Problem-5. (14 points) One of the most important considerations in retail operat
ID: 448858 • Letter: P
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Problem-5. (14 points) One of the most important considerations in retail operations is the amount of inventory carried for seasonal products. Matching supply with demand is not easy because some of the seasonal products are manufactured overseas and have to be ordered with a long lead time. Consider the following: The length of the season to sell a fashion apparel or shoe is less than 3 months. In contrast, the manufacturers require that orders be given at least 6 months in advance to guarantee availability of products at the beginning of a sales season. The long lead times prevent retailers from placing additional orders during the season because any additional items would not be received before the season is over This puts department stores such as Nordstrom in a difficult situation; order too few in advance and you lose potential sales during the season, and order too much in advance and you have unsold merchandise at the end of the season One group of seasonal merchandise sold by Nordstrom is baby's shoes. The company gathers regional sales forecasts for the upcoming year and orders shoes from the manufacturers well ahead of the sales season. Information on two products, including the purchasing cost per unit, sales price per unit, salvage value per unit at the end of the season, mean demand, and standard deviation of demand for each item are provided below Demand forecast: Demand is normally Purchasing cost per unit (c Sales price per unit Salvage value per unit (s) distributed Item Average (mean) demand Forecast error (standard deviation of demand) #1 Baby Boy summer sandal (size 12-18 months) #2 Baby Girl summer sandal (size 12-18 months) 16.00 $24.99 $4.99 22,500 2756 $19.00 $32.99$12.99 23,500 4550 NOTE: SHOW ALL YOUR WORK. USE 4 DECIMAL PLACES IN YOUR CALCULATIONS a) (3 points) For many years, the company aimed at 95% se rvice level for all the items in the baby's shoes, i.e., the order quantity for each item has been determined to avoid stock-outs 95% of the time. Compute the order quantity for each item to guarantee this service level. Complete the table below. Show all your work Item Target service Order level 95% 95% Safety stock Probability of a stockout during the level quantity season P(D>a) #2Explanation / Answer
The purchasing cost of Baby Boy = $16
The selling Price = $24.99
Profit = $24.99-$16 = $8.99
The unit cost = $16-$4.99 = $11.01
This Questions are solved by the news paper boy problem model
The news paper boy model = C1/ (C1+C2)
Where C1 is the cost of unsold = Profit = $8.99
C2 is the purcahsing cost = $11.01
The news paper boy model = 8.99/(8.99+11.01) = 0.4495
This is the probability , The value of Z when probability =0.4495 is 1.64
In standard Normal distribution Z = 1.64
Z= (X-Mean)/SD
1.64 = (X-22500)/2756
1.64*2756+22500 =X
The quantity to be purchased = 27019
The 95% of stock level
X-1.96*SE, X+1.96*SE
27019-1.96*2756, 27019+1.96*2756
[21617.24, 32420]
FOR A BABY GIRL SUMMER
The purchasing cost of Baby Girl Summer = $19
The selling Price = $32.99
Profit = $24.99-$16 = $13.99
The unit cost = $19-$12.99 = $6.01
This Questions are solved by the news paper boy problem model
The news paper boy model = C1/ (C1+C2)
Where C1 is the cost of unsold = Profit = $13.99
C2 is the purcahsing cost = $6.01
The news paper boy model = 13.99/(13.99+6.01) = 0.6995
This is the probability , The value of Z when probability =0.6995 is 0.525
In standard Normal distribution Z = 0.525
Z= (X-Mean)/SD
0.525 = (X-23500)/4550
0.525*4550+23500 =X
The quantity to be purchased = 25888.75
The 95% of stock level
X-1.96*SE, X+1.96*SE
25889-1.96*4550, 25899+1.96*4550
=[16971, 34817]
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