# a chain of ski equipment shops in Vancouver

a chain of ski equipment shops in Vancouver

Instructions:

Charlie’s Ski Sports, a chain of ski equipment shops in Vancouver, purchases skis from a manufacturer each fall
for the upcoming winter season. The most popular intermediate model costs \$160 and sells for \$240. Any skis
left over at the end of the winter are sold at a blow-out sale for \$100. Sales over the years are quite stable.
Gathering data from all its stores, Charlie’s Ski Sports developed the following probability distribution for
demand:
Demand 150 175 200 225 250
Probability 0.05 0.2 0.35 0.3 0.1
Charlie also knows from experience that if their stores are stocked out of this ski (i.e., no more inventory) and
the customer wants it, Charlie will lose business on ski and other related snow equipment as customers will
shop at his competitors and tend not to return. He quantifies lost sales to be valued at \$40.00 whenever
customer demand for this intermediate model ski exceeds his supply.

Help Charlie determine how many skis to order for the upcoming winter season by answering the questions
below. The manufacturer will take orders only for multiples of 20. Assume the demand/costing information
provided is accurate for the upcoming season.
a. Construct a payoff matrix.
b. What decision should be made according to the maximax decision rule?
c. What decision should be made according to the maximin decision rule?
d. What decision should be made according to the EMV decision rule?
e. What decision should be made according to the minimax regret decision rule?
f. What decision should be made according to the EOL decision rule?
g. How much should Charlie be willing to pay to obtain a forecast of customer demand that is 100%
accurate?
h. Which decision rule would you recommend Charlie use? Provide a clear explanation why you are
recommending a particular decision rule.

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*Note: For this question, the use of Excel is highly recommended (but not necessary) to create the appropriate
payoff matrix and solve the problem using the different criteria. Print outs from Excel are acceptable for this
question but make sure to demonstrate several example calculations of the cells in your payoff table. Please
make sure to have a concluding statement as shown in lecture or marks will be deducted. Do not include any
Excel formula printouts with your submission.

Question 2 – 15 Marks:
You and your friend have come up with an entrepreneurial idea that has great potential and you both are
trying to decide to invest in the project or not. Your initial investment for research and development (R&D) is
estimated to be \$9000 total and there’s a 50-50 chance that it will be successful. If the results of the R&D
phase turn out to be successful, you will need a total of \$20,000 to invest in the product’s development. If the
product goes through the development phase, uncertainty remains about the product’s demand on market and
thus uncertainty about the profit will be realized. You categorize the product demand as high, medium and
low with respective probabilities of 0.5, 0.3 and 0.2. Your best estimate of revenue projection under high
demand is \$75000; at medium demand, revenue is projected at \$55,000; and, at a low demand for the product,
revenue is projected at \$21,000. Another option is that if the R&D phase is successful, you could sell the rights
of the product for an estimated \$18,000 and not engage its development.
a) Develop the decision tree by hand and solve it according to the EMV decision criterion. State the
optimal decision according to the EMV decision criterion.
b) Create the decision tree using Treeplan.xla. Print it out and include it with your submission.
c) State the risk profile of the optimal decision according to the EMV criterion.
d) You and your friend would like to explore the sensitivity of your decision to the probability of the R&D
phase being successful or not. Create a sensitivity table (ie Data Table in Excel) showing how your
initial decision to invest \$9000 might change (and its respective EMV) if the probability of a successful
R&D phase varies from 0% to 100% in steps 10%. Provide a clear statement of what the Data Table
means.

Question 3 – 20 Marks:
The City of Vancouver is considering whether or not to replace its fleet of gasoline-powered automobiles with
electric cars (true!!!). The manufacturer of electric cars claims that the city will experience significant cost
savings over the life of the fleet if it chooses to pursue the conversion. If the manufacturer is correct, the city
will save an estimated \$1.2 million dollars. If the new technology within the electric cars is faulty, as some
critics suggest, the conversion to electric cars will cost the city \$725,000. A third possibility is that less serious
problems will arise and the city will break even with the conversion. A consultant hired by the city estimates
the probabilities of these 3 outcomes are 0.40, 0.30 and 0.30 respectively. The city has an opportunity to
implement a pilot program that would indicate the potential cost or savings resulting from a switch to electric
cars. The pilot program involves renting a small number of electric cars for 3 months and running them under
typical conditions. The pilot program would cost the city \$60,000. The city’s consultant believes that the
results of the pilot program would be significant but not conclusive; she provides the city with the following
compilation of probabilities based on her past experience consulting with other cities under the same
conditions. According to the consultant, the reliability for the pilot program in the past has been:

Actual City Outcomes of Electric Car Conversions
Savings Loss Breakeven
Pilot Predicted: Savings 0.601 0.10 0.40
Pilot Predicted: Loss 0.102 0.40 0.20
Pilot Predicted: Breakeven 0.30 0.50 0.40
1
For example, 0.60 in the table above represents the probability of the pilot predicting a savings, given that a conversion
to electric cars actually resulted in a savings of \$1.2 million in other cities. 2Likewise, 0.10 represents the probability of
the pilot predicting a loss, given that a conversion to electric cars actually resulted in a savings of \$1.2 million in other
cities. etc

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a) Develop a decision tree for the City of Vancouver given the information above. Draw this decision tree by
hand and evaluate it using the EMV decision criterion. Provide a concluding statement with respect to the
optimal decision.
b) Use Treeplan.xla to evaluate the decision tree in part a). Print out your decision tree and include it with