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ORC711S - Operations Research - 2nd Opp - June 2023 |
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n Am I BIA u n IVER s ITY
OF SCIEn CE Ano TECHn OLOGY
FACULTY OF ENGINEERING AND THE BUILT ENVIRONMENT
DEPARTMENT OF Civil, Mining and Process Engineering
QUALIFICATION : Bachelors of Engineering in Mining Engineering
QUALIFICATION CODE: 08BMEG
LEVEL: 7
COURSECODE: ORC711S
COURSENAME: OPERATIONSRESEARCH
SESSION:JUNE 2023
DURATION: 3 HOURS
PAPER:THEORY
MARKS: 100
EXAMINER(S)
MODERATOR:
FIRST OPPORTUNITY QUESTION PAPER
Dr Lawrence Madziwa
Prof Mallikarjun Rao Pillalamarry
INSTRUCTIONS
1. Answer all questions.
2. Read all the questions carefully before answering.
3. Marks for each questions are indicated at the end of each question.
4. Please ensure that your writing is legible, neat and presentable.
PERMISSIBLEMATERIALS
1. Examination paper.
THIS QUESTION PAPER CONSISTS OF 5 PAGES (Including this front page)
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l. A mine crusher serves haul trucks. It has a single access lane and one truck controller to
guide the trucks. It takes 12 minutes to navigate the lane, tip and clear the lane. Trucks
arrive at the crusher at the rate of 4 per hour.
[14]
a. Determine the average number of trucks that will stack up waiting to dump the ore.[2]
b. Find the average time a truck must wait in line before it can dump the ore.
[4]
c. Calculate the average time it takes a truck to clear the lane once it has notified the
crusher that it is in the vicinity and want to dump the ore.
[4]
d. The crusher site has a rule that a truck controller can on the average tip a maximum of
45 minutes out of every hour. There must be 15 minutes of idle time available to
relieve the tension. Will this crusher site have to hire an extra air truck controller? [4]
2. You are responsible for transporting three items on a limited space of 4 tons from
Windhoek to Swakopmund. There are three different items that your company can
transport between Windhoek and Swakopmund. Each item has a weight in tons, a net
profit in thousands of dollars, and an unlimited number of items that are available for
shipping as shown in Table below. Use dynamic programming to determine how
many of each item should be shipped to maximize profits.
[20]
Item
1
2
3
Weight
2
3
1
Profit/ Unit($)
31
47
14
Number
Available
unlimited
unlimited
unlimited
3. A new Uranium mine, in Namibia has decided, as a matter of urgency, to build a new
road as an upgrade to the existing one to faci Iitate efficient transportation of materials.
The road wor~s has been divided into five stages which are built simultaneously.
Within Namibia, there are six large companies to undertake the construction of any of
the five stage and each company has been invited to submit a tender for each stage of
the project. The tenders (in millions of Namibian dollars) are as follows:
Company Stage
1
2
3
4
5
A
49
84
63
82
68
B
53
92
62
No bid
67
C
54
86
67
78
68
D
46
86
62
76
No bid
E
57
94
66
83
70
F
50
82
65
80
72
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a. Assuming that none of the companies is large enough to undertake the work of
more than one stage, advise the mine how the five contracts should be
allocated. What is the minimum total cost for the project?
[l 0]
b. The mine is installing power lines to different areas on the mine. The mine
wants to minimize the total length of the power line. The network of all
positions requiring electricity is shown below with the associated distances
between all points. Recommend how to best connect all the positions in the
network.
[1 0]
1
4
\\
11 /
'--._j
c. Discuss three network models that can be used to resolve some of the mining
challenges and give examples of how you can apply them in mining.
[6]
4. Show that the average inventory of an inventory model with backorder is:
Average inventory= (Q-S)2/2Q
[10]
b. Neon lights on the processing plant are replaced at the rate of 100units per
day. The physical plant orders the neon lights periodically. It costs $100 to initiate
a purchase order. A neon light kept in storage is estimated to cost about $0.02 per
day. The lead time between placing and receiving an order is 12 days. Determine
the following optimal order level for this situation, at what point is the order
placed and the associated costs.
[1 0]
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5. A project which is about to start comprises the following activities:
Table I Act1. v1. t.1esdescnpt1on and predecessors
Activity
Immediate preceding
activities
A
-
B
A
C
A
D
C
E
C
F
D,E
G
-
H
A,G
I
G
J
H
K
H
L
J, K
M
F,L
N
B,M
0
l,M
p
0
Q
N,P
Duration
4
13
5
11
3
4
3
5
4
17
2
3
3
3
2
3
4
Ignoring holiday periods, the project must be completed by the end of week 38. If the project
is delayed beyond this date it is estimated that it will cost the firm $5,000 a week.
a. Draw a critical part network to present the project and determine the critical path.
What is the earliest time at which the project can be completed and what penalty
cost (if any) will be incurred?
[ I OJ
b. Activity K is a two week course to train new salesmen. The hotel which will be
used for the course has been booked for weeks 12 and 13. In light of your analysis
should this booking be changed?
[2]
c. If activities L and E can be done in parallel, some savings can be made as they
use common resources. What are the minimum savings that must be made to
justify these activities being done at the same time?
[4]
d. Briefly outline how the critical path method can be adapted to deal with projects
where the activity durations involve uncertainty.
[4]
(End of Exam)
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