Question

Assume that the probabilities of demand in Problem 28 are no longer valid; the decision situation is now one without probabilities. Determine the best number of boxes of cards to stock, using the following decision criteria. a. Maximin b. Maximax c. Hurwicz (a=4) d. Minimax regret

28. Ths manager of the greeting card section of Mazey's department store is considering her arder for a pareutar line of Christmas cards The enst of each bos of cards is $3, cach box will be sold for $S during the Christmas season. After Christmas. the cards will be sold for $2 a box. The cand soctice mnager believes thua all leftover cards can be sold at that price. The estimated demand during the Christmas season for the tinc of Christmas cards, with associated probabilities, is as followS Probability Demand (boxes) 25 15 26 .30 27 28 20 15 29 30 t0 a Develop the payoiff table for this decision situation. b Compute the expected value for each alternative and aidentify the best decisionh s Compute the espected value of perfect information 90434401120209 566816768312475648 n.jpg Assume that the probabilities of demand in Problem 28 are no longer valid; the decision situation is now one without probabilities. Determine the best number of boxes of cards to stock, using the following decision eriteria a Maximin b.Maximax e Hurwiez (a 4) d. Minimax regret

Answer 1

Below is the screenshot of the formula applied to get the payoff table -

Book1 Excel Abhishek Rai Insert Page Layout Formulas Data Review View Help Tell me what you want to do A Share File AutoSum A s Cut General Calibri Fill E Copy Paste 트트園Merge & Center. | $. % , 58£2 Conditional Format as CellInsert Delete Format Formatting TableStyles Sort & Find & ClearFter Select B 1 u·B-ク· · Format Painter Clipboard Font Alignment Number Cells Editing C19 Demand (number of Order Box 25 26 27 26 IF 587 5C55,( C55 (5-3-115B7-055)3-201,587 587-5055,11055 5-31587-D55) IF 587 5C55,(E555-3-567-E55 587 5C55,(F55 5-3)-587-F55 587 27 IFISB9 SCS5, IID55 5-3)5B9-DS5) 3-21.SB9 15-3 10 29 12

Below is the pay off table obtained -

Order Box	Demand (number of boxes)
	25	26	27	28	29	30
25	50	50	50	50	50	50
26	49	52	55	58	61	64
27	48	51	54	57	60	63
28	47	50	53	56	59	62
29	46	49	52	55	58	61
30	45	48	51	54	57	60

Maximin Criteria -

Below is the table with minimum payoff -

Order Box	Demand (number of boxes)
	25	26	27	28	29	30	Minimum
25	50	50	50	50	50	50	50
26	49	52	52	52	52	52	49
27	48	51	54	54	54	54	48
28	47	50	53	56	56	56	47
29	46	49	52	55	58	58	46
30	45	48	51	54	57	60	45

From Above -

Maximum of Minimum payoff = 50

Corresponding Order Value = 25

Maximax Criteria -

Below is the table with maximum payoff -

Order Box	Demand (number of boxes)
	25	26	27	28	29	30	Maximum
25	50	50	50	50	50	50	50
26	49	52	52	52	52	52	52
27	48	51	54	54	54	54	54
28	47	50	53	56	56	56	56
29	46	49	52	55	58	58	58
30	45	48	51	54	57	60	60

From Above -

Maximum of Maximum payoff = 60

Corresponding Order Value = 30

Hurwicz Criteria -

Below is the table with weighted payoff -

Order Box	Demand (number of boxes)
	25	26	27	28	29	30	Maximum	Minimum	Alpha*Maximum	(1-Alpha)*Minimum	Weighted Payoff
25	50	50	50	50	50	50	50	50	20	30	50
26	49	52	52	52	52	52	52	49	20.8	29.4	50.2
27	48	51	54	54	54	54	54	48	21.6	28.8	50.4
28	47	50	53	56	56	56	56	47	22.4	28.2	50.6
29	46	49	52	55	58	58	58	46	23.2	27.6	50.8
30	45	48	51	54	57	60	60	45	24	27	51

From Above -

Maximum of weighted payoff = 51

Corresponding Order Value = 30

Minimax Regret-

Below is the table with regret payoff -

Payoff Table
	Order Box	Demand (number of boxes)
		25	26	27	28	29	30
	25	50	50	50	50	50	50
	26	49	52	52	52	52	52
	27	48	51	54	54	54	54
	28	47	50	53	56	56	56
	29	46	49	52	55	58	58
	30	45	48	51	54	57	60
Regret Table
	Order Box	Demand (number of boxes)
		25	26	27	28	29	30	Maximum
	25	0	2	4	6	8	10	10
	26	1	0	2	4	6	8	8
	27	2	1	0	2	4	6	6
	28	3	2	1	0	2	4	4
	29	4	3	2	1	0	2	4
	30	5	4	3	2	1	0	5

From Above -

Minimum of Maximum regret payoff = 4

Corresponding Order Value = 28 or 29