobs through Two Machines
		Examples based on sequencing of n jobs through two machines
	5.5 Sequencing of n Jobs through Three Machines
		Example based on sequencing of n jobs through three machines
	5.6 Sequencing of n Jobs through m Machines
		Example based on the sequencing of n jobs through m machines
		Typical examples
		Questions
		Practice Problem
Chapter 6: Replacement Models
	6.1 Introduction
	6.2 Replacement of Items that Deteriorate with Time
		6.2.1 Replacement Policy When the Value of Money Does Not Change with Time
			Examples based on the replacement policy when the value of money does not change with time
		6.2.2 Replacement Policy When the Value of Money Changes with Time
			Examples based on the replacement policy when value of money changes with time
	6.3 Replacement When the Equipment/Assets Fail Completely All of a Sudden
		Examples based on the replacement policy when the equipment fails completely all of a sudden
		Questions
		Practice Problem
Chapter 7: Game Theory
	7.1 Introduction
		7.1.1 Terminology in Game Theory
	7.2 Two-Person, Zero-Sum Games (with Saddle Point)
	7.3 The Maximin-Minimax Principle
		Examples based on the two-person, zero-sum games with saddle point
	7.4 Two-Person, Zero-Sum Games (without Saddle Point)
		Examples based on the two-person, zero-sum game without saddle point
	7.5 The Principle of Dominance
		Examples based on the principle of dominance
	7.6 Graphical Method for Solving Games
		The concept of a 2 × n zero-sum game
		The concept of an m × 2 zero-sum game
			Examples of the graphical method for solving games
		Questions
		Practice Problem
Chapter 8: Queuing Theory
	8.1 Introduction
		8.1.1 Elements of the Queuing System
		8.1.2 Kendall Notation
	8.2 Single-Server Queuing Model with Poisson Arrivals and Exponential Service Times ( M/M/1)
		Examples based on the single-server queuing model
	8.3 Multiple-Server Queuing Model with Poisson Arrivals and Exponential Service Times ( M/M / m)
		Examples based on the multiple-server queuing model
	8.4 Little’s Relationships for Queuing Models
		Questions
		Practice Problem
Chapter 9: Dynamic and Integer Programming
	9.1 Introduction to Dynamic Programming
	9.2 Terms Used in Dynamic Programming
	9.3 Characteristics of Dynamic Programming
		Examples based on dynamic programming
	9.4 Introduction to Integer Programming
	9.5 Formulating Integer Programming Problems
		Examples based on formulating the integer programming problem
	9.6 Solution of Integer Programming Using the Branch-and-Bound Method
		Examples based on the branch-and-bound method
	9.7 Solution of Integer Programming Using the Cutting Plane Method
		Examples based on the cutting plane method
		Questions
		Practice Problem
Chapter 10: Goal Programming and Decision Making
	10.1 Goal Programming Introduction
	10.2 Goal Programming Formulation
		Examples based on goal programming formulation
	10.3 Graphical Solution Method of Goal Programming
		Examples based on the graphical solution method of goal programming
	10.4 The Analytic Hierarchy Process (AHP)
		10.4.1 Steps in AHP
			Example based on AHP
	10.5 Introduction to Decision Making
		10.5.1 Decision-Making Components
	10.6 Decision-Making Environments
		10.6.1 Decision Making under Uncertainty
			Examples based on decision making under uncertainty
		10.6.2 Decision Making under Risk
			Examples based on decision making under risk
	10.7 Decision Trees
		Examples based on decision tree
		Questions
		Practice Problem
Chapter 11: Optimization Modelling with an Open Source Tool (Excel)
	11.1 Introduction
		Examples based on the linear programming graphical method using Excel
		Examples based on the linear programming simplex method using Excel
		Examples based on transportation and assignment problems using Excel
		Examples based on network models using Excel
		Example based on sequencing using Excel
		Example based on integer programming using Excel
		Example based on decision making using Excel
		Example based on dynamic programming using Excel
Multiple Choice Questions
	Answers to Multiple Choice Questions
Bibliography
Index
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