Applied Operation Research

G.H. RAISONI SCHOOL OF BUSINESS MANAGEMENT Sessional Examination 2009-10 Third Semester Master of Business Administration Paper-I: Applied Operation Research Time:- 3 Hours Max.Marks: 80 1)Attempt Five Questions 2)At least Two Questions from each section are compulsory. 3)All questions carry equal marks. SECTION A

Q.1.A steel company is negotiating with its union for revision of wages to its employees. The Management with the help of a mediator,has prepared a payoff matrix shown below. Plus sign represents wage increases, while negative sign stand for wage decreases. Union has also constructed a tabel which is comparable to that developed by the management. The management does not have the specific knowledge of game theory to the best st-rategy or strategies for the firm. You have to assist the management on the select problem. What game value and strategies are available to the oposing group?

OR

Q.1 What is Game Models? Explain its Terminology? Q.2. A Management students identifies the following list of activities and sequencing along with the time estimates for various activites related to the completion of his project.

a. Construct the Project Network. b. Find the Expected duration and Variance of each activity. c. Find the Critical Path and the Expected Project completion time. d. What is the Probability of completing the project on or before 35 days? Q.3. The Following is a table showing details of a Project:-

Indirect Cost is Rs.400 Per Day Find the optimum duration and the associated minimum Project Cost. Q.4. A company is considering the purchases of new machine at Rs.15000. The economic life of the economic life of the machine is expected to be 8 years. The salvage value of the end machine at the of the life will be

Rs. 3000. The annual runing costs are estimated to be Rs. 7000. a. Assuming an interest rate of 5% determine the present worth of future costs of the proposed machine.

b. Compare the new machine with the presently owned machine that has an annual operating cost Rs.5000

and cost of repair Rs.1500 in the second year with an annual increases of Rs.500 in the Subsequent years Q.5. The Failure rates of 1000 street bulbs in a colony are summarized in table.

The cost of replacing on indivudual bulb is Rs.60. if all the bulbs are replaced simultaneouly it would cost Rs.25 per bulb. i) Replace the bulbs individually when they fail. ii)Replace all the bulbs simultaneoulsy at fixed intervals and replace the individual bulbs as and when they fail in service during the fixed interval.

SECTION B Q.6.a) Find an optimal sequence for the following sequencing problem four jobs and five machines when passing is not allowed of which processing time (in hours) is given below:-

Q.6.b) Find the sequence that minimizes the total elapsed time required to complete the following tasks an two machines.

Q.7. A firm has a single channel service station with the following arrival and service time probability distribution.

Service Time Probability (minutes) 10 0.1 5 0.08 15 0.25 10 0.14 20 0.3 15 0.18 25 0.25 20 0.24 30 0.1 25 0.22 30 0.14 the customer's arrival at the service station is random phenomenon and the time between the arrival varies from 10min to 30min. The service time varies from 5min to 30min. The queuing process begins at 10.am and proceeds for nearly 8 hours. An arrival goes to the service facility immediately if it is free otherwise it will wait in a queue. The queue discipline is first-come first served. If the attendent wages are Rs.10 per hour then wourld it be an economical proposition to engage a second attandent? Answer using Monte Carlo Simulation Technique. Inter Arrival Time(Minutes)

Probability

Q.8. A backery keeps stock of a popular brand of cake, previous experience shows the daily demand pattarn for the item with associated probabilities as given below:-

Use of the following sequence of random numbers to stimulate the demand for next 10 days. Random No. 25 39 65 76 12 05 73 89 19 49 Also estimate the daily average demand for the cakes on the basis of stimulated data. Q.9. Alpha logistic company has to load a cargo out of four items whose details are shown in table. The maximum weight of the cargo is 7 tons. Find the optimal cargo loading using dynamic Programming method such that the total return is maximized.

Q.10. Recent developments in the field of computer technology have enable operation research to integrates its models into informations system and thus make itself a part of decision-making procedures of many organisation. Comment.

Activity A B C D E F G H I J K L M

Description Search of literature Deciding the Project Preliminiary Work Formal Proposal Project Committee's Approval Progress Report Formal Research Data Collection Analysis Conclusion Draft Final Draft Presentation

Activity Time (days) Immediate Predecessor Optimistic Likely Pessimistic 2 6 9 2 4 12 B 1 1.5 5 C 1 2 3 A,D 1.5 2 4.5 E 0.5 1 1.5 A,D 4.5 5 11.5 E 2 5 8 G,H 4 5.5 10 I 1.5 2.5 4.5 I,F 2 3.4 8 J,K 2.5 3 1.4 L 0.5 1 1.5

a. Construct the Project Network. b. Find the Expected duration and Variance of each activity. c. Find the Critical Path and the Expected Project completion time. d. What is the Probability of completing the project on or before 35 days?

Ac

Activity

Immediate Predecessor

A B C D E F G

B B B E A,D,C

Normal Time(weeks) 10 8 5 6 8 5 12

Crash

Cost(Rs.000) 20 15 8 11 9 5 3

Time(weeks) 7 6 4 4 5 4 8

Cost(Rs.000) 30 20 14 15 15 8 4

Indirect Cost is Rs.400 Per Day Find the optimum duration and the associated minimum Project Cost.

JOB A B C D

M1 7 6 5 8

M2 5 6 4 3

MACHINE M3 2 4 5 3

M4 3 5 6 2

Additional cost to s

Union strat Company strategies C1 C2 C3 C4

Activity A B C

Description Search of literature Deciding the Project Preliminiary Work

Immediate Predecessor B

Activity Time (days) Optimistic 2 2 1

D E F G H I J K L M

Activity

Immediate Predecessor

A B C D E F G

B B B E A,D,C

Formal Proposal Project Committee's Approval Progress Report Formal Research Data Collection Analysis Conclusion Draft Final Draft Presentation

C A,D E A,D E G,H I I,F J,K L

Normal Time(weeks) Cost(Rs.000) 10 20 8 15 5 8 6 11 8 9 5 5 12 3

1 1.5 0.5 4.5 2 4 1.5 2 2.5 0.5

Crash Time(weeks) 7 6 4 4 5 4 8

Item (i) Weight (wi)/Unit (in tons) Return (ri)/Unit (in rupees)

1 2 1000

2 1 400

3 4 2100

Failure Rates of Street Bulbs End of Month 1 2 3 4 Probability of failure to 0.05 0.2 0.4 0.65 date

Item (i) Weight (wi)/Unit (in tons)

1 2

2 1

Return (ri)/Unit (in rupees)

1000

400

3 4

5 0.85

6 1

4 3

2100 1400

M5 9 10 8 6

MACHINE JOB

JOB M1

M2

A B C D

7 6 5 8

5 6 4 3

TASK MACHI NE-1 MACHI NE-2

A

B

2

5

6

8

Additional cost to steel company Union strategies U1

U2

U3

U4

2.5

2.7

3.5

0.2

2 11.4 3

1.6 1.2 1.4

0.8 1.5 1.9

0.8 1.3 0

Activity Time (days) Likely Pessimistic 6 9 4 12 1.5 5

2 2 1 5 5 5.5 2.5 3.4 3 1

Crash Cost(Rs.000) 30 20 14 15 15 8 4

3 4.5 1.5 11.5 8 10 4.5 8 1.4 1.5

4 3 1400

Inter Arrival Time(Minutes) 10 15 20 25 30

MACHINE

Probability 0.1 0.25 0.3 0.25 0.1

Service Time Probability (minutes) 5 0.08 10 0.14 15 0.18 20 0.24 25 0.22 30 0.14

M3

M4

M5

2 4 5 3

3 5 6 2

9 10 8 6

C

D

E

F

G

H

I

4

9

6

8

7

5

4

7

4

3

9

3

8

11