6. Everest Outfitters has designed four styles of outdoor winter wear for the 20

Question

6. Everest Outfitters has designed four styles of outdoor winter wear for the 2007 winter season: Alps, Pyrenees, Andes and Rockies. Everest can produce some outerwear styles well in advance of the selling season with the remaining styles produced after the 2007 Winter Outerwear Fashion Trade (WOFT) show that occurs before the selling season. At the time it makes its initial production decision, Everest's forecast for each style's demand is normally distributed with means and standard deviations listed in the table below. The table also lists results from the Newsvendor model when expected profit is maximized. Style Price Mean Std C,C, Q Expected dev Profit 200 500 125 16 48 584 21,458 120 1,000 350 17 30 1,124 23,835 100 1,500 275 16 24 1,570 31,70 150 750 250 30 60 858 36,820 Alps Andes Pyrenees Rockies Mean- expected demand: Std dev - standard deviation of demand, C - overage cost; C - underage cost Q Newsvendor optimal order quantity After the trade show, and before it makes its final production decision, Everest will know exact a) 12pts] Suppose Everest chooses to produce the Alps style before the WOFT show. What is the b) 12pts) Because the WOFT show concludes shortly before the selling season, Everest has limited demand for each style. probability that Everest will have more than 250 units of Alps inventory left at the end of the season? capacity for production before the WOFT show. Recall,each style is produced either before or after WOFT show (i.e, no style is produced both before and after the show), How many units should Everest produce before the WOFT Trade show? after the WOFT show. As a result, it needs to produce at least 1700 units Style Price Mean Std ccQExpected Max Mis-M Newstendor Profit match R Profit dev 24000 2542 4.35 30000 6165 5.48 36000 4250 2.71 200 500 125 16 48 584 21.458 Andes 120 1,000 350 17 30 1124 23,835 Pyrenees 100 1,500 275 16 24 1,570 31,750

Explanation / Answer

a0

more than 250 left so demand is less than (584 -250) = 334

p(alps<334)

alps ~ N(500, 125)

p(alps<334)

= 0.09208905

b)

in stock probabilities are

alps

> dnorm((1124-1000)/350, 0,1)
[1] 0.3746745

andes

> dnorm((584-500)/125, 0,1)
[1] 0.3183097

pyrenes

> dnorm((1570-1500)/275, 0,1)
[1] 0.386225

rockies
> dnorm((858-750)/250, 0,1)
[1] 0.3634002

we probuce the two which are most likely to go out of stock

andes:1124

rockies 858

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