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Operations Research I Question Paper

Operations Research I

Course:Bachelor Of Commerce

Institution: Kca University question papers

Exam Year:2009

UNIVERSITY EXAMINATIONS: 2009/2010
SECOND YEAR STAGE I EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 201: OPERATIONS RESEARCH I (SATURDAY)
DATE: DECEMBER 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
a) Briefly describe the historical developments of operations research during the World War II
(5 Marks)
b) State four components of holding costs (4 Marks)
c) Outline the assumptions made while solving a transportation problem (4Marks)
d) A company is interested in the analysis of two products which can be made from the idle time of
labour and machine. It was found on investigation that the labour requirement for the first and
second products was 2 and 3 hours respectively and the total available man hours was 24. Only
product 1 requires machine hour utilization of one hour per unit and at present only 9 spare
machine hours are available. Product 2 requires one unit of a by-product per unit and the daily
availability of the by-product is 6 units.According to the marketing department the sales potential
of product 1 cannot exceed 5 units.In a competitive market, product 1 can be sold at a profit of sh 3
and product 2 at a profit of sh 5 per unit.
Required
Formulate the problem as linear programming problem. (6 Marks)
e) Greencom ltd intends to launch a new mobile handset into the market. The management of the
company are uncertain of some variables, namely the selling price and the annual sales volume of
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the mobile handsets. The following information relates to the possible values of the above variables
and their associated probabilities:
Selling price Probability Annual sales probability
per unit(sh) Volume(units)
6,000 0.2 1,000,000 0.3
6,500 0.5 2,000,000 0.4
7,000 0.3 3,000,000 0.3
Additional information:
1. Variable cost per unit is expected to remain constant at sh 5,500 over the period under
consideration.
2. Fixed costs per annum amount to sh 900,000,000.
Required
i) Simulate the company’s profit for a period of 5 years using the following random
numbers: 1,4,3,0,8,2,7,9,4,5 (9Marks)
ii) The average annual profit of the company (2 Marks)
QUESTION TWO
a) Mr Kimondo manages a large movie theatre complex called cinema I,II,III and IV. Each of the
four auditoriums plays a different film. The schedule is set so that starting times are staggered to
avoid the large crowds that would occur if all the four movies started at the same time. The theatre
has a single ticket booth and a cashier who can maintain an average service rate of 280 movie
patrons per hour. Service times are assumed to follow an exponential distribution. Arrivals are
poisson distributed and average 210 per hour. In order to determine the efficiency of the current
ticket operations, Kimondo wishes to examine several queue operating characteristics.
Required
(i) Find the average number of movie goers waiting in the queue to purchase a ticket.
(ii) What percentage of time is the cashier busy?
(iii)What is the average time a customer spends in the system?
(iv)What is the average time a customer spends in the queue to get to the ticket window?
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(v) What is the probability that there are more than two people in the system? More than three
people? More than four? (15 Marks)
b) State practical limitations of queuing theory (5 Marks)
QUESTION THREE
a) Explain the difference between assignment and transportation problems. (4 Marks)
b) Joyland fast-food chain wants to build four stores in Nairobi. In the past the chain used five
different construction companies and having been satisfied with their work, they have been
invited to bid on each job.The final bids (in thousand of shillings) were as shown in the table
below:
JOBS
Construction
companies
STORE 1 STORE 2 STORE 3 STORE 4
A 171 158 165 168
B 176 155 163 168
C 175 156 165 172
D 165 153 161 170
E 178 159 167 166
Since the fast-food chain wants to have each of the new stores ready as quickly as possible, it
will be award at most one job to one company.
Required
i) The assignments to be made in order to minimize the total cost. (12 Marks)
ii) The minimum cost of using the construction companies . (2 Marks)
iii) The construction company which will not be assigned any job. (2 Marks)
QUESTION FOUR
HPI ltd is a distributor of an industrial chemical . The chemical is supplied in drums which have to be
stored at a controlled temperature. The company’s objective is to maximize profits. However the
management team disagrees on the stock control policy and holds the following different views:
The managing directors view:
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The company’s managing director (MD) wishes to improve the stock holding policy by applying the
economic order quantity (EOQ) model. Each drum of the chemical costs shs 5,000 and it is sold for shs
6,000. The annual demand is estimated to be 10,000 drums which the MD assumes to be evenly
distributed over 300 working days in a year. The cost of delivery is estimated to be shs 2,500 per order
and the annual variable holding cost per drum at shs 4,500 plus 10% of the purchase price.
Using these data the MD calculates the EOQ and proposes that it should be used as the basis for future
purchasing decisions of the industrial chemical.
The finance director’s view:
The company’s finance director points out that there is a three days lead time for an order and that
demand has not been entirely even over the past year. Moreover if the company has no drums of the
chemical in stock, it will lose specific orders and contribution since potential customers will source
the chemical from competitors. He gives the frequency of the lead time demand over the last year as
follows:
Demand during lead time Frequency
(No. of drums)
106 4
104 10
102 16
100 40
98 14
96 14
94 2
Under these circumstances, the MD decided to seek further advice on the course of action to be taken
by the company.
Required:
a) The EOQ as originally determined by the company’s managing director. (6 Marks)
b) The optimal safety stock level assuming that the supplier’s contract requires that the order
quantity be constant for all the orders in a year. (14 Marks)
5
QUESTION FIVE
East African Motors Ltd. has listed the following activities as necessary in introducing a new model in
the market.
Activity Preceding Activity Expected Duration (week)
I - 6
II - 3
III I 5
IV I 4
V I 3
VI III 5
VII IV 5
VIII II,IV,V 5
IX VIII 2
X VI,VII,IX 3
Required:
a) Draw the critical path network for the project and determine the critical path and its duration.
(7 Marks)
b) If the start of activity II is delayed by 3 weeks, activity V by 2 weeks and activity VII by 2
weeks, how is the total time for the project affected? (4 Marks)
c) Assume that the times given in the table above are the expected times of the activities, the
durations of which are normally distributed with the following standard deviations:
Activity I II III IV V VI VII VIII IX X
Standard
Deviation 1 0.5 1 1 0.5 0.5 1 1 0.5 1
The costs of the project are estimated to be Sh.250,000. If it is completed within 24 weeks the
expected returns should be about Sh.2,500,000 but if the deadline of 24 weeks is not met, the
product will fall to penetrate the market and a net revenue of only Sh.50,000 is expected.
Determine the expected profit on this project.
(Ignore the delays referred to in (b) and the possible effect of uncertainty in non-critical
activities). (9 Marks)
(Total: 20 Marks)

Operations Research I Question Paper

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