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ISYE371 Operations Research
Group Assignment #1
Due date: March 4th, 2024
Instructions: I NEED TO SEE YOUR WORK! You MUST provide assumptions,
formulas, graphs, flowcharts and reasoning for each situation. PUT YOUR NAME ON
ALL PAGES AND NUMBER EACH PAGE. Remember the format to provide an answer
to each given problem is MS Words. NO scanned handwritten image of any type is allowed.
See syllabus instructions for submissions. Peer evaluations required.
Problem 1 (25 points)
Pliskin and Tell (1981). Patients suffering from kidney failure can either get a transplant
or undergo periodic dialysis. During any one year, 30% undergo cadaveric transplants, and
10% receive living-donor kidneys. In the year following a transplant, 30% of those who
undergo the cadaveric transplants and 15% of living-donor recipients go back to dialysis.
Death percentages among the two groups are 20% and 10%, respectively. Of those in the
dialysis pool, 10% die, and of those who survive more than one year after a transplant, 5%
die and 5% go back to dialysis. Represent the situation as a Markov chain.
Problem 2 (25 points)
A museum has six rooms of equal sizes arranged in the form of a grid with three rows and
two columns. Each interior wall has a door that connects adjacent rooms. Museum guards
move about the rooms through the interior doors. Represent the movements of each guard
in the museum as a Markov chain.
Problem 3 (25 points)
A die-rolling game uses a 4-square grid. The squares are designated clockwise as A, B, C,
and D with monetary rewards of $4, -$2, -$6, and $9, respectively. Starting at square A,
roll the die to determine the next square to move to in a clockwise direction. For example,
if the die shows 2, we move to square C. The game is repeated using the last square as a
starting point.
(a) Express the problem as a Markov chain.
(b) Determine the expected gain or loss after the die is rolled 5 time.
Problem 4 (25 points)
Given the system shown in the figure, calculate Mean
Time Between Failures (MTBF) of the system,
assuming the time to failure for each
component follows an exponential
distribution with parameters: λA, λB, and λC.
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