PROBLEM: Cookie Inventory
Suppose that you are controlling the inventory of daily cookies in your coffee shop. Since each customer buys two cookies at the same time, you observed that the daily demand for cookies is either 10 or 12 or 14 or 16 or 18. Based on your observations since you started your coffee shop, you have built the table below, which gives the probabilities of each daily demand value (in number of cookies).
You buy cookies every morning before opening your coffee shop. You buy cookies in multiples of 5. You have the following information about your cookie sales:
- Each pack of cookie you purchase contains 5 cookies
- Each pack of cookie costs you $15
- Each cookie is sold for $5
- If you have unsold cookie at the end of the day, you can sell each unsold cookie for $1 to farmers as animal food
Answer the following questions based on the above information.
a) Formulate a decision analysis problem by constructing the payoff table with the information given above. That is, describe your alternatives, states of natures, and calculate the payoff (profit) for each alternative and state of nature pair, and note the prior probabilities for each state of nature.
b) Based on the maximax criterion, how many packs of cookies you should buy in the morning? Show how you reach to your solution.
c) Based on the maximin criterion, how many packs of cookies you should buy in the morning? Show how you reach to your solution.
d) Based on the maximum likelihood criterion, how many packs of cookies you should buy in the morning? Show how you reach to your solution.
e) Based on the Baye's decision rule, how many packs of cookies you should buy in the morning? Show how you reach to your solution.
f) Suppose that you meet a medium who can tell you how many cookies that you will sell before you buy cookies. Would you pay her $2 every morning to do a reading for your cookie sales? Why or why not? Explain your solution and Show how you reach to your solution.