Question

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.

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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 1

Answer:

(a) Large Order

(b) Medium Order

(c) Medium Order

(d) Medium Order

(d) Medium Order

Solution is given below:

(a) 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) Maximin:

	Amount of Snow
Size of Orders	Heavy	Normal	Light	Minimum
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) Minmax 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) 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) Expected Opportunity Loss

	Regret Table
	Amount of Snow
Size of Orders	Heavy	Normal	Light	Expected Regret
Probability	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.