Statistics

Statistics

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.