The owner of the Snow Fun Ski Resort wants to decide how the resort should be run in the coming winter season. The resort’s profits for this year’s skiing season will depend on the amount of snowfall during the winter. On the basis of prior experience, the probability distribution of snowfall and the resulting profit is summarized below.
The owner of the Snow Fun Ski Resort wants to decide how the resort should be run in the coming
winter season. The resort’s profits for this year’s skiing season will depend on the amount of snowfall
during the winter. On the basis of prior experience, the
resulting profit is summarized below.
The owner has recently received an offer from a larger hotel chain to operate the resort for the winter,
guaranteeing a $45,000 profit for the season. The owner is also considering leasing snowmaking
equipment for the season. If the equipment is leased, the resort will be able to operate full time,
regardless of the amount of natural snowfall. The owner can only make one decision here (i.e., if the
sells the operation rights to the hotel, there is no consideration of leasing snowmaking equipment).
If the owner decides to use snowmakers to supplement the natural snowfall, the profit for the season
will be $120,000 minus the cost of leasing and operating the snowmaking equipment. The leasing cost
will be about $12,000 per season, regardless of how much it is used. The operating costs will be $30,000
per 20” (or fraction thereof) of snow that is required to be made to obtain at least 60” ofsnow – i.e., if
the natural snow is less than 20”, the cost will be $90,000; if the natural snow is between 20” and 40”,
the operating cost will be $60,000; and if the natural snow is more than 40”, the operating cost will be
$30,000.
a) Draw a decision tree for this scenario
b) Solve the decision tree using EMV and state the optimal decision strategy.
There will be uncertainty in the figures presented above as follows:
• Snowfall:
o Probability of more than 40” of snow: 0.1 to 0.6
o *note the probability 20” to 40” of snow is always 20%.
• Leasing Costs:
o The leasing cost can range from $5,000 to $14,000 per season
• Operating Costs:
o The operating costs can range from $25,000 to $37,000 per 20” of snow
c) Perform one-way sensitivity analysis for each of the uncertainties listed above and graph your
results. Which variables will cause you to change your decision?
d) Construct a tornado diagram for the uncertainties described above. Which variables are most
important? Explain.
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