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Quantitative Techniques: Theory and Problems

Book Description

Quantitative Techniques: Theory and Problems adopts a fresh and novel approach to the study of quantitative techniques, and provides a comprehensive coverage of the subject. Essentially designed for extensive practice and self-study, this book will serve as a tutor at home. Chapters contain theory in brief, numerous solved examples and exercises with exhibits and tables.

Table of Contents

  1. Cover
  2. Title Page
  3. Contents
  4. Preface
  5. 1. Linear Programming – Formulation
    1. Linear Programming
    2. Decision Variables
    3. Objective Function
    4. Constraints
    5. Non-negativity Restriction
    6. Divisibility
    7. Steps Involved in the Formulation of LP Problem
    8. Product Mix Problems
    9. Make or Buy Decision Problems
    10. Choice of Alternative Problems
    11. Sales Budget Problem
    12. Product Budget Problem
    13. Purchase Budget Problem
    14. Portfolio Mix Problem
    15. Advertising Problem
    16. Capital Mix Problem
    17. Diet Problem
    18. Nutrition Problems
    19. Bending Problems
    20. Trim Problem
    21. Transportation Problem
    22. Job Schedulings
    23. Assignment Problem
    24. Theoretical Questions
    25. Practical Questions
  6. 2. Linear Programming – Graphical Method
    1. Closed Half Plane
    2. Feasible Solution
    3. Feasible Region
    4. Convex Set
    5. Convex Polygon
    6. Extreme Points or Vertexes or Corner Points
    7. Redundant Constraint
    8. Multiple Solution
    9. Unbounded Solution
    10. Infeasible Problem
    11. Practical Steps Involved in Solving LPP by Graphical Method
    12. Solved Problems
    13. Multiple Solution Problems
    14. Theoretical Questions
    15. Practical Questions
  7. 3. Linear Programming – Simplex Method
    1. Practical Steps in Solving Maximization Problems
    2. Multiple Solution
    3. Unbounded Solution
    4. Infeasible Problem
    5. Degeneracy
    6. Practical Steps Involved in Solving Minimisation Problems
    7. Practical Steps Involved in Solving Maximisation Problems
    8. Practical Steps Involved in Formulating Dual Problem from the Primal Problem
    9. Theoretical Questions
    10. Practical Questions
  8. 4. Assignment Problems
    1. What is Assignment Problem
    2. Hungarian Method
    3. Balanced Assignment Problem
    4. Unbalanced Assignment Problem
    5. Dummy Job/Facility
    6. An Infeasible Assignment
    7. Practical Steps Involved in Solving Minimisation Problems
    8. Practical Steps Involved in Solving Maximisation Problems
    9. Solved Problems
    10. Minimization Problems
    11. Maximization Problems
    12. Theoretical Questions
    13. Practical Questions
  9. 5. Transportation Problems
    1. What is Transportation Problem
    2. Balanced Transportation Problem
    3. Unbalanced Transportation Problem
    4. Dummy Origin/Destination
    5. Practical Steps Involved in Solving Transportation Problems of Minimization Type
    6. Practical Steps Involved in Solving Transportation Problems of Maximization Type
    7. Mathematical Model for Transportation Problem
    8. Finding Initial (or Basic) Feasible Solution
    9. Introducing an Infinitely Small quantity 'e' in Case the Total Number of Allocation is Less than "M + N–1"
    10. Application of Optimality Test
    11. Looping and Reallocation Matrix
    12. Minimisation Problems (Not Involving Looping)
    13. Minimisation Problem (Involving Looping)
    14. Maximisation Problems (Not Involving Looping)
    15. Maximisation Problems (Involving Looping)
    16. Transhipment Problem
    17. Theoretical Questions
    18. Practical Questions
  10. 6. Critical Path Method (CPM) – Drawing Network
    1. Meaning of CPM
    2. Usefulness of CPM
    3. Assumptions of CPM/PERT
    4. Activity (or Task or Job)
    5. Event (or Node or Connector)
    6. Network (or Arrow Diagram)
    7. Working Methodology of Critical Path Analysis
    8. Conventions Followed in Drawing Networks
    9. Dummy Activity/Arrow
    10. Can a Critical Path Change During the Course of a Period?
    11. Drawing a Network when Activities Represented by Nodes are Given
    12. Drawing Network when Activities (Including Dummy Activities Represented by Nodes are Given
    13. Preparation of Network when Activities are Given
    14. Preparation of Network Involving Use of Dummy Activities
    15. How to Compute Earliest Start Time for Each Node (E)
    16. How to Compute Latest Finish Time for Each Node (L)
    17. Slack Time for An Event
    18. Head Event Slack (HES)
    19. Tail Event Slack (TES)
    20. Earliest Finish Time (EFT)
    21. Latest Start Time (LST)
    22. Total Float
    23. Free Float
    24. Independent Float
    25. Interfering Float
    26. Calculation of Earliest Start Time, Latest Finish Time and Floats
    27. Theoretical Questions
    28. Practical Questions
  11. 7. PERT
    1. Meaning of PERT
    2. Distinction Between CPM and PERT
    3. Usefulness of PERT
    4. How to Incorporate Uncertainty in PERT Model
    5. Practical Steps Involved in Solving PERT Problems
    6. Solved Problems
    7. Calculation of Expected Duration Variances of Activities
    8. Calculation of Probability
    9. Theoretical Questions
    10. Practical Questions
  12. 8. Crashing, Resource Allocation and Smoothing
    1. Crashing
    2. Resource Smoothing
    3. Resource Levelling
    4. Time Cost Trade Off
    5. Resource Allocation
    6. Resource Smoothing
    7. Theoretical Questions
    8. Practical Questions
  13. 9. Queuing Theory
    1. Meaning of Queuing Model
    2. Objective of a Queuing Model
    3. Application of a Queuing Model
    4. Relationship between Service and Cost
    5. Arrival
    6. Service
    7. Server
    8. Time Spent in the Queuing System
    9. Queue Discipline
    10. Kendall’s Notation
    11. State of Queuing System
    12. Poisson Process
    13. Relationship Between Poisson Process and Exponential Probability Distribution
    14. M/M/1 Queuing Model
    15. Optimal Value of Service Rate
    16. Fundamental Components/Elements of a Queuing Process
    17. Conditions for Single Channel Queuing Model
    18. Limitations of Single Queuing Model
    19. Applicability of Queuing Model to Inventory Problems
    20. Practical Formulae Involved in Queuing Theory
    21. Solved Problems
    22. Theoretical Questions
    23. Practical Question
  14. 10. Statistical Decision Theory
    1. Meaning of Statistical Decision Theory
    2. Components of a Problem
    3. Three Types of Problems in Decision Making Under Different Environment
    4. Methods Used for Decision-Making with Uncertainty
    5. Expected Monetary Value
    6. Expected Regret
    7. Expected Value of Perfect Information
    8. Solved Problems
    9. Theoretical Questions
    10. Practical Questions
  15. 11. Simulation
    1. Meaning of Simulation
    2. Steps in the Simulation Process
    3. Application of Simulation
    4. Application of Simulation to the Problem of Financial Planning
    5. Advantages of Simulation
    6. Disadvantages of Taking a Simulation Approach
    7. Steps in the Hertz Simulation Model
    8. Monte Carlo Simulation
    9. Meaning of Pseudo-random Numbers
    10. Computer Simulation
    11. Solved Problems
    12. Theoretical Questions
    13. Practical Questions
  16. 12. Decision Tree
    1. Meaning of Decision Tree
    2. Steps Involved in Drawing a Decision Tree
    3. Illustration
    4. Roll-back Technique
    5. Solved Problems
    6. Theoretical Questions
    7. Practical Questions
  17. Copyright