# Decision Theory

The Loebuck Company must decide how many cases of milk to stock each week to meet demand. The probability distribution of demand during a week is shown in the following table. Each case costs the grocer $10 and sells for $12. Unsold cases are sold to a local farmer ( who mixes the milk with feed from livestock) for $2 per case. if there is a shortage, the grocer considers the cost of customer ill will and lost profit to be $4 per case. The grocer must decide how many cases of milk to order each week.

Demand cases Probability

15 .20

16 .25

17 .40

18 .15

1.00

A. Construct the payoff table for this decision situation.

B. Compute the expected value of each alternative amount of milk that could be stocked, and select the best decision.

C. Construct the opportunity loss table and determine the best decision.

D. Compute the expected value of perfect information.

https://brainmass.com/statistics/probability-theory/decision-theory-112042

#### Solution Preview

A. Construct the payoff table for this decision situation.

Since the number of cases of milk to stock each week is under the control of the decision maker ,the number of cases of milk to order each week can be treated as course of action (Decision choice) and the demand of cases of milk is uncertain and only known with probability, therefore it is considered as a 'State of Nature'

From the given data

Marginal Profit MP = Selling price -Cost

=$12-$10

=$2

Marginal loss ML Loss on unsold milks OR Loss on shortage

= $8 *(S-D) OR $4 (D-S)

Where D is the demand and S is the Stock

Conditional Profit = MP*Number of Milks Cases Sold -ML

The following Pay off table can be Constructed based on the above data

Demand

Cases Probability Course of action ...

#### Solution Summary

Decision Theory. Calculation of EMV, EOL, EPPI and EVPI.