Quantitative Techniques: Theory and Problems

1093 Pages·2002·40.9 MB·English

by  P. C. Tulsian and Vishal Pandey

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