Question

A concessionaire for the local ballpark has developed a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd).

​ Large Average Small Probability

.3 .5 . 2

Alternative 1 9,000 12,000 -2,000

Alternative 2 22,000 6,000 6,000

Alternative 3 15,000 12,000 5,000

If the probabilities associated with the states of nature are 0.30 for a large crowd, 0.50 for an average crowd, and 0.20 for a small crowd, determine:

(a) the opportunity loss table. (b) minimum expected opportunity loss (EOL).

Answer 1

Given

	Large	Average	Small
Probability	0.3	0.5	0.2
Alternative 1	9000	12000	-2000
Alternative 2	22000	6000	6000
Alternative 3	15000	12000	5000

If the probabilities associated with the states of nature are 0.30 for a large crowd, 0.50 for an average crowd, and 0.20 for a small crowd

The opportunity loss table is:;

	Large	Average	Small
Alternative 1	13000	0	8000
Alternative 2	0	6000	0
Alternative 3	7000	0	1000

b)

The minimum expected opportunity loss (EOL)

Minimum EOL=6000 with Alternative 2

...............................................................................................................................

Steps for part A are

The Expected opportunity loss is found by subtracting the best outcome in the same column.

	Large	Average	Small
Alternative 1	22000-9000=13000	0	6000-(-2000)=8000
Alternative 2	0	12000-6000=6000	0
Alternative 3	22000-15000=7000	0	6000-5000=1000

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