Data Analysis - Payoff Matrix

[brisco]

Hi everyone. I am having trouble filling out the alternatives part of the payoff matrix for this question. The question is:

This Fish House (TFH) in Norfolk, Virginia, sells fresh fish and seafood. TFH receives daily shipments of farm-raised trout from a nearby supplier. Each trout costs $2.45 and is sold for $3.95. To maintain its reputation for freshness, at the end of the day TFH sells any leftover trout to a local pet food manufacturer for $1.25 each. The owner of TFH wants to determine how many trout to order each day. Historically, the daily demand for trout is:

Demand / Probability
10 / 0.02
11 / 0.06
12 / 0.09
13 / 0.11
14 / 0.13
15 / 0.15
16 / 0.18
17 / 0.11
18 / 0.07
19 / 0.05
20 / 0.03

a) Construct a payoff matrix for this problem.

The question I have is what are the decision alternatives for this problem. I know that the states of nature are the different levels of demand, but I'm having a hard time figuring out the decision alternatives so I can construct my payoff table. Any help would be greatly appreciated. Thanks!

 

[tkhunny]

There is only one decision, purchase amount.

1) Demand is at least 10. Make sure you order at least that many. If you order only 10, you never will sell any for salvage. This is good for you and bad for the pet food guys. If demand is greater than 10, you will have to tell someone that you are sorry for running out.

This brings up the intangible effect. How much does it affect the demand distribution when you hurt someone's feelings? That's harder to include in the model.

2) Demand is at most 20. Don't order more than that without a very good reason. Obviously, if you have 20 and 20 are ordered, this is the maximum possible profit, but it is attached to a rather low probability event.

3) Notice that the mean of the distribution is 15. That would be a good first guess for an optimal solution. However, this still hurts someone's feelings a whopping 44% of the time!

4) As it turns out, 15 gves the optimum profit, but 16 is barely less. Dropping your hurt feelings down to 26% and losing 1¢ of expected profit may be a good idea.

5) Further, 17 will drop your hurt feelings to only 15% and you'll have to give up only another 2½% of your expected profits.

6) Carrying this all the away, if you order 20, you never will hurt anyone's feelings, but this will require you to give up over 17% of your expected maximum profits.

7) There isn't actually a negative result of any kind until you order 23. If only 10 folks show up, that will hurt, but you'll keep the pet food guys in business.

8) A total negative expectation doesn't kick in until 34 are ordered. Hoping for a big party weekend might be a big risk.

Like I said, only the purchase amount can be chosen. There are several important factors to consider. The fish business isn't so simple, is it?