EM680 Exam 3

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EM680 Exam 3
Set your Analytic Solver Options to 1000 trials, Sim Random Seed of 999.
On the Engine tab, make sure it is set to Automatically Select Engine, and
Assume Non-Negative is true.
For Decision Trees, Display all parameter values visibly. Do not embed any
parameter values in the decision tree nodes, only refer to them. I want you to
be able to change any parameter value in a single cell and have the decision
tree reanalyze automatically.
1. KopterKing Inc. makes personal helicopters. KKI has just received a
credit request for the full purchase price from a new customer who
wants to purchase a helicopter. Based on historical data, KKI uses the
following assumptions in its decision whether to grant credit.
If KKI denies the customer credit, there is a 25 percent chance that the
customer will buy the helicopter with cash anyway.
If KKI grants credit, there is a 65 percent chance the customer will be a good
credit risk.
If KKI grants credit and the customer is a good credit risk, KKI will collect 100
percent of the purchase price.
If KKI grants credit and the customer is a bad credit risk, KKI has a decision to
make. KKI has two options. Under the zrst option, KKI would continue to send
the customer a bill and hope it is eventually paid. Under this option, KKI will
collect 100 percent, 50 percent, or 0 percent of the amount owed, with
probabilities 0.1, 0.3, and 0.6, respectively, at no cost to KKI. Under the second
option, KKI would vigorously pursue the collection of the amount owed. To do
so would cost KKI 20 percent of the amount owed, regardless of the amount
eventually collected. Under this second option, KKI will again collect 100
percent, 50 percent, or 0 percent of the amount owed, with probabilities 0.25,
0.55, and 0.2, respectively.
The helicopter sells for $15,000 and costs KKI $6,000 to produce.
Use a decision tree for your analysis.
a. What is the complete, optimal decision strategy for KKI (all stages) and
the optimal expected payoff? (15 pts)
b. The decision whether to send bills or vigorously pursue payment is
based on the expected payoff of that decision. Which data parameter has the
biggest in{uence on the outcome of that decision? Show proof. (5 pts)
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c. KKI anticipates its costs rising, but is reluctant to raise prices. At what
cost does the decision to grant credit change? (use $100 increments). Use
Sensitivity Analysis (5 pts)
2. WeAreSmart Inc., a consulting company, self-insures its employee health
insurance claims. That is, it collects a zxed amount each month from every
employee for health care costs and then it pays the entire claim amounts
using its own funds to make up the difference. WAS would like to estimate its
total health care payments for the coming year.
The total number of employees at the start of the year is 13474. WAS expects
the number of employees to change each month over the coming year by a
percentage that is uniformly distributed between -1 percent and 4 percent
(relative to the previous month). Employees contribute $120 each per month
toward their health care costs, while the average claim is $225 per month.
The average claim itself is expected to grow each month by an amount given
by a normal distribution with a mean of 1 percent and a standard deviation of
2 percent.
a. What is the expected cost to WAS of covering employee health care
costs in the coming year? (15 pts)
b. What is the maximum cost to WAS of covering employee health care
costs in the coming year? (5 pts)
c. What is the probability that costs will exceed $20million? (5 pts)
3. Moderately Good Furniture Inc. makes a chairs, desks, and tables. They
would like to know the proper mix of furniture to manufacture in order to
maximize prozts. Manufacturing is limited by the following constraints:

Prices of each type of furniture are expected to vary according to a triangular
distribution.
Costs of each type of furniture are expected to vary according to a uniform
distribution.
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MGF would like to know the precise number of each type of furniture to
manufacture to maximize prozt according to the above data. Fractional
decisions are not acceptable.
a) What are the optimal decisions and mean expected prozt for the above
problem? (15pts)
b) Marketing has added the following forecasted demands for each type of
furniture: Chairs (300), Desks (135), Tables (140). What are the new optimal
decisions and mean max prozt value? (6pts)
c) Marketing has now added a requirement that at least 20 of each item
must be made. What are the new optimal decisions and mean max prozt
value? (building from part b) (4pts)
4. Cindy Blumenthal owns a newsstand in Nowheresville, Indiana. She buys
papers wholesale at 50 cents each, and sells them for 75 cents. She wonders
about the optimal daily order quantity of papers. Based on previous days, she
has found that demand can be modeled by a normal distribution with a mean
of 50 and standard deviation of 5. When she has more papers than
customers, she can recycle all the extra papers at 5 cents each. However, if
she has more customers than papers, she not only loses the potential prozt
from each paper, but also customer goodwill. She estimates that when
customers znd they cannot buy a paper from her, they will go to a competitor
for the following 5 days, and then return (loss of 6 days total). (for simplicity’s
sake, she will count all 6 days of loss on the day she had the unmet demand
instead of spreading it out over 6 days).
a) Create a spreadsheet model that will znd the optimal order
quantity and expected mean prozt. (15 pts)
b) Building on the solution from (a), what is the most money Cindy
could expect to lose on any given day? Show proof. (2 pts)
c) Cindy believes it is not worthwhile unless she makes 7 dollars a
day. What is the probability she will make less than $7 (based on the
quantity found in (a))? (3 pts)
d) Cindy is not sure she believes the quantity found in part (a) is really
the optimal quantity. She would like to see a graph of all the possible
quantities from 1-100 (in increments of 1) and the resulting mean prozt for
each. Provide such a graph. (5 pts)
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