Question

1. The Omega Mu (?M) service fraternity sells refreshments at the University men’s field hockey games. It is attempting to decide on the best ordering policy for one of the items it sells: the Bulldog Ice Cream Bar. The bars come in cartons of 50, so the fraternity can buy 100, 50, or 0 bars from the distributor. The weather on game day can be sunny, cloudy, or rainy. If it is sunny, 100 bars will be sold; if cloudy 50 bars will be sold; and if rainy, 0 bars will be sold. The order must be placed one week in advance, so the fraternity has no way of knowing what the weather will be on game day. The bars cost ?M $1.00 each and sell for $2.50. Any unsold bars must be discarded and written off.

a. Develop a decision table for this problem.

b. Using the Maximax method, how many bars should be bought?

c. Using the Maximin method, how many bars should be bought?

d. Using the Equally Likely method, how many bars should be bought?

e. Using the Minimax Regrets method, how many bars should be bought?

2. Based on past history, the probabilities of sunny, cloudy, and rainy weather are .6, .3, and .1, respectively.

a. How many bars should be bought?

b. The distributor will let Omega Mu wait until the morning of the game to place an order. In that way, they will know what the weather will be with certainty? However, the distributor will charge an expediting fee for the order. How much should ?M be willing to pay to wait until game day?

Answer 1

1. Building the decision table based on profits earned at three decisions and situations:

Profit= Selling Price of bars*number of bars sold- Cost price of bars*number of bars bought

Have a look at formulas below:

The decision table:

From the table we can see, by maximax which is the best of best situation, 100 bars should be bought.

From the table we can see, by maximin which is the best of worst situation, 0 bars should be bought.

Now lets create the regret table.

Have a look at concept and formula:

From the regret table, by minimax regret approach, 0 bars should be bought.

For solving with probablity we create EMV (expected monetary value) table:

From the above table, with the given probabilities, 100 bars should be bought.