6 A company has three alternatives A B C for locating a new

6. A company has three alternatives (A, B, C) for locating a new manufacturing facility. Analysis has led to the belief that there are four possible states of the world that may occur over a five year period. The probability of each outcome is given below. Probability 0.2 0.3 0.4 0.1 Outcome The expected payofts for each altermative under each possible outcome is

Solution

(a)

An alternative \'i\' is dominated by another alternative \'j\' when for every given outcome (states of nature), the payoff from \'j\' is greater than that of \'i\'. Here, this does not hold for any combination (i,j) i.e. AB, AC, or BC. So, there is no dominated alternative.

(b)

Regret matrix

Minimum of the maximum regret is Alternative \'C\'. o, it should be the correct decision.

(c)

* 10,000 x 0.2 + 15,000 x 0.3 + 16,000 x 0.4 + 20,000 x 0.1 = 14,900

Alternative B is optimal.

(d)

Expected Value of perfect information = Expected value with perfect information - max. EMV

Expected value with perfect information = $15,000 x 0.2 + $17,000 x 0.3 + $18,000 x 0.4 + $20,000 x 0.1 = $17,300

max. EMV = $16,600

So, Expected Value of perfect information = $17,300 - $16,600 = $700

(e)

Let the payoff of \'A\' under option 4 be \'PA\'

Then, 10,000 x 0.2 + 15,000 x 0.3 + 16,000 x 0.4 + PA x 0.1 >= 16,600

or, PA >= 37,000

So, the payoff of A under option 4 should at least be $37,000 in order to defeat B as optimal.

	Outcome	Max.
Alternative	1	2	3	4	Regret
A	$5,000	$2,000	$2,000	$0	$5,000
B	$3,000	$0	$0	$1,000	$3,000
C	$0	$1,000	$1,000	$2,000	$2,000