MBA SEMESTER II MB0048 –Operation Research- 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 Operation Research methods have been valuable in aiding executive decisions. [5 Marks] b. Discuss the usefulness of Operation Research 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 –Operation Research- 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 Operation Research? Mention different phases in an Operation Research study. Point out some limitations of O.R? [10 Marks] 2. What are the common methods to obtain an initial basic feasible solution for a transportation problem whose cost and requirement table is given? Give a stepwise procedure for one of them? [10 marks]

3. a. What are the properties of a game? Explain the “best strategy” on the basis of minmax criterion of optimality. [5 Marks] b. State the assumptions underlying game theory. Discuss its importance to business decisions. [5 Marks]

4. a. Compare CPM and PERT explaining similarities and...

...multiplied by their profit or cost contributions
After having enough experiences in model building one may skip verbal description, the following are certain examples of LP model formulation that you can use to strengthen your ability to translate a real – life problem into a mathematical model .
Linear Programming used in Marketing management
• Media Selection : The linear programming technique helps in determining the advertising media mix so as to maximize the effective exposure, subject to limitation of budget, specified exposure rates to different market segments. Specified minimum and maximum number of advertisements in various media
• Travelling sales problem : The salesman’s problem is to find the shortest route from a given duty to each of the specified cities and then returning to the original point of departure , provided no city would be visited twice during the tour such a type of problems can be solved with the help of the modified assignment technique .
• Physical distribution : Linear programming determines the most economic and efficient manner of locating manufacturing plants and distribution centres for physical distribution.
Q.2. Explain the concept and computational steps of the simplex method for solving linear programming problems. How would you identify whether an optimal solution to a problem obtained using simplex algorithm in unique or not ?
What is the difference...

...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...

...May 2012
Master of Business Administration - Semester 2
MB0048: “OperationsResearch”
(4 credits)
(Book ID: B1301)
ASSIGNMENT- Set 1
Marks 60
Note: Each Question carries 10 marks. Answer all the questions.
Marks 60
1. (a) What is linear programming problem?
Ans: Linear programming (LP, or linear optimization) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. Linear programming is a specific case of mathematical programming (mathematical optimization).
More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
(b) A toy company manufactures two types of dolls, a basic version doll- A and a deluxe version doll-B. Each doll of type B takes twice as long to produce as one of type A, and the company would have time to make maximum of 1000 per day. The supply of plastic is sufficient to produce 1000 dolls per day (both A & B combined). The deluxe version requires a fancy dress for which there are only 500 per day available. If the company makes a profit of Rs 3.00 and Rs 5 per doll, respectively on doll A and B, then how many of each doll should be produced per day in order to maximize the total profit....

...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...

...machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week, and the unit costs, are as follows:
Capacity
Machine (units)
1 1500
2 1500
3 1000
Product
Machine A B C
1 $1.00 $1.20 $0.90
2 $1.30 $1.40 $1.20
3 $1.10 $1.00 $1.20
Use the transportation model to develop the minimum-cost production schedule for the products and machines. Show the linear programming formulation.
2. Scott and Associates, Inc. is a consulting firm that has 4 new clients. Based on different background and experiences of the leaders, the various leader-client assignments differ in terms of projected completion times. The possible assignments and estimated completion times in days are
Client
Project Leader 1 2 3 4
Jackson 10 16 32 10
Ellis 14 22 40 22
Smith 22 24 34 34
Burton 14 18 36 24
What is the optimal assignment?
3. Wilson Distributors, Inc. is opening two new sales territories in the western states. Three individuals currently selling in the Midwest and the East are being considered for promotion to regional sales manager positions in the new sales territories. Management has estimated total annual sales (in thousands of dollars) for...

...Problem1.3-1
Application：Logistical planning of shipments Organization:Federal Express
Federal Express is the world’s largest express transportation company,providing fast and reliable services for important documents ,packages,and freight.It’s success was gave the credit to the use of OperationsResearch.
OperationsResearch modeling was a way of life for Federal Express,there were three famous Model planning system,one is origin-destination flow model which worked out a 26-city system that make FedEx’s first success.This model and the planning had served as the foundation for the $8 billion plus corporation that is the Federal Express today.
Since the advent of the industrial revolution, the world has seen a remarkable growth in the
size and complexity of organizations. The artisans’ small shops of an earlier era have
evolved into the billion-dollar corporations of today. An integral part of this revolutionary
change has been a tremendous increase in the division of labor and segmentation of management
responsibilities in these organizations. The results have been spectacular. However,
along with its blessings, this increasing specialization has created new problems,
problems that are still occurring in many organizations. One problem is a tendency for the
many components of an organization to grow into relatively autonomous empires with
their own goals and value systems, thereby losing sight...

...Assignment (Production & Operations Management)
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Answer 1. (b)
Planning
Planning involves commitment of resources. Once committed the resources loose theflexibility of their redeployment and the navigational management becomes restricted. If planning based on incorrect premises or inadequate data has been followed up with development of infrastructure, procurement and installation of machinery contracting for services to build up the production system for proposed goods and services, there may be very few options to undo thosecommitments. The enterprise may run into a serious problem.
Objective of Planning
Planning should result into the following:-a.Identification of Product to be offered its design and distinctive features from the productsalready existing in the market. b.Selection of the Process and Technology to be used for production.c.Location and Layout of Plant and facilities where goods and services should be produced.d.Material Handling Equipment (MHE) to be used.e.Capacity of the Plan to be installed.f.Forecasting of demand or sales.g.Production planning to include procurement of material, sequencing of machine operations,scheduling of activities and outline organization/control systems.h.Logistics Details along with warehousing and distribution system.
Basic Stage of Planning
The entrepreneur plans to achieve the objectives of planning through...

...for IS project selection in Health care institutions by implementing Goal programming and Analytical Hierarchy programming. Utilizing the outcomes of past investigations of health awareness organizations, four sets of value measures are distinguished. These measures, through the Analytic Hierarchy process (AHP), are weighted. These weights are then, infused into a goal-programming model to help select the best project for client of the health care institutions.
Keywords: Information System, Goal Programming, Analytical Hierarchy Process, Health care Institutions
II. INTRODUCTION:
Information Systems in Health service institutions is a far reaching, and it can be intended to deal with all the parts of a healing center operation, for example, restorative, regulatory, money related, lawful and the relating administration handling. Traditional methodologies incorporate paper-based data transforming and in addition inhabitant work position and versatile information obtaining and presentation.
In 2011 at International Conference on Social Science and Humanity, the best introduction for Information systems in Hospitals was made, which is:
“Health Care Information systems could be characterized as enormous, joined frameworks that underpin the extensive data prerequisites of healing centers, incorporating patient, clinical, auxiliary and monetary administration. Health care institutions are greatly unpredictable organizations with extensive...