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AOR802S - APPLIED OPERATIONS RESEARCHS - 2ND OPP - JANUARY 2024 |
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nAm I BIA UnlVERS ITY
OF SCIEnCE
Facultyof Health,Natural
ResourceasndApplied
Sciences
Schoolof NaturalandApplied
Sciences
Departmentof Mathematics,
Statisticsand Actuarial Science
13JacksonKaujeuaStreet
PrivateBag133B8
Windhoek
NAMIBIA
T: •264 61207291:
E: msas@nust.na
W: www.nust.na
QUALIFICATION: BACHELOR of SCIENCE HONOURS IN APPLIED MATHEMATICS
BACHELOR of SCIENCE HONOURS IN APPLIED STATISTICS
QUALIFICATIONCODE: 08BSHM
08BSHS
LEVEL:8
COURSE: APPLIED OPERATIONS RESEARCH
COURSECODE: AOR802S
DATE: JANUARY 2024
SESSION: 1
DURATION: 3 HOURS
MARKS: 161 (To be converted to 100%)
SECOND OPPORTUNITY/SUPPLEMENTARY: EXAMINATION QUESTION PAPER
EXAMINER:
MODERATOR:
Prof Sunday A. Reju
Prof O/uwole D. Makinde
INSTRUCTIONS
1. Answer all questions on the separate answer sheet.
2. Please write neatly and legibly.
3. Do not use the left side margin of the exam paper. This must be allowed for the
examiner.
4. No books, notes and other additional aids are allowed.
5. Mark all answers clearly with their respective question numbers.
6. Use of COMMA is NOT ALLOWED for a DECIMAL POINT.
PERMISSIBLE MATERIALS
1. Non-Programmable Calculator
ATTACHMENTS
NONE
This paper consists of 3 pages including this front page.
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QUESTION 1 [20 MARKS]
(a) Discuss the Kendall's classification of Queuing Systems?
(S Marks)
Explain specifically the M/M/1 queuing system and the process N(t) describing its state at
time t as a birth-death process. Provide its state independent parameter equations and define
its Traffic Intensity.
(b) Consider a drive-in banking service modelled as an M/M/1 queuing system with customer
arrival rate of 2 per minute. It is desired to have fewer than 5 customers line up 99% of the
time. How fast should the service rate be?
(4 Marks)
(c) Trucks arrive at garage for a stop-over service according to a Poisson process at a rate of
one per every 13 minutes, and the garage service time is an exponential rate variable with
mean 9 minutes.
(i) Find the average number L of trucks, the average time W a truck spends in the garage, and
the average time Wq a truck spends in waiting for service.
(5 Marks)
(ii) Due to increased traffic, suppose that the arrival rate of the trucks increases by 5%. Find
the corresponding changes in L, W, and Wq.
(S Marks)
(iii) Discuss your observations.
(1 Marks)
QUESTION 2 [50 MARKS]
(a) Discuss Game Reduction by Dominance procedure.
(4 Marks)
(b) Simplify by using reduction by dominance the game defined by the following payoff
matrix, showing progressively the reduced pay-off matrix:
(18 Marks)
B
ab c
A
[2 -1
AB 4 -4
-;sl
C 3 -3 -8
D 2 -5 -4
(c) Distinguish between game players' pure and mixed strategies, with clear characteristics
of the latter.
(6 Marks)
(d) Eufenia has a 250-gallon capacity home heating oil tank, presently empty, meant to
store oil against the next winter. Consider the following winter heating oil quantity
needed and the oil prices during probable four levels of winter severity:
WINTER SEVERITY
Mild Winter (MW)
Average Winter (AW)
OIL STORAGE NEEDED
110 Gallons
180 Gallons
OIL PRICES PER GALLON
N$1.00
N$1.85
Applied Operations Research(AOR802S)
2nd Opportunity November 2023
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Severe Winter (SW)
Prolonged Winter (PW)
230 Gallons
250 Gallons
N$2.00
N$3.00
Formulate a game model and employ the Minimax criterion technique to determine the
gallons of oil Eufenia should stockpile at the current price of N$1 per gallon to avoid wasted
unused oil and to maximise his saving.
(17 Marks)
QUESTION 3 [25 MARKS]
(a) A licensed mining company in possession of a natural resource field has 0.25 chance for
diamond discovery. However, the company has the options to either mine the resource or to
sell it the field to another mining company wishing to buy the land for $90,000,000. The cost
of mining by the licensee is $100,000,000 with a revenue yield of $800,000,000 if diamond is
found. Formulate a game of strategy model to perform a mathematical decision analysis of
the problem and determine the decision of the licensee, stating appropriate assumptions for
your method.
(8 Marks)
(b) State the Maximum Likelihood Criterion and confirm the above decision obtained in (a)
with the criterion.
(4 Marks)
(c) Assuming the company feels that the true chances of discovering diamond are likely to be
between 15% and 35%, define sensitivity analysis and the decision crossover point, and hence
show that the decision is sensitive to these prior probabilities, providing an appropriate
sketch to substantiate your decision analysis and conclusion.
(13 Marks)
QUESTION 4 [66 MARKS]
(a) Using the linear programming problem (LPP) approach in obtaining the solution of the
game with the following payoff matrix:
1 -1
JJ -3 0
0 -2
-2 -3
Obtain the optimal mixed strategies for the two players and the value of the game,
discussing your solutions.
(SO Marks)
(b) Consider the following Queueing System Data:
END OF EXAMINATION
TOTAL MARKS:161 (CONVERTTO 100%)
Applied OperationsResearch(AOR802S)
2nd Opportunity November 2023
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