LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.C.A. DEGREE EXAMINATION - COMPUTER APP.
FIFTH SEMESTER – NOVEMBER 2012
CA 5953 - RESOURCE MANAGEMENT TECHNIQUES
Date : 15/11/2012
Time : 9:00 - 12:00
Dept. No.
Max. : 100 Marks
CA5953 RESOURCE MANAGEMENT TECHNIQUES- SET 2
PART A
Answer ALL Questions
(10 X 2 = 20 Marks)
1. What is entry criteria in simplex procedure?
2. When a linear programming problem is said to have infeasible solution?
3. Write an algorithm for Column Minima method.
4. Define Travelling Sales Man problem.
5. What is integer programming problem?
6. How Gomory’s constraint is formulated in pure integer programming problem?
7. Define the following terms: i. Total Float ii. Free Float.
8. Distinguish between PERT and CPM.
9. What is queue discipline?
10. In a bank, customers on an average arrive 10 per hour. Each customer spends 5 minutes to get
service. Is single counter enough to handle the queue?
PART B
Answer ALL Questions
11a. Solve graphically the following linear programming problem.
Maximize Z = 3x1 + 5x2
Subject to 4x1 + 3x2 ≤ 12
x1 + 4x2 ≤ 4
2x1 + 5x2 ≤ 10
x1 , x2 ≥ 0
(or)
11b. Solve the following linear programming problem
Maximize Z = 4x1 + 3x2
Subject to 4x1 + 3x2 ≤ 12
x1 + x2 ≥ 2
x1 , x2 ≥ 0
(5 X 8 = 40 Marks)
12a. Find the initial allocation to the following transportation problem by VAM.
Destination→
D1
D2
D3
D4
Availability
Origin↓
O1
7
9
3
2
16
O2
4
4
3
5
14
O3
6
4
5
8
20
Requirement
11
9
22
8
(or)
12b. . A department has 4 employees with 4 jobs to be performed. The time, in hours, each employee
will take to perform each job is given in the following matrix. How should the jobs be allocated to the
employees so as to minimize the total time.
Employee→
I
II
III
IV
Job↓
A
8
26
17
11
B
13
28
4
26
C
38
19
18
15
D
19
26
24
10
13a. Describe Gomory’s cutting plane algorithm to solve pure integer programming problem
(or)
13b. Explain branch and bound method for integer programming problem.
14a. A small project consists of 7 activities, the details of which are given below:
Activity
A
B
C
D
E
F
G
Predecessor A
A
C
B
D,E
F
Activity
T0
1
2
3
4
3
2
3
Tm
4
5
3
10
6
5
6
Tp
7
20
3
22
15
14
9
i.
ii.
iii.
Draw network diagram and find critical path.
Find mean and standard deviation of each activity.
Find mean and standard deviation of the whole project.
(or)
14b. Given the following information:
Activity
1-2
1-3
1-4
Duration(Days) 3
2
7
2-5
6
2-7
9
3-5
5
4-7
15
5-6
10
6-7
7
i.
ii.
Draw network diagram and determine the critical path.
For each activity, find earliest start and finish, latest start and finish, total float, free float and
independent float.
15a. In a tool crib, manned by a single assistant, operators arrive at the tool crib at the rate of 10 per hour.
Each operator needs 3 minutes on an average to be served. Find out the loss of production due to time
lost in waiting for an operator in a shift of 8 hours if the rate of production is 100 per shift.
(or)
15b. A repair shop attended by a single mechanic has an average of 4 customers per hour. The service
time of mechanic is 6 minutes. Arrivals are Poisson and service rate has the exponential distribution.
Find the following:
i.
Average time spent by a customer in the shop.
ii.
Busy time of the mechanic.
iii.
Average number of customers in the queue.
PART C
Answer any TWO Questions
(Question 16 is compulsory)
16a. Solve the following linear programming problem
(2 x 20 = 40 Marks)
Maximize Z = x1 +2x2 + x3
Subject to 2x1 + x2 - x3 ≤ 2
2x1 - x2 + 5x3 ≤ 6
4x1 + x2 + x3 ≤ 6
x1 , x2, x3 ≥ 0
16b. Describe MODI method to find the optimal solution for a transportation problem.
17a. A company has 3 production centers and 4 warehouses. The production capacity at each center and
storing capacity at each warehouse and the unit cost of transport from a center to a warehouse are given it
the following matrix. Find the minimum transportation cost.
Warehouse→ W1
W2
W3
W4
Availability
Production
center↓
C1
19
30
50
10
7
C2
70
30
40
60
9
C3
40
8
70
20
18
Requirement 5
8
7
14
17b. Five jobs 1,2,3,4,and 5 are to be assigned to 5 persons A,B,C,D, and E of which the job 2 can not be
performed by person A, job 3 can not be done by person C and job 1 can not be done by person E. The
time taken, in minutes, by each of them on the jobs those that they can perform is given. Work out the
optimal assignment cost.
Job→
1
2
3
4
5
Person↓
A
16
18
22
25
B
14
12
13
16
17
C
17
14
11
18
D
10
8
5
12
15
E
20
15
7
3
18a. What are the characteristics of queuing system?
18b. A tax consultant firm has 4 service centers in its office. Customers arrive on an average 10 per
hour. The average service time is 20 minutes. Calculate the average no. of customers in the system,
average no. of customers waiting to be serviced, average time a customer spends in the system and
waiting for service. Calculate busy time of tax consultant on a 8-hour day.