Code: 14E00205
MBA II Semester Supplementary Examinations December/January 2015/2016
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Time: 3 hours Max. Marks: 60
OPERATIONS RESEARCH
(For students admitted in 2014 only)
All questions carry equal marks
*****
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SECTION - A
Answer the following: (05 X 10 = 50 Marks)
- Write a short note on cross-functional specialization requirements in operations research applications.
OR
A company produces two types of leather belts Type-A and Type-B. A type gives a profit of Rs.10/- per belt and B-gives Rs.5/- per belt. The raw material supply is sufficient for making 850 belts per day. Type-A requires a special buckle and 500 are available per day. There are 700 buckles available for Type-B. Type A needs twice as much time as that required for Type-B and the company can produce 500 belts, if all of them were of Type-A. Formulate a LP model fro this problem and solve it graphically. - Find the optimum transportation plan such that the total transportation cost is lowest.
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Markets
Plant
S1 S2 S3 S4 Capacity
F1 4 6 8 13 50
F2 13 11 10 8 70--- Content provided by FirstRanker.com ---
F3 14 4 10 13 30
F4 9 11 13 8 50
Total 25 35 105 20OR
- The captain of a cricket team has to allot five middle-order batting positions to five batsmen. The average runs scored by each batsman at these positions are as follows:
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Batsmen
Batting positions
II III IV V
P 40 40 35 25 50
Q 42 30 16 25 27--- Content provided by FirstRanker.com ---
R 50 48 40 60 50
S 20 19 20 18 25
T 55 53 58 60 59
Find the assignment of batsmen to position that would give the maximum number of runs for the team. - A workstation has six jobs waiting to be processed. They arrived at the end of day 0 and it is now the beginning of day I. It is now time zero. Times are expressed in terms of days.
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Job Time Since
Job Arrived
Processing
Time Due Date
A 12 8 24--- Content provided by FirstRanker.com ---
B 7 2 11
C 18 6 31
D 5 12 25
E 6 7 8
F 19 5 6--- Content provided by FirstRanker.com ---
Use the information in the above table, what sequence would you use if you want to minimize the make span of the jobs. -
OR
Solve the game graphically and find the optimum strategies for each of the player.
Player - B
1 -3 3 5 -1--- Content provided by FirstRanker.com ---
6 4 1 2 2 -5
0
Player - A - A crew of mechanics at the department of transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. Find out various characteristics of the queue-such as waiting time in the queue/system, average queue length/system length and idle time for the service.
OR
- In railway marshalling yard, goods trains arrive at the rate of 30 trains per day. Assuming that inter- arrival time and service time distribution follows an exponential distribution with an average of 30 minutes, calculate the following:
(a) The mean queue size.
(b) The probability that queue size exceeds10.
(c) If the input of train increases to an average of 33 per day, what will be the changes in (a) and (b)? - New age power solutions limited provides electric generator services [of 5 KVA, 10 KVA, 25 KVA capacities] on lease basis or daily rentals to apartments, industrial activities, public meetings, marriage halls etc. As the maintenance cost increases rapidly the company replaces generators periodically. The purchase price of a 5 KVA generator is INR 2,50,000. Annual maintenance and repairs cost and resale value are detailed in the following table.
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Year Resale value (INR Maintenance & repairs
cost (INR)
is no 6
7
1 2 3 4 5 8--- Content provided by FirstRanker.com ---
150000 120000 100000 75000 50000 50000 50000 25000
20000 25000 30000 40000 50000 75000 100000 125000
Assuming that there is no time value for money, determine the optimal replacement policy.OR
- In a youth hostel there are 100 rooms, each room is fitted with a tube light. The bulbs are replaced when they fail individually and group replacement is also done at regular intervals. The probability of failure of tube lights for the four quarters is given below:
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Q1 Q2 Q3 Q4
0.15 0.20 0.50 0.15
Cost of individual replacement is INR 125/-, whereas for group replacement, the cost is INR 30/- suggest a suitable replacement policy.
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SECTION -B
(Compulsory Question) 01 X 10 = 10 Marks
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- Case study:
Find out the critical path for the project, whose activities, precedence relation and durations are given below. Find out mean project completion time and estimated standard deviation in completing the project.
(a) Find out the probability of the project takes more than 30 weeks to complete.
(b) Find out the probability of the project gets completed fewer than 21 weeks.
S.No Activity Precedence relationship Duration - [in weeks]--- Content provided by FirstRanker.com ---
Optimistic Normal Pessimistic
1 A 1 3 5
2 B A 1 2 3
3 C A 2 5 8
4 D A, B 1 4 7--- Content provided by FirstRanker.com ---
5 E C 2 2 2
6 F D, E 1 5 9
7 G B 2 6 10
8 H D 3 6 15
9 | G, H 1 2 3--- Content provided by FirstRanker.com ---
10 J F, H 2 5 8
11 K G 4 9 14
12 L K 1 2 3
13 M L 13 2 3
14 N I,J 4 5 6
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