IMT-25

Operation Research .................................................. Page 1 of 4 ............................................................................... IMT-25

Subject Code: IMT-25

Subject Name : Operation Research

Objective: To develop working knowledge on operation research techniques and appreciation of applications thereof to business problems. Contents : Linear Programming problem

Integer Programming and Quadratic Programming

Transportation problem

Assignment problem

Queuing Theory

Decision Analysis

Simulation

Networking – PERT and CPM

Notes:

a. Write answers in your own words as far as possible and refrain from copying from the text books/handouts.

b. Answers of Ist Set (Part-A), IInd Set (Part-B), IIIrd Set (Part – C) and Set-IV (Case Study) must be sent together.

c. Mail the answer sheets alongwith the copy of assignments for evaluation & return.

d. Only hand written assignments shall be accepted.

A. First Set of Assignments: 5 Questions, each question carries 1 marks.

B. Second Set of Assignments: 5 Questions, each question carries 1 marks.

C. Third Set of Assignments: 5 Questions, each question carries 1 marks. Confine your answers to 150 to 200 Words.

D. Forth Set of Assignments: Two Case Studies : 5 Marks. Each case study carries 2.5 marks.

ASSIGNMENTS FIRST SET OF ASSIGNMENTS Assignment-I = 5 Marks

PART– A

1. State the different types of models used in operation research? Explain briefly the general method for solving these O.R models?

2. Customer arrives at sales counter by a poison process with a mean rate of 20 per hr. The time required to serve a customer has an exponential distribution with a mean of 100 seconds. Find the average waiting & queue length of customer.


3. Obtain the optimal strategy for both persons & the value of game:

4. Prepare network, activity time estimates, determine the expected project completion time &

variance.

Activity Time estimates ( days)

to Tm tp 1-2 5 8 17

1-3 7 10 1

2-3 3 5 7

2-4 1 3 5

3-4 4 6 8

3-5 3 3 3

4-5 3 4 5

5. What is queuing theory? Discuss the service mechanism in queuing theory.

SECOND SET OF ASSIGNMENTS Assignment-II = 5 Marks

PART– B

1. Determine a sequence for the 5 jobs that will minimize the elapsed time.

Job 1 2 3 4 5

A 5 1 9 3 10

B 2 6 7 8 4

2. What is meant by optimality test in a transportation problem? How would you determine

whether a given transportation solution is optimal or not?

3. OR advocates a system approach and its procedure is concerned with optimization. Discuss.

4. Discuss the importance and applications of PERT and CPM in project planning and control.

5. Write short notes on n- Johnson’s algorithm for n jobs m machines

B1 B2

A1 1 -3

A2 3 5

A3 -1 6

A4 4 1

A5 2 2

A6 -5 0


THIRD SET OF ASSIGNMENTS Assignment-III = 5 Marks

PART– C 1. Solve the following transportation problem by VAM:

1 2 3 Supply 1 5 1 7 10 2 6 4 6 80 3 3 2 5 15 Demand 70 20 50

2. Write short notes on :

a) Failures in replacement theory. b) Decision tree analysis.

3. The maintenance cost & resale value per year of machine whose purchase price is Rs 7000 is given below:

Yr 1 2 3 4 Maintenance cost 900 1200 1600 2100 Resale value 4000 2000 1200 600

When should the machine be replaced?

4. Specify the characteristics of M/M/1 queue model.

5. Discuss the following terms in game theory: Saddle point; Pure strategy; Two person zero

sum game; Principle of dominance. FOURTH SET OF ASSIGNMENTS Assignment-IV = 2.5 Each Case Study

CASE STUDY - I

A firm manufactures three products A,B,C the profits are RS 3, Rs 2, & Rs 4respectively. The firm has two machines M1& M2 and below given is the required processing time in minutes for each machine on each product

MACHINE PRODUCT A B C

M1 4 3 5

M2 2 2 4

Machines M1 & M2 have 2000 & 2500 machine minutes respectively. The firm must manufacture 100 A’s, 200 B’s & 50 C’s, but not more than 150 A’s. Set up an LPP to maximize profits.


CASE STUDY-II

A fruit vendor purchases fruits for Rs 3 a box and sells for Rs 8 a box. The high markup reflects the perish ability of the fruit and the great risk of stocking it., the product has no value after the first day it is offered for sale. The vendor faces the problem of how many boxes to order for tomorrow’s business. A 90 day observation of the past sales gives the following information. Daily Sales No. of days sold Probability 10 11 12 13 Total

18 36 27 9 90

.20

.40

.30

.10 1.00

Determine the number of boxes he should order to maximize its profit. Also find the expected monetary value and regret table.

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IMT-25