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

your submission.

c) Would the optimal decision change if the pilot program only costs the city $35,000? If so, provide a

concluding statement with respect to the new optimal decision.