IV Semester M.B.A. Degree Examination, July 2016 (2007-08 Scheme) MANAGEMENT P – 4 : Advanced Operations Research Time : 3 Hours
Max. Marks : 75 SECTION – A
1. Answer any six questions. Each carries 2 marks.
(2× 6 =12)
a) Define LPP. b) What do you mean by optimal solution ? c) What is saddle point ? d) Define simulation. e) Define Group replacement. f) Explain Kendall’s notation a/b/c : d/e. g) Define a loop in transportation problem. h) Define float. SECTION – B Answer any three questions. Each carries 8 marks.
(3× 8 = 24)
2. Explain the steps in simulation process. 3. Explain in brief the main characteristics of queuing system. 4. Solve the following LPP by Graphical method Max Z = 6 x1+12 x2 subject to the constraints x1 + 2 x2 ≤ 10 2 x1 – 5 x2 ≤ 20 x1 + x2 ≤ 15 and x1 ≥ 0, x2 ≥ 0. P.T.O.
PG – 955
*PG955*
-2-
5. A truck owner finds from his past records that the maintenance costs per year of a truck whose purchase price is Rs. 8,000 are as below : Year
:
1
2
3
4
5
6
7
8
Maintenance cost : 1000
1300
1700 2000 2900 3800 4800 6000
Resale price
2000
1200
: 4000
600
500
400
400
400
Determine at what time it is profitable to replace the truck. 6. What is a game in game theory ? What are the properties of a game ? Explain the best strategy on the basis of minimax criterion of optimality. SECTION – C Answer any two questions. Each carries 12 marks.
(2×12=24)
7. Discuss in brief linear programming as a technique for resource utilization. 8. Find the optimal solution for the following transportation problem. M1
M2
M3
M4
M5
Supply
F1
4
2
3
2
6
8
F2
5
4
5
2
1
12
F3
6
5
4
7
7
14
Demand
4
4
6
8
8
9. A firm has a single channel service station with following arrival and service time probability distributions. Inter arrival time (minutes)
Probability
Service time (minutes)
Probability
10
0.10
5
0.08
15
0.25
10
0.14
20
0.30
15
0.18
25
0.25
20
0.24
30
0.10
25
0.22
30
0.14
*PG955*
PG – 955
-3-
The customer’s arrival at the station is a random phenomenon and the time between the arrivals varies from 10 minutes to 30 minutes. The service time varies from 5 minutes to 30 minutes. The queuing process begins at 10. a.m. 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 FCFS. If the attendants’ wares are Rs. 10 per hour and the customer’s waiting time costs Rs. 15 per hour, then would it be an economical proposition to engage a second attendant ? Use monte Carlo technique. SECTION – D Compulsory :
(1×15=15)
10. The owner of chain of fast food restaurants is considering a new system for accounting and inventory control. A computer company sent the following information about the computer system installation.
Time (days)
Immediate Predecessor
Optimistic
Most likely
Pessimistic
A
−
4
6
8
B
A
5
7
15
C
A
4
8
12
D
B
15
20
25
E
B
10
18
26
F
C
8
9
16
G
E
4
8
12
H
D, F
1
2
3
I
G, H
6
7
8
Activity
a) Construct network diagram for the project. b) Determine the critical path and compute the expected completion time. c) Determine the probability of completing the project in 55 days. ———————
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