Operations Research Question Paper
Operations Research
Course:Bachelor Of Science In Information Technology
Institution: Kca University question papers
Exam Year:2011
UNIVERSITY EXAMINATIONS: 2010/2011
THIRD YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
SCIENCE IN INFORMATION TECHNOLOGY
BIT 2207: OPERATIONS RESEARCH
DATE: APRIL 2011 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
a) Explain five essential characteristics of Operations Research, citing relevant examples. (10 Marks)
b) Explain any two types of models used in Operations research. (6 Marks)
c) Using relevant examples, explain the following terms as used in the Linear Programming model:
i) Entering variable
ii) Leaving variable
iii) New pivot equation
iv) Feasible solution (4 Marks)
d) Using appropriate examples, explain any two applications of the sequencing problem in your daily
life. (4 Marks)
(e) The firm you work for is thinking of replacing a particular machine whose cost price is K£ 12,200.
The scrap value of this machine is only K£ 200. The maintenance costs are found to be as follows:
Year 1 2 3 4 5 6 7 8
Maintenance
costs (K£)
220
500
800
1,200
1,800
2,500
3,200
4,000
Determine when the firm should get the machine replaced, assuming that the value of money doesn’t
change with time. (6 Marks)
2
QUESTION TWO
a) List the three methods of obtaining a basic feasible solution in a Transportation problem. Which is
the best among them and why? (5 Marks)
b) Using an appropriate example explain Degeneracy in a Transportation problem. How would you
resolve the degeneracy? (3 Marks)
c) Four different jobs can be done on four different machines. The set-up and take down time costs are
assumed to be prohibitively high for changeovers. The matrix below gives the cost in K£ of
producing job i on machine j
Machines
Jobs M1 M2 M3 M4
J1 3 7 11 6
J2 8 5 9 6
J3 4 7 10 7
J4 10 4 8 3
Required
(i)How should the jobs be assigned to the various machines so that the total cost is minimized?
(ii) What is the total cost of the assignment in (i) above? (12 Marks)
QUESTION THREE
a) Define event, activity, looping, dangling and event float as used in Network Analysis. (5 Marks)
b) (i) Construct a PERT network for the following information and determine the critical path and
project duration. (10 Marks)
Activity Immediate
predecessor
Most optimistic
time
Most likely
time
Most
pessimistic time
A - 1 2 3
B A 2 4 6
C A 2 6 10
D B 6 8 10
E C 4 6 8
F C 6 10 14
G E 8 10 12
H F 12 14 16
I G,H 4 8 12
J G,H 10 12 14
K I 2 4 6
L J 6 10 14
(ii) Assuming the schedule allows 40 days to complete the whole project, calculate the probability of
completion by the scheduled date. (5 Marks)
3
QUESTION FOUR
a) Write short notes on the various assumptions made in single channel Queuing theory. (4 Marks)
b) Explain the following terms as used in Queuing theory
(i) Arrival patterns
(ii) Balking, reneging, jockeying and collusion
(iii) Service disciplines (6 Marks)
c) A duplicating machine maintained for office use is used and operated by people in the office who
need to make copies, mostly secretaries. Since the work to be copied varies in length (number of
pages per the original) and copies required, the service rate is randomly distributed but it does
approximate a Poisson distribution having a mean service rate of 10 jobs per hour. Generally, the
requirements for use are random over the 8-hour working day but arrive at the rate of 5 per hour.
Several people have noted that a waiting line develops occasionally and have questioned the policy
of maintaining only one unit. If the time of a secretary is valued at K£ 3.5 per hour, make an
analysis to find;
(i) Equipment utilization (2 Marks)
(ii) The percent time an arrival has to wait (2 Marks)
(iii) The average time spent in the system (2 Marks)
(iv) The average cost of waiting and operating the machine (2Marks)
(vi) The length of queue at any time (2 Marks)
QUESTION FIVE
a) What are the different costs associated with inventory control systems? (4 Marks)
(b) Explain both the analytical and graphical methods of obtaining the Economical order quantity.
(6 Marks)
(c) (i) Find the sequence for the following eight jobs that will minimize the total elapsed time for the
completion of all the jobs. Each job is processed in the same order AB. At all times the no passing rule
is considered to be in effect. The servicing times for each machine are given below:
Jobs
Machines I II III IV V VI VII VIII
A 5 4 22 16 15 11 9 4
B 6 10 12 8 20 7 2 21
(ii) Determine the total elapsed time in (i) above and the idle times for both machines (10 Marks)
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