Question

Stan's No Touch Car Wash is looking to implement a new ERP system. Lazlo Gali has been charged with selecting one of 5 alternative approaches to the project. Complicating the analysis is the fact that each alternative will yield different results depending on which of the 4 economic scenarios occurs.

Lazlo has studied each of the alternatives and scenarios and believes the table below accurately represents the potential outcomes. Each row represents a different approach to the project. Each column represents the outcomes associated with a specific economic scenario.

scenario	1	2	3	4
Alt 1	-71.2	-279.2	-12.5	194.9
Alt 2	31.1	197.1	485.6	-547.6
Alt 3	467.3	-567.7	649.2	649
Alt 4	616.5	-330.3	530.9	255.6
Alt 5	429.9	-520.4	67.9	696.5

Specify the outcome suggested for each of the following criteria:

Maximin =
Maximax =
Minimax Regret =

Answer 1

Maximin Rule:

In above table we obtain the minimum value for each row. Then take the maximum value from MIN column.

So, the best decision is Alternative 1, because Alternative 1 has maximum value in MIN column is -279.2 , using the Maximin criterion.

Maximax Rule:

In above table we obtain the maximum value for each row. Then take the maximum value from MAX column.

So, the best decision is Alternative 5, because Alternative 5 has maximum value in MAX column is 696.5, using the Maximax criterion.

Minimax Regret:

1:First find max value in State of Nature 1 is 616.5.

Now Subtract each value of State of Nature 1 from 616.5.

2:

max value in State of Nature 2 is 197.1

Now Subtract each value of State of Nature 2 from 197.1

3:

max value in State of Nature 3 is 649.2.

Now Subtract each value of State of Nature 3 from 649.2.

4:

max value in State of Nature 4 is 696.5.

Now Subtract each value of State of Nature 4 from 696.5.

Now make a table:

	1	2	3	4
Alt1	616.5-(-71.5) = 687.7	197.1-(-279.2) = 476.3	649.2-(-12.5) = 661.7	696.5-194.9 =501.6
Alt2	616.5-31.1 = 585.4	197.1-197.1 = 0	649.2-485.6 = 163.6	696.5-(-547.6) = 1244.1
Alt3	616.5-467.3 = 149.2	197.1-(-567.7) = 764.8	649.2-649.2 = 0	696.5-649 = 47.5
Alt4	616.5-616.5 = 0	197.1-(-330.3) = 527.4	649.2-530.9 = 118.3	696.5-255.6 = 440.9
Alt5	616.5-429.9 = 186.6	197.1-(-520.4) = 717.5	649.2-67.9 = 581.3	696.5-696.5 = 0

So our table looks like:

So, obtain the maximum regret for each decision alternative, and select the alternative with the lowest maximum regret.

So, the best decision is Alternative 4, because lowest maximum regret is 527.4 in Max Regret column, using the Minimax Regret criterion.