L02 Five Decision Problems
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School
York University *
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Course
5120
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
Pages
5
Uploaded by Keekii
QUESTION 1
–
INSURANCE
You are in the automotive retail business and trying to decide
whether to buy an insurance policy to cover hail damage on
your inventory of more than 200 cars and trucks.
Thunderstorms occur frequently and they sometimes produce
golfball-sized hail that can severely damage automobiles. The
estimates of the potential damage from hail in the next year
are:
Hail Damage in thousands of dollars & Probabilities
Damage
0
15
30
45
60
75
90
105
P(D)
0.25 0.08 0.10 0.12 0.15 0.12 0.10 0.08
You are considering the following three alternatives for dealing
with this risk:
1)
You can buy an insurance policy for $45,000 that would
cover 100% of any losses that occur.
2)
You can buy an insurance policy for $25,000 that would
cover all losses in excess of $35,000.
3)
You can choose to
“
self-insure
”
, in which case you will not
have to pay any insurance premium but you will absorb any
losses that occur.
QUESTION 2
–
PRODUCT DEVELOPMENT PROJECT (Heizer, “Operations
Management”, p.183)
Page Engineering designs and constructs air conditioning and heating
systems for hospitals and clinics.
Currently, the com
pany’s staff is
overloaded with design work.
There is a major design project due in 8
weeks.
The penalty for completing the design late is $14,000 per week,
since any delay will cause the facility to open later than anticipated, and
cost the client significant revenue.
If the company uses its inside
engineers to complete the design, it will have to pay them overtime for
all work.
Page has estimated that it will cost $12,000 per week (wages
and overhead), including late weeks, to have company engineers
complete the design. Page is also considering having an outside
engineering firm do the design.
A bid of $92,000 has been received for
the completed design.
Yet another option for completing the design is
to conduct a joint design by having a third engineering company
complete all electromechanical components of the design at a cost of
$56,000.
Page would then complete the rest of the design and control
systems at an estimated cost of $30,000.
Page has estimate the following probabilities of completing the project
within various time frames when using each of the three options.
Those estimates are shown in the following table:
PROBABILITY OF COMPLETING THE DESIGN
OPTION
ON TIME
1 WEEK LATE
2 WEEKS LATE
3 WEEKS LATE
Internal Engineers
0.4
0.5
0.1
-
External Engineers
0.2
0.4
0.3
0.1
Joint Design
0.1
0.3
0.4
0.2
QUESTION 3
–
LITIGATION
Suppose that you have sued your employer for damages
suffered while you recently slipped and fell on an icy surface at
work.
Specifically, your injury resulting from this accident was
sufficiently serious that you, in consultation with your attorney,
decided to sue your company for $500,000.
Your company's
insurance provider has offered to settle this suit with you out of
court.
If you decide to reject the settlement and go to court,
your attorney is confident that you will win the case but is
uncertain about the amount that the court will award you in
damages.
He has provided his assessment of the probability
distribution of the court's award to you:
Amount Probability
$0
0.025
$50,000
0.075
$100,000
0.100
$200,000
0.125
$300,000
0.175
$400,000
0.200
$500,000
0.300
In addition, there are extra legal fees of $10,000 you will have
to pay if you go to court.
The company is offering a settlement
of $200,000.
You are intending to make your decision based on
maximizing the expected net payoff from the situation.
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QUESTION 4
–
BIDDING WAR
Southern Gas Company (SGC) is preparing to make a bid for oil
and gas leasing rights in a newly opened drilling area in the Gulf
of Mexico.
SGC is trying to decide whether to place a high bid
of $16 million or a low bid of $7 million.
SGC expects to be
bidding against their major competitor, Northern Gas Company
(NGC) and predicts NGC to place a bid of $10 million with a
probability of 0.4 or a bid of $6 million with a probability of 0.6.
Geological data collected at the drilling site indicates a 0.15
probability of the reserves at the site being large, a 0.35
probability of being average, and a 0.5 probability of being
unusable.
A large or average reserve would most likely
represent a net asset value of $120 million or $28 million,
respectively, after all drilling and extraction costs are paid.
The
company that wins the bid will drill an exploration well at the
site for a cost of $5 million.
QUESTION 5 - INVESTMENT
You are an investor with $10,000 available to invest, and have
the following options regarding the allocation of your available
funds:
(1) You can invest in a risk-free savings account with a
guaranteed 3% annual rate of return in every state of the
world
(2) You can invest in a fairly safe stock, where the possible
annual rates of return are 6%, 8%, or 10%; or
(3) You can invest in a riskier stock, where the possible annual
rates of return are 1%, 9%, or 17%.
Note that you can place all of his available funds in any one of
these options or split the $10,000 into two $5000 investments
in any two of these options. The joint probability distribution of
the possible return rates for the two stocks is given below:
Risky stock return (R)
R=1%
R=9%
R=17%
Safe stock
Return (S)
S=6%
0.10
0.05
0.10
S=8%
0.25
0.05
0.20
S=10%
0.10
0.05
0.10