# An Introduction to Optimization Techniques

DOI link for An Introduction to Optimization Techniques

An Introduction to Optimization Techniques book

# An Introduction to Optimization Techniques

DOI link for An Introduction to Optimization Techniques

An Introduction to Optimization Techniques book

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An Introduction to Optimization Techniques introduces the basic ideas and techniques of optimization. Optimization is a precise procedure using design constraints and criteria to enable the planner to find the optimal solution. Optimization techniques have been applied in numerous fields to deal with different practical problems.

This book is designed to give the reader a sense of the challenge of analyzing a given situation and formulating a model for it while explaining the assumptions and inner structure of the methods discussed as fully as possible. It includes real-world examples and applications making the book accessible to a broader readership.

Features

- Each chapter begins with the Learning Outcomes (LO) section, which highlights the critical points of that chapter.
- All learning outcomes, solved examples and questions are mapped to six Bloom Taxonomy levels (BT Level).
- Book offers fundamental concepts of optimization without becoming too complicated.
- A wide range of solved examples are presented in each section after the theoretical discussion to clarify the concept of that section.
- A separate chapter on the application of spreadsheets to solve different optimization techniques.
- At the end of each chapter, a summary reinforces key ideas and helps readers recall the concepts discussed.

The wide and emerging uses of optimization techniques make it essential for students and professionals. Optimization techniques have been applied in numerous fields to deal with different practical problems. This book serves as a textbook for UG and PG students of science, engineering, and management programs. It will be equally useful for Professionals, Consultants, and Managers.

Introduction to Optimization Techniques. Introduction. Need of Optimization. Historical Perspective. Optimization Terms/ Parameters. Types of Optimization. Advanced Optimization Techniques. Optimization by Design of experiments. Applications of Optimization Techniques. Limitations of Optimization Techniques. Optimization method in engineering and management applications. **Linear Programming. **Introduction. Examples of LP Problems. Formulation of Linear Programming Problem. Examples based on LP formulation. General form of LPP. Basic Assumptions of LPP model. Solutions to Linear Programming Problem. Type of solution to Linear Programming Problem. Examples based on LP graphical solution. Simplex Method. Big – M method / Method of Penalty. Two-phase method. Duality in Linear Programming Problem. Sensitivity Analysis. Advantages of Linear Programming Model. Limitations of Linear Programming Model. Chapter Summary. Questions. **Transportation Problem and Assignment Problem. **Introduction. Mathematical Form of the Transportation Problem. Solution of a Transportation Problem. Degeneracy in Transport Problems. Unbalanced Transportation Problem. Introduction to Assignment Problem. The Nature of Assignment Problem. Mathematical Formulation of Assignment Problem. Assignment Algorithm (Hungarian Assignment Method). The Maximal Assignment Problem. Unbalanced Assignment Problem. Chapter Summary. Questions. **Network Models. **Introduction. Dummy Activities. CPM & PERT. Introduction to Shortest Path Method. The maximum flow problem. Traveling Salesman Problem (TSP). Chinese Postman Problem (CPP). Chapter Summary. Questions. Practice Problem. **Sequencing**. Introduction. Gantt Chart. Sequencing of n Jobs through One Machine. Sequencing of n Jobs through Two Machines. Sequencing of n Jobs through Three Machines. Sequencing of n Jobs through m Machines. Chapter Summary. Questions. Practice Problem. R**eplacement Models**. Introduction. Replacement of items that deteriorate with time. Replacement when the equipment/assets fail completely all of a sudden. Chapter Summary. Questions. Practice Problem. **Game Theory**. Introduction. Two -person zero sum game (with saddle point). The Maximin - Minimax Principle. Two-Person Zero Sum Games (without saddle point). The principle of dominance. Graphical method for solving games. Chapter Summary. Questions. Practice Problem. **Queuing theory. **Introduction. Single-Server Queuing Model with Poisson Arrivals and Exponential Service Times (M / M /1). Multiple-Server Queuing Model with Poisson Arrivals and Exponential Service Times (M / M /m). Little’s Relationships for Queueing Models. Chapter Summary. Questions. Practice Problem. **Dynamic and Integer programming. **Introduction to Dynamic programming. Terms used in Dynamic Programming. Characteristics of Dynamic Programming. Introduction to Integer Programming. Formulating Integer Programming Problems. Solution of Integer Programming using branch and bound method. Solution of Integer Programming using cutting plane method. Chapter Summary. Questions. Practice Problem. **Goal programming and decision making. **Goal programming introduction. Goal programming formulation. Graphical solution method of goal programming. The Analytical Hierarchy Process (AHP). Introduction to Decision Making. Decision-Making Environments. Decision Trees. Chapter Summary. Questions. Practice Problem. **Optimization Modelling with Open Source Tool (Excel). **Introduction. Examples based on linear programming graphical method using excel. Examples based on linear programming simplex method using excel. Examples based on transportation and assignment problem 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.