MBA205 & OPERATIONS RESEARCH

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DRIVE	FALL 2017
PROGRAM	MASTER OF BUSINESS ADMINISTRATION (MBA)
SEMESTER	II
SUBJECT CODE & NAME	MBA205 & OPERATIONS RESEARCH
CREDITS	2, 4 CREDITS
MARKS	30

Note: Answer all questions. Kindly note that answers for 10 marks questions should be approximately of 400 words. Each question is followed by evaluation scheme.

Assignment Set -1

Question 1 Define the Linear programming problem in operation Research. Also, explain various assumptions, advantages and limitations of linear programming problem.

A Linear programming problem in operation Research

Assumptions of linear programming problem

Advantages of linear programming problem

Limitations of linear programming problem

Answer: In organisations, managers are required to make judicious use of scarce resources, such as men, materials, machines and capital, to minimise costs and maximise profits. A technique that is used to select the best alternative from a set

Question 2 a. Discuss the concept of Degeneracy in transportation problem

b. The ABC Tool Company has a sales force of 25 men who work out from Regional offices. The company produces four basic products lines of hand tools. Mr. Jain, the sales manager, feels that 6 salesmen are needed to distribute product line 1, 10 salesmen are needed to distribute product line 2, 4 salesmen to product line 3 and 5 salesmen to product line 4. The cost per day of assigning salesmen from each of the offices for selling each of the product lines are as follows;

Regional office	Product Lines
	𝑷𝟏	𝑷𝟐	𝑷𝟑	𝑷𝟒
R1	20	21	16	18
R2	17	28	14	16
R3	29	23	19	20

Now, 10 salesmen are allowed to office R1, 9 salesmen to office R, and 7 salesmen to office R.

How many salesmen should be assigned from each office to selling each product line in order to minimize costs?

Degeneracy in transportation problem

Optimum allocation.

Optimum transportation cost

Answer: a) Degeneracy in transportation problem

A basic solution to an m-origin, n destination transportation problem can have at the most m+n-1 positive basic variables (non-zero), otherwise the basic solution degenerates. It follows that whenever the number of basic cells is less than m + n – 1, the transportation problem is a degenerate one. The degeneracy can develop in two ways:

Case 1 - The degeneracy develops while

Question 3 a. Elaborate the meaning of Simulation.

b. What are different Practical applications of simulation

A Meaning of Simulation.

Practical applications of simulation

Answer: a) Simulation is a representation of real-life situations. It is a method in which a replica of a real-world process or system is developed over a period of time. The simulated model acts in the same manner as the selected physical or abstract process or system behaves in reality. For example, aircraft pilots are given training through simulation models as training with real aircrafts can incur huge costs as well as involve various risks. Similarly, in education sector, teachers are trained on the simulated models of students (a group of individuals who imitate as students). This avoids the risk of spoiling the future of students if the teacher is not able to

Assignment Set -2

Question 1 a. Define the meaning of assignment problem in operation Research.

b. A Departmental head has four subordinates and four task to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimate of the times each man would take to perform each task is given in the following matrix-

Tasks	Subordinates
	I	II	III	IV
A	8	26	17	11
B	13	28	4	26
C	38	19	18	15
D	19	26	24	10

How should the tasks be allocated to subordinates to minimize the total man-hours?

A Description of assignment problem

Optimum allocation through Hungarian method

Answer: a) An assignment problem is a special type of transportation problem. In an assignment problem, the same number of facilities (sources of supply) needs to be allocated to the same number of jobs (points of destinations) so that the transportation cost is minimised or the profit is maximised. An assignment problem can occur while assigning:

·       Machines to factory orders

·       Salespeople to sales territories

·       Teachers to classes

·       Police vehicles to patrolling areas

·        

Question 2. Define following criteria’s used for decision making under Uncertainty

a. Optimism (maximax or minimin) criterion

b. Pessimism (maximin or minimax) criterion

c. Equal probabilities (Laplace) criterion

d. Coefficient of optimism (Hurwicz) criterion

e. Regret (salvage) criterion

Answer: a) Optimism (maximax or minimin) criterion: Here, the decision maker tries to achieve the largest possible profit (Maximax) or minimum possible cost (minimin). If the entries in the payoff matrix are the one which the decision maker wants as large as possible, for example, profits or sales revenue, he/she selects the alternative that represents the maximum of the maximum payoff. In case where the entries of the payoff matrix are one which the decision maker wants as small as possible, he/she goes for the minimum of the

Question 3 a. Explain the importance and utility of the replacement model in business organizations.

b. The maintenance cost and re-sale value per year of a machine whose purchase price is Rs. 7000 is given below-

Year	1	2	3	4	5	6	7	8
Maintenance cost (Rs.)	900	1200	1600	2100	2800	3700	4700	5900
Resale value (Rs.)	4000	2000	1200	600	500	400	400	400

Importance and utility of the replacement model Replacement Year

Answer: a) In an organisation, replacement problems arise when fixed assets, such as machines, equipment, and other tools, need to be replaced due to reduced efficiency, failure or breakdown. Sometimes, replacement takes place when more efficient equipment is available in the market or the maintenance of the existing equipment is incurring a huge cost on an organisation. However, an organisation needs to decide when the

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