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Cms 300 Operation Research Ii Question Paper
Cms 300 Operation Research Ii
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2011
1
UNIVERSITY EXAMINATIONS: 2010/2011
EXAMINATION FOR THE BACHELOR OF COMMERCE
CMS 300 OPERATION RESEARCH II
DATE: DECEMBER 2011 TIME: 2 HOURS
INSTRUCTIONS: Answer Question ONE and any other TWO Questions
Question 1 (30 Marks)
(a) Differentiate between the following terms in network analysis:
(i) A stage coach problem and a reliability problem [2 Marks]
(ii) A source and a sink. [2 Marks]
(b) The following gives the running costs per year and resale prices of an electrical
equipment whose purchase price is US dollars 5000
Year 1 2 3 4 5 6
Running cost ($) 1400 1600 1700 2000 2100 2400
Scrap value ($) 3500 2800 2000 1800 1000 1000
Determine when the equipment should be replaced. [6 Marks]
(c) The following failure rates have been observed for a certain type of light bulb:
End of week 1 2 3 4 5 6 7 8
Probability of failure
to date
0.05 0.13 0.25 0.43 0.68 0.88 0.96 1.00
Given that the number of light bulbs in the beginning are 1000, and the cost of replacing an
individual failed bulb is Kshs 35. The decision is made to replace all bulbs simultaneously at fixed
intervals, and also to replace individual bulbs as they fail in services. If the cost of group
replacement is Kshs 25 per bulb.
(i) Determine the replacement policy [8 Marks]
2
(ii) Find the best interval between group replacements. [2 Marks]
(d) Suppose that a player in a gambling game has $1 and with each play of the game wins $1
with a probability p > 0 or loses $1 with probability1- p > 0 . The game ends when the player
either accumulates $3 or goes broke. This game is a Markov chain with states representing the
player’s current holding of money, that is $0, $1, $2, or $3, and with transition matrix given by
State 0 1 2 3
3
2
1
0
? ? ? ?
?
?
? ? ? ?
?
?
-
-
0 0 0 1
0 1 0
1 0 0
1 0 0 0
p p
p p
i. Draw the state transition diagram for this matrix [6 Marks]
ii. Hence using explanations identify which states are: absorbing states, and transient states
[4 Marks]
Question 2 (20 Marks).
(a) Explain the main objective for a Shortest route problem [2Marks]
(b) A Sales agent of an insurance company wishes to travel from his office at point A to town
G. The table below shows the distances between intermediate points to G.
Towns A-B A-D A-C B-E D-E C-F F-G E-G
Distance (Km) 5 7 14 5 4 3 3 6
(i) Develop a master list for the above problem. [3 Marks]
(ii) Use the shortest route algorithm to find the shortest route from A to G.
[7 Marks]
(c) The Western Circuit Management needs to determine under which roads telephone lines
should be installed to connect all stations with a minimum total length of line (in units). Nodes and
distances for potential links are given below.
B
A
O
T
D
5
4
7
3
2
4 C
4 E
1
5
7
1
3
Starting from node O, outline step by step solution for this problem [8 Marks]
Question 3 (20 Marks)
(a) (i) Explain the term Stochastic process [2 Marks]
(ii) Explain Five characteristics of a Markov Chain. [5 Marks]
(b) A manufacturing company has a certain piece of equipment that is inspected at the end of
each day and classified as just overhauled, good, fair or inoperative. If the item is inoperative it is
overhauled, a procedure that takes one ay. Suppose the four classifications can be denoted by 1, 2,
3 and 4 respectively. Assume that the working condition of the equipment follows a markov chain
with a transition matrix
1 2 3 4
4
3
2
1
? ? ? ?
?
?
? ? ? ?
?
?
1 0 0 0
0 0
0 0
0 0
2
1
2
1
2
1
2
1
4
1
4 3
If it costs US$ 1050 to overhaul a machine (including lost time) on average and US$ 750 as
production lost if a machine is found inoperative. Using steady state probabilities, compute the
expected per day cost of maintenance. [13 marks]
Question 4 (20 MARKS)
(a) (i) Explain any three properties of dynamic programming problems [6 Marks]
(ii) Explain Any Two application areas of dynamic programming problems [4 Marks]
(b) A company has to transport some goods from city A to city J. The cost of transportation
between different cities is given in the following network.
Find the optimal route connecting cities A and J using dynamic programming algorithm.
5
3
2
7
6
7
4
3
9
9
3
4
6
A
B
C
D
F
E
I
H
G
J
5
6
8
3
4
[10 Marks]
Question 5 (20 Marks)
(a) Define a general non linear programming problem explaining each parameter used.
[4 Marks]
(b) A manufacturing company produces two products: radios and TV sets. sales price
relationship for these two products are given below:
Product Quantity demanded Unit price
Radios 1,500-5p p
TV sets 3,800-10q q
The total cost function for these two products are given by 200x + 0.1x2 and 300x + 0.1y2
300y+0.1y2, respectively. The production takes place on two assembly lines. Radio sets are
assembled on assembly line I and TV sets are assembled on assembly II. Because of the limitations
of the assembly line capacities, the daily production is limited to no more than 80 radio sets and 60
TV sets. The productions of both products require electronic components. The production of each
of these sets requires five units and six units of electronic equipment components, respectively.
The electronic components are supplied by another manufacturer, and the supply is limited to 600
units per day. The company has 160 employees, that is, the labour supply amounts to 160 mandays.
The company has set 1 man-day of labour, whereas 2 man-days of labour are required for a
TV set. The company wish to find the number of units of radio and TV sets it should produce in
order to maximize the total profit.
(i) Formulate the above problem as a non linear programming problem. [10 Marks]
(ii) Write a LINGO program statements that would solve the above problem [6 Marks]
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