Question

Soccer Outlet sells soccer equipment to both local teams and individual customers. They need to decide whether to order 100, 200, 300, or 400 pairs of the latest type of soccer shoe that has just come on the market. Soccer Outlet will sell these shoes for PhP1400 per pair after paying PhP1000 per pair from the manufacturer. After the current soccer season ends, Soccer Outlet will discount any remaining pairs to PhP500. Assume the demand for these shoes can be 100, 200, 300, or 400 pairs during the season.

After surveying customers about their likelihood of purchasing this new soccer shoe, Soccer Outlet feels the probability that demand will be 100, 200, 300, and 400 pairs of shoes is 30%, 35%, 25%, and 10% respectively.

a) How many pairs of soccer shoes should Soccer Outlet purchase
and how much is the expected value?  

b) Using expected opportunity loss, how many pairs of soccer shoes should Soccer Outlet purchase?  

c) What is the most Soccer Outlet would be willing to pay for additional information?

d) Using Hurwicz criterion with a = 0.4, how many pairs of soccer shoes should Soccer Outlet purchase?
How much is the expected payoff?   

Answer 1

As per expected value criterion, 200 pairs of soccer shoes must be purchased.

Note - To form a table

Demand is state of nature and supply is course of action.

Each soccer shoes is purchased at 1000 and sold at 1400, so the profit is 400 and if unsold during the season, it sold at 500 which ultimately results in loss of 500.

So if demand is 100 and we supply 100, we make profit on 100 shoes i.e. 100*400 = 40,000

If demand is 100 and we supply 200, we make profit on first 100 shoes i.e. 40,000 and for next 100 shoes we have to bear loss i.e. 100*500 = 50,000

So overall Income = 40,000-50,000 = -10,000.

This is continued for every calculations.

For preparing regret table, highest value of each state of nature is deducted from other values of state of nature. Then mu;tiplied with probability.

According to expected opportunity loss, we choose the criteria with minimum loss i.e. 33,000 that is alternative 2.

C) The soccer outlet must be willing to pay atmost 24,000 fpr additional information.

Using Hurwicz criterion with a = 0.4, 100 pairs of soccer shoes should Soccer Outlet purchase.

The expected pay off is 40,000.