In: Statistics and Probability
Lori Henderson 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 expects to receive under each
scenario.
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?
SelectSmall orderMedium orderLarge orderItem 1
b. What decision should be made according to
the maximin decision rule?
SelectSmall orderMedium orderLarge orderItem 2
c. What decision should be made according to
the minimax regret decision rule?
SelectSmall orderMedium orderLarge orderItem 3
d. What decision should be made according to
the EMV decision rule?
SelectSmall orderMedium orderLarge orderItem 4
e. What decision should be made according to
the EOL decision rule?
SelectSmall orderMedium orderLarge order
Answer:-
Given That:-
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 expects to receive under each scenario.
Brenda estimates the probability of heavy, normal, and light snowfalls as 0.25, 0.6, and 0.15, respectively.
(a) Large Order
(b) Medium Order
(c) Medium Order
(d) Medium Order
(e) Medium Order
a. What decision should be made according to the maximax
decision rule?
SelectSmall orderMedium orderLarge orderItem 1
Maximax:
Amount of snow | ||||
Size of Orders | Heavy | Normal | Light | Maximum |
Large | 10 | 7 | 3 | 10 |
Medium | 8 | 8 | 6 | 8 |
Small | 4 | 4 | 4 | 4 |
Out of the Maximum values 10 is the maximum value of Large Size.
b. What decision should be made according to the maximin
decision rule?
SelectSmall orderMedium orderLarge orderItem 2
Maximin:
Amount of snow | ||||
Size of Orders | Heavy | Normal | Light | Maximum |
Large | 10 | 7 | 3 | 3 |
Medium | 8 | 8 | 6 | 6 |
Small | 4 | 4 | 4 | 4 |
Out of the Minimum values, 6 is the maximum value of Medium size.
c. What decision should be made according to the minimax
regret decision rule?
SelectSmall orderMedium orderLarge orderItem 3
Mimmax Regret:
Regret Table:
Amount of snow | ||||
Size of Orders | Heavy | Normal | Light | Maximum |
Large | 0 | 1 | 3 | 3 |
Medium | 2 | 0 | 0 | 2 |
Small | 6 | 4 | 2 | 6 |
Out of the Maximum regret values 2 is the minimum value of Medium Size.
d. What decision should be made according to the EMV
decision rule?
Select Small orderMedium orderLarge orderItem 4
EMV:
Amount of snow | ||||
Size of Orders | Heavy | Normal | Light | EMV |
Probability | 0.25 |
0.6 |
0.15 | |
Large | 10 | 7 | 3 | 7.15 |
Medium | 8 | 8 | 6 | 7.7 |
Small | 4 | 4 | 4 | 4 |
Out of the EMV values 7.7 is the maximum value of Medium Size
e. What decision should be made according to the EOL
decision rule?
SelectSmall orderMedium orderLarge order
Expected Opportunity Loss
Regret Table | ||||
Amount of snow | ||||
Size of Orders | Heavy | Normal | Light | Expected Regret |
Probablity | 0.25 | 0.6 | 0.15 | |
Large | 0 | 1 | 3 | 1.05 |
Medium | 2 | 0 | 0 | 0.5 |
Small | 6 | 4 | 2 | 4.2 |
Out of the Expected Regret values, 0.5 is the minimum value of Medium Size.
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