Table Of Content

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