1) What is the meant by the term ‘feasible region’?
Its feasible region is a convex polyhedron, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality.

2) What is an infeasible solution? How is this condition recognized in simplex method? A infeasible solution is one that does not satisfies all linear and non-linear constraints. When the solution is along with the artificial variable even when the aolution is optimized then its is a infeasible solution

3) What is an unbounded solution? How is this condition recognized in simplex method? A linear program is unbounded if the optimal solution is unbounded, i.e. it is either ∞ or −∞. In simplex when the

entry values are negative its solution is unbounded.

4. Define slack and surplus variables in a LPP?
a slack variable is a variable that is added to an inequality constraint to transform it to an equality.
In Linear programming a surplus variable is a variable which is subtracted from a constraint to turn the inequality into an equation. This is required to turn an inequality into an equality where a linear combination of variables is greater than or equal to a given constant in the former..

5.What are the artificial variables?
One type of variable introduced in a linear program model in order to find an initial basic feasible solution; an artificial variable is used for equality constraints and for greater-than or equal inequality constraints. 6.Define optimal basic feasible solution?

An optimal solution to a linear program is a feasible solution with the largest objective function value (for a maximization problem). The value of the objective function for the optimal solution is said to be the value of the linear program.

7.Define the dual of a LPP?
Linear programming in which the maximum and minimum number are the same number.
8.What is the principle of duality in LPP?
the duality principle states that...

...MBA SEMESTER II MB0048 –OperationResearch- 4 Credits (Book ID: B1137) Assignment Set- 1 (60 Marks) Note: Each question carries 10 Marks. Answer all the questions
1. a. Explain how and why OperationResearch methods have been valuable in aiding executive decisions. [5 Marks] b. Discuss the usefulness of OperationResearch in decision making process and the role of computers in this field. [5 Marks]
2. Explain how the linear programming technique can be helpful in decision-making in the areas of Marketing and Finance. [10 Marks]
3. a. How do you recognise optimality in the simplex method? b. Write the role of pivot element in simplex table?
[5 Marks] [5 Marks]
4. What is the significance of duality theory of linear programming? Describe the general rules for writing the dual of a linear programming problem. [10 Marks]
5. Use Two-Phase simplex method to solve: Minimize z= + + + ≥ 0, + ≤3 ≥4 ≥ 0 and is unrestricted. =5
[10 Marks]
Subject to constraints:
6. Use Branch and Bound method to solve the following L.P.P: Maximize z= 7 + 9 Subject to constraints: - + 3 ≤6 7 + ≤7 , ≥ 0 and are integers. ≤ 35
[10 Marks]
MBA SEMESTER II MB0048 –OperationResearch- 4 Credits (Book ID: B1137) Assignment Set- 2 (60 Marks) Note: Each question carries 10 Marks. Answer all the questions
1. What are the essential characteristics of...

...problem obtained using simplex algorithm in unique or not ?
What is the difference between a feasible solution, a basic feasible solution, and an optimal solution of a linear programming problem ?
What is the difference between simplex solution procedure for a maximization and a minimization problem?
Using the concept of net contribution, provide an intuitive explanation of why the criterion for optimality for maximization problem is different from that of minimization problems.
Outline the steps involved in the simplex algorithm for solving a linear programming maximization problem. Also define the technical terms used therein.
Ans :
Q.3. “Liner programming is one of the most frequently and successfully employed OperationsResearch techniques to managerial and business decisions” Elucidate this statement with some examples.
Q.4. Describe the transportation problem and give its mathematical model. Explain by taking an illustration, the North-west corner rule, the least cost method and the vogel’s approximation method to obtain the initial feasible solution to a transportation problem. Discuss the various methods of finding initial feasible solution of a transportation problem and state the advantages, disadvantages and areas application for them
Q.5. What is an assignment problem ? It is true to say that it is a special case of the transportation problem ? Explain. How can u formulate an assignment problem as...

...APPLIED OPERATIONAL RESEARCH FOR MANAGEMENT
NOTES
1 ANNA UNIVERSITY CHENNAI
UNIT I
INTRODUCTION TO LINEAR
PROGRAMMING (LP)
INTRODUCTION
OperationsResearch (OR) (a term coined by McClosky and Trefthen in 1940) was
a technique that evolved during World War II to effectively use the limited military resources
and yet achieve the best possible results in military operations. In essence you can state
that OR is a technique that helps achieve best (optimum) results under the given set of
limited resources. Over the years, OR has been adapted and used very much in the
manufacturing sector towards optimization of resources. That is to use minimum resources
to achieve maximum output or profit or revenue.
Learning Objectives
The learning objectives in this unit are
1. To formulate a Linear programming problem (LPP) from set of statements.
2. To solve the LPP using graphical method ( For 2 variables)
3. To solve the LPP using primal simplex method ( For > 2 variables and all 2 variables and all
mixed constraints)
5. To solve the LPP using dual simplex method ( For > 2 variables and the solution is
infeasible)
6. We also have a look at the effect of changing the values of parameters on the
decision variables (Sensitivity Analysis)
Applications of OperationsResearch in functional areas of Management
The models of OR can be used by economists, statisticians, administrators and...

...OPERATIONSRESEARCH
INTRODUCTION
OperationsResearch is a unique discipline, one of its kinds, best of breeds, employing several highly developed and advanced analytical techniques which in turn aids in effective decision making. It is often regarded as a sub-field of mathematics. Operationsresearch (OR) are not only deeply involved with making and taking effective decisions. It is also concerned with minimizing losses, optimization, simulations, forecasting and predicting within an organization.
According to Morse and Kimball, OperationsResearch is a scientific method of providing executive departments with quantitative basis for decisions regarding the operations under their control.
HISTORY
OperationsResearch, took birth as a new field of study in Britain in 1939 -40 at the start of World War II in the efforts of military planners, and it has developed and expanded execeedingly in the last five to six decades. After the war, the techniques were used in areas such as business, industry and society. Since then, operational research has extended into a field widely used in industries ranging from petrochemicals to airlines, finance, logistics, and government, moving to a focus on the development of mathematical models that can be used to analyze and optimize complex systems, and has become an...

...DEPARTMENT OF APPLIED MATHEMATICS BSc Honours in OperationsResearch and Applied Statistics SMO 1101 Introduction to OperationsResearch TUTORIAL QUESTIONS
1. List and discuss the six major steps in the quantitative modeling process. 2. What is the difference between a i. descriptive and a normative model? ii. discrete and a continuous variable? 3. Show that the set ℜ n is a convex set. 4. Is the linearity assumption, in LP models, realistic in applications? 5. Print-Rite assembles printers for personal computers. These printers are assembled at five different points along the production line. Each production line consists of five work teams with different levels of skill. Each team can be assigned to any of the five assembly points. The following table gives the time, in minutes, to perform the tasks at each assembly point for the individual teams. Assembly 2 26 24 26 24 26 Point 3 40 30 28 36 30 4 30 32 36 30 40 5 26 18 18 20 24
Team A B C D E
1 20 22 24 20 20
Formulate a linear programming model that will minimize the total assembly time for a printer. 6. Why is implementation a difficult aspect of the quantitative modeling process?
Caston Sigauke 2006
1
7. A post office requires different numbers of full-time employees on different days of the week. The number of full-time employees required on each day is given in the table below. Employee Requirements for Post Office Day 1 = Monday Day 2 = Tuesday Day 3 =...

...Operations Management II
Introduction to OperationsResearchOperationsResearch (OR)
Definition
OperationsResearch is the representation of real world systems by mathematical models together with the use of quantitative methods (Algorithms) for solving such models, with a view of optimising. - (J.E Beasley)
“The attack of modern science on complex problems arising in the direction and management of large systems of men, machines, materials and money in industry, business, government and defence. The distinctive approach is to develop a scientific model of the system incorporating measurements of factors such as change and risk, with which to predict and compare the outcome of alternative decisions, strategies or controls. The purpose is to help management determine its policy and action scientifically”.
- (T. Lucey)
Other definitions
• The discipline of applying advanced analytical methods to help make better decisions.
• Using techniques such as mathematical modelling to analyse complex situations, OR gives executives the power to make more effective decisions and build more productive systems.
OR methods include :
1. Simulation: Giving you the ability to try out approaches and test ideas for improvement.
2. Optimisation : Narrowing your choices to the very best when there are virtually innumerable feasible...

...MB0048-Unit-01-Introduction to OperationsResearch
Unit-01-Introduction to OperationsResearch
Structure:
1.1 Introduction
Learning objectives
1.2 Historical Background
Definitions of OperationsResearch
1.3 Scope of OperationsResearch
1.4 Features of OperationsResearch
1.5 Phases of OperationsResearch
1.6 Types of OperationsResearch models
1.7 OperationsResearch Methodology
Definition
Construction
Solution
Validation
Implementation
1.8 OperationsResearch Techniques and Tools
1.9 Structure of the Mathematical Model
1.10 Limitations of OperationsResearch
1.11 Summary
1.12 Terminal Questions
1.13 Answers to SAQs and TQs
Answers to Self Assessment Questions
Answers to Terminal Questions
1.14 References
1.1 Introduction
Welcome to the unit on OperationsResearch Management. OperationsResearch Management focuses on the mathematical scoring of consequences of a decision aiming to optimise the use of time, effort and resources, and avoid blunders. The act of obtaining the best results under any given circumstances is known as optimising. The key purpose of OperationsResearch (OR) is to...

...INTRODUCTION TO
OPERATIONSRESEARCH,
SEVENTH EDITION
Reviewers seem to agree that this is clearly the best edition yet. Here is a sampling of
comments:
“The new edition seems to contain the most current information available.”
“The new edition of Hillier/Lieberman is very well done and greatly enhances this classic text.”
“The authors have done an admirable job of rewriting and reorganizing to reflect modern management practices and the latest software developments.”
“It is a complete package.”
“Hillier/Lieberman has recaptured any advantage it may have lost (to other competitors)
in the past.”
“The changes in this new edition make Hillier/Lieberman the preeminent book for operationsresearch and I would highly recommend it.”
INTRODUCTION TO
OPERATIONSRESEARCH
McGraw-Hill Series in Industrial Engineering and Management Science
CONSULTING EDITORS
Kenneth E. Case, Department of Industrial Engineering and Management, Oklahoma State University
Philip M. Wolfe, Department of Industrial and Management Systems Engineering, Arizona State University
Barnes
Statistical Analysis for Engineers and Scientists: A Computer-Based Approach
Bedworth, Henderson, and Wolfe
Computer-Integrated Design and Manufacturing
Blank and Tarquin
Engineering Economy
Ebeling
Reliability and Maintainability Engineering
Grant and Leavenworth
Statistical Quality Control
Harrell, Ghosh, and...