Reg. No. ________
Karunya University
(Karunya Institute of Technology and Sciences)
(Declared as Deemed to be University under Sec.3 of the UGC Act, 1956)
End Semester Examination – November/ December - 2012
Subject Title:
Subject Code:
RESOURCE MANAGEMENT TECHNIQUES
09MA303
Time: 3 hours
Maximum Marks: 100
Answer ALL questions (5 x 20 = 100 Marks)
1.
Compulsory:
a.
b.
A company has three operational departments (weaving, processing and packing) with
capacity to produce three different types of clothes namely suitings, shirtings and woolens
yielding the profit Rs. 2, Rs.4 and Rs.3 per meter respectively. One meter suiting requires
3 minutes in weaving, 2 minutes in processing and 1 minute in packing. Similarly one
meter of shirt requires 4 minutes in weaving, 1 minute in processing and 3 minutes
packing while one meter wollen requires 3 minutes in each department. In a week, total
run time of each department is 60,40 and 80 hours for weaving, processing and packing
departments respectively. Formulate this on LLP.
(5)
Use penalty method to solve:
x
2
x
3
x
x
Maximize z
1
2
3
4
Subject to the constraints
x
2
x
3
x
15
x
2
x
5
x
20
2
x
3
x
15
,2
, x1  2 x2  x3  x4  10 , x
1
2
3
1
2
3
1
2
3
x
0
.
1,x
2,x
3,x
4
2.
a. Explain Primal LPP and Dual LPP.
(5)
b. Solve the transportation problem for which the costs, origin availabilities and destination
requirements are given in the following table:
(15)
Destinations
1 2
1 1 2
Origins
2 3 3
3 4 2
4 3 1
Requirements
20 40
3.
(15)
a.
b.
3 4 5 6
1 4 5 2
2 1 4 3
5 9 6 2
7 3 4 6
30 10 50 25
Available
30
50
75
20
(OR)
Explain MODI method for finding the optimality of transportation problem.
(10)
Prove using duality theory that the following LPP is feasible but has no optimal solution.
Minimize Zx1x2x3
Subject to
x1 x3 4
x1 x2 2x3 3
(10)
and x1, x2, x3 0
4.
a.
Write down the algorithm for dual simplex method.
(10)
[P.T.O]
b.
5.
a.
b.
6.
a.
b.
7.
a.
b.
8.
a.
b.
9.
a.
b.
An airline company has drawn up a new flight schedule involving five flights. To assist in
allocating five pilots to the pilots, it has asked them to state their preference scores by
giving each flight a number out of 10. The higher the number, the greater is the preference.
Certain of these flights are unsuitable to some pilots owing to domestic reasons. These
have been marked with M.
Flight Number
1
2
3
4
5
A
8
2
M
5
4
B
10 9
2
8
4
Pilot
C
5
4
9
6
M
D
3
6
2
8
7
E
5
6
10
4
3
What should be the allocation of the pilots to flights in order to meet as many preferences
as possible?
(10)
(OR)
Bringout the difference between the transportation problem and assignment problem. (5)
A company purchases 10,000 items per year for use in its production shop. The unit cost is
Rs. 10 per year, the holding cost is Rs.80 per month and cost of making a purchase is
Rs. 200.Determine the following: no shortages are allowed, optimal order quantity,
optimal total yearly cost, number of orders per year and time between the orders.
(15)
Explain Johnson algorithm to solve two jobs through M – Machines.
(10)
A book binder has one printing press, one binding machine, and the manuscripts of a
number of different books. The time required to perform the printing and binding
operations for each book are shown below. Determine the order in which books should be
processed, in order to minimize the total time required to turn out all the books:
Book
:
1 2
3 4 5 6
Printing time (hrs)
:
30 120
50 20 90 110
Binding time (hrs)
:
80 100
90 60 30 10
(10)
(OR)
Explain the components of a Queuing system.
(5)
A super market has two girls running up sales at the counter. If the service time for each
customer is exponential with mean 4 minutes, and if people arrive in a Poisson fashion at
the rate of 10 an hour
i. What is the probability of having to wait for service?
ii. What is the expected percentage of idle time for each girl?
iii. If a customer has to wait, what is the expected length of his waiting time?
(15)
What are the basic steps in simulation?
(5)
The cost of a machine is Rs. 6,100 and its scrap value is Rs.100. The maintenance costs
found from experience are as follows:
Year
:1
2
3
4
5
6
7
8
Maintenance cost (Rs.):100
250
400
600
900
1200
1600
2000
When should the machine be replaced?
(15)
(OR)
What are the advantages and limitation of simulation techniques?
(10)
The demand per day for a particular item has the following probability distribution.
Demand
:
2
3
4
5
6
Probability
:
0.10
0.20
0.35
0.27
0.08
(10)
Simulate the demand for ensuring 10 days using the following random numbers: 21, 81,
92, 23, 96, 20, 68, 57, 79, 84.