Brenda Kelley runs a specialty ski clothing shop outside of Boone, North Carolin

Question

Brenda Kelley runs a specialty ski clothing shop outside of Boone, North Carolina. She must place her order for ski parkas well in advance of ski season because the manufacturer produces them in the summer months. Brenda needs to determine whether to place a large, medium, or small order for parkas. The number sold will depend largely on whether the area receives a heavy, normal, or light amount of snow during the ski season. The following table summarizes the payoffs Brenda ex- pects to receive under each scenario. Amount of Snow Size of Order Heavy Normal Light Large 10 7 3 Medium 8 8 6 Small 4 4 4 Payoffs (in $1,000s) Brenda estimates the probability of heavy, normal, and light snowfalls as 0.25, 0.6, and 0.15, respectively. a. What decision should be made according to the maximax decision rule? b. What decision should be made according to the maximin decision rule? c. What decision should be made according to the minimax regret decision rule? d. What decision should be made according to the EMV decision rule? e. What decision should be made according to the EOL decision rule?

Explanation / Answer

Here Payoff matrix

a. What decision should be made according to the maximax decision rule?

Answer : The maximax rule tell us that for every case we have to see that what is the maximum payoff and we have to maximize it.

so for large order : maximum is for HEavy = $ 10,000

for Medium order : maximum is for Heavy and normal = $ 8000

for small order : maximum is same for all : $ 4000

so now 10000 is maximum among these 3, we will order snow size heavy.

(b) For minimax rule, we will see that for every case we have to see that what is the minimum payoff and we have to maximize it.

so for large order : minimum is for HEavy = $ 3,000

for Medium order : minimum is for Heavy and normal = $ 6000

for small order : minimum is same for all : $ 4000

so now we see that maximum is for medium order so we will order medium order.

(c)What decision should be made according to the minimax regret decision rule?

THe best return and worst return table

Here the regret table is

so here minimum worst regret is 2 for medium order so we will order medium level of order.

(d) EMV for large order = 0.25 * 10 + 0.6 * 7 + 0.15 * 3 = 7.15

EMV for medium order = 0.25 * 8 + 0.6 * 8 + 0.15 * 6 = 7.70

EMV for small order = 0.25 * 4 + 0.6 * 4 + 0.15 * 4 = 4

so we should use medium order.

(E) Expected Opportunity loss table is same as regret table

Expected Opportunity Loss value

FOr large = 0 * 0.25 + 1 * 0.6 + 3 * 0.15 = 1.05

For medium = 2 * 0.25 + 0 * 0.6 + 0 * 0.15 = 0.50

For Small = 6 * 0.25 + 4 * 0.6 + 2 * 0.15 = 4.2

so minimum would be for medium so we will use Medium order.

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