operationsanalysisdecisiontrees_2

A.2

Even though independent gasoline stations have been having a difficult time, Susan Helms has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susan developed the following table:

For example, if Susan constructs a small station and the market is good, she will realize a profit of $50,000. a. Develop a decision table for this decision.

  Good MarketFair Small 50,000 Medium 80,000 Large 100,000 Very Large 300,000    

Poor Market Market Row Min Row Max 20,000 -10,000 -10,000 50,000 30,000 -20,000 -20,000 80,000 30,000 -40,000 -40,000 100,000 25,000 -160,000 -160,000 300,000 maximum -10,000 300,000 maximin maximax

b. What is the maximax decision? Using the maximax criterion, the decision is to open a very large station. c. What is the maximin decision? Using the maximin criterion, the decision is to not open a station (i.e., do nothing). d. What is the equally likely decision?   Small

Good Fair Poor Market Market Market Row Min Row Max Average 50,000 20,000 -10,000 -10,000 50,000 20,000

Medium Large Very Large  

80,000 100,000

30,000 30,000

300,000

25,000 -160,000 -160,000 300,000 55,000 maximum -10,000 300,000  maximin maximax  

 

-20,000 -40,000

-20,000 -40,000

80,000 30,000 100,000 30,000

Using the equally likely criterion, the decision is to open a very large station.

e. Develop a decision tree. Assume each outcome is equally likely, then find the highest EMV.

A.3

Clay Whybark, a soft-drink vendor at Hard Rock Cafe’s annual Rockfest, created a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd):

The probabilities associated with the states of nature are 0.3 for a big demand, 0.5 for an average demand, and 0.2 for a small demand. a. Determine the alternative that provides Clay Whybark the greatest expected monetary value (EMV).   Big Average Small EMV Probabilitie s 0.3 0.5 0.2  Larger 22000*0.3+12000*0.5-2000*02=1 stock 22,000 12,000 -2,000 2200 Average 14000*0.3+10000*0.5+6000*02=1 stock 14,000 10,000 6,000 0400 9000*0.3+8000*0.5+4000*02=750 Small stock 9,000 8,000 4,000 0     maximum 12200 Therefore, Best EVM is 12,200

The largest EMV is for Large Stock.

b. Compute the expected value of perfect information (EVPI).

  Big Average Small Maximum Probabilities 0.3 0.5 0.2  Larger stock 22000 12000 -2000  Average stock 14000 10000 6000  Small stock 9000 8000 4000  Perfect Information (Maximum in column) 22000 12000 6000  Perfect*probabilit 0.3*22000=66 0.5*12000=60 0.2*6000=12 y 00 00 00 13800

Best Expected Value Exp Value of Perfect Info

 

 

 

12200

 

 

 

1600

The expected value of perfect information (EVPI) is 1,600.