Question

F and G were not answered on my last question. can i get some help please?

ENPHUH Quantitative Methods The craft vendors in spice market are to be relocated into one large mega craft market that can hold the majority of vendors. The idea is that the several locations are too dispersed and cause friction when cruise ship visitors and all inclusive guests are to be entertained. There is a great deal of controversy about the optimal location. The minister of tourism commissioned a study and four competing locations were examined. The data in the payoff table shows the possible value of revenue ($000] to the different locations per week under three scenarios Future Growth Conditions Mall Site Stable Moderate 2.500 2,500 2,430 2510 1,140 2,100 1.460 2180 High 2,510 2,710 3.200 3,050 Which site would be selected if the decision makes used the (a) LaPlace criterion? (b) Maximin criterion? (c) Maximax criterion? (d) Minmax regret criterion? (e) Hurwicz (realism) criterion with alpha (a) - 0.77 () If the probability of stable is 0,35, of moderate is 0.33, of high is 0.32; what decision should be made under risk? (g) What is the expected value of perfect information (EVP)?

Answer 1

Future growth Conditions
Mall Site	Stable	Moderate	High
1	2500	2500	2510
2	2430	2510	2710
3	1140	2100	3200
4	1460	2180	3050

a)

Laplace criterion:

Average payoff for Site 1 = (2500+2500+2510)/3 = 2503.33

Average payoff for Site 2 = (2430+2510+2710)/3 = 2550

Average payoff for Site 3 = (1140 + 2100 + 3200)/3 = 2146.66

Average payoff for Site 4 = (1460 + 2180 + 3050)/3 = 2230

Maximum of average payoff = $2550 thousands for site 2.

Hence, based on the Laplace criterion, site 2 should be chosen.

b)

Maximin criterion:

Minimum payoff for Site 1 = 2500

Minimum payoff for Site 2 = 2430

Minimum payoff for Site 3 = 1140

Minimum payoff for Site 4 = 1460

Maximum of minimum payoff = $2500 thousands for site 1.

Hence, based on the Maximin criterion, site 1 should be chosen.

c)

Maximax criterion:

Maximum payoff for Site 1 = 2510

Maximum payoff for Site 2 = 2710

Maximum payoff for Site 3 = 3200

Maximum payoff for Site 4 = 3050

Maximum of maximum payoff = $3200 thousands for site 3.

Hence, based on the Maximax criterion, site 3 should be chosen.

d)

Minimax regret criterion:

The maximum value under Stable condition is 2500,

The maximum value under Moderate condition is 2510,

The maximum value under High condition is 3200

The regret table for given payoff is:

Mall Site	Stable	Moderate	High
1	2500-2500 = 0	2510 - 2500 = 10	3200 - 2510 = 690
2	2500 - 2430 = 70	2510 - 2510 = 0	3200 - 2710 = 490
3	2500 - 1140 = 1360	2510 - 2100 = 410	3200 - 3200 = 0
4	2500 - 1460 = 1040	2510 - 2180 = 330	3200 - 3050 = 150

The maximum regret for site 1 is 690

The maximum regret for site 2 is 490

The maximum regret for site 3 is 1360

The maximum regret for site 4 is 1040

Minimum of maximum regret = $490 thousands for site 2.

Hence, based on the Minimax regret criterion, site 2 should be chosen.

e)

Hurwicz criterion:

Weighted average payoff using Hurwicz criterion = $\alpha$ * Maximum payoff + (1 - $\alpha$ ) Minimum payoff

Weighted average payoff for site 1 = 0.77*2510 + 0.23*2500 = 2507.7

Weighted average payoff for site 2 = 0.77*2710 + 0.23*2430 = 2645.6

Weighted average payoff for site 3 = 0.77*3200 + 0.23*1140 = 2726.2

Weighted average payoff for site 4 = 0.77*3050 + 0.23*1460 = 2684.3

Maxmimum of Weighted average payoff = $2726.2 thousands for site 3.

Hence, based on the Hurwicz criterion, site 3 should be chosen.

f)

Based on Expected value

Expected value of payoff for site 1 = 0.35*2500 + 0.33*2500 + 0.32*2510 = 2503.2

Expected value of payoff for site 2 = 0.35*2430 + 0.33*2510 + 0.32*2710 = 2546

Expected value of payoff for site 3 = 0.35*1140 + 0.33*2100 + 0.32*3200 = 2116

Expected value of payoff for site 4 = 0.35*1460 + 0.33*2180 + 0.32*3050 = 2206.4

Maxmimum expected payoff = $2546 thousands for site 2.

Hence, based on the expected value of payoof, site 2 should be chosen.

g)

Expected Value of Perfect Information (EVPI):

Maximum payoff based on expected value of payoff for each site = 2546

Maximum payoff if perfect information is available = 0.35*2500 + 0.33*2510 + 0.32*3200 = 2727.3

Expected Value of perfect information = 2727.3 - 2546 = 181.3

The Expected Value of Perfect Information is 181.3 thousand dollars.