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Specifications of Optimization Techniques

Book Details

  • 978-93-83733-24-8
  • English
  • 2014
  • Paper Back
  • -

Contents

  • 1. Introduction
    Objectives, Introduction, Statement of an Optimization Problem, Various Optimization Techniques, Classification of Optimization Problems, Application of Operations Research in the Field of Engineering, Exercise.
     
    2. Linear Programming
    Objectives, Introduction, Mathematical Preliminaries, Mathematical Description of a Linear Programming Problem (LPP), Mathematical Formulation of LPP, Definitions and Prerequisites, Reduction of FS to BFS, Graphical Method for Solving an LPP, Illustrative Examples, Exercise.
     
    3. Simplex and Revised Simplex Method
    Objectives, Introduction to Simplex Method, Simplex Table, To Obtain an Initial BFS, Computational Procedure of Simplex Method, Artificial Variables Technique, Big M-Method (Charne’s M-Method), Two-Phase Method, Illustrative Examples, Exercise 3.1, Revised Simplex Method, Standard form I, Standard form II (For Artificial Variables), Illustrative Examples, Exercise 3.2.
     
    4. Duality and Post Optimality Analysis
    Objectives, Introduction, Primal-Dual Relationship, Definition of Primal-Dual Problems, Algorithm for Converting Any Primal into its Dual, To Read the solution to the Dual From the Final Simplex Table of the Primal and Conversely, Illustrative Exmaples, Exercise 4.1, Sensitivity Analysis (or Post Optimality Analysis), Changes in the Costs (cj) of the Objective Function, Change in the Right Hand Side Constants (bi), Change in the Component ‘aij’ of the Coefficient Matrix A, Addition of New Variable, Addition of a New Constraint, Sensitivity Analysis Applications in Civil Engineering, Exercise 4.2.
     
    5. Transportation and Assignment Problem
    Objectives, Introduction, Important Definitions, Solution of a Transportation Problem, Some Useful Terminologies, Transportation Algorithm (Modified Distribution i.e. MODI Method or u – v method), Unbalanced Transportation Problem, Degeneracy and its Resolution, Resolution of Degeneracy Occuring at the Initial Stage, Resolution of Degeneracy at any Intermediate Stage, Illustrative Examples, Exercise 5.1, Assignment Problem, Unbalanced Assignment Problem, Travelling Salesman Problem (TSP), Exercise 5.2.
     
    6. Non Linear Programming: Unconstrained Optimization Techniques
    Objectives, Introduction, Unconstrained Optimization Techniques, One Dimensional Minimization, Elimination Methods, Interpolation Methods, Optimization with Calculus, Kuhn-Tucker Conditions, Direct Search Methods, Random Search Method, Random Walk Method, Univariate Method, Pattern Search Method, Simplex Method, Descent Methods (or Gradient Methods or Indirect Search Methods), Steepest Descent (Cauchy) Method, Newtons Method, Exercise.
     
    7. Non Linear Programming: Constrained Optimization Techniques
    Objectives, Introduction, Characteristics of a Constrained Problem, Direct Method, Complex Method, Method of Feasible Directions, Indirect Methods, Transformation Techniques, Sequential Unconstrained Minimization Techniques, Cutting Plane Method, The Concept of Cutting Plane Algorithms, Exercise.
     
    8. Dynamic Programming
    Objectives, Introduction, Principle of Optimality, Exercise.