Fashionables is a franchisee of The UnLimited, the well-known retailer of fashio
ID: 3184271 • Letter: F
Question
Fashionables is a franchisee of The UnLimited, the well-known retailer of fashionable clothing. Prior to the winter season, The UnLimited offers Fashionables the choice of five different colors of a particular sweater design. The sweaters are knit overseas by hand, and because of th lead times involved, Fashionables will need to order its assortment in advance of the selling season. As per the contracting terms offered by The UnLimited, Fashionables will also not be able to cancel, modify or reorder sweaters during the selling season. Demand for each color during the season is normally distributed with a mean of 500 and a standard deviation of 225. Further, you may assume that the demand for each sweater is independent of the demand for any other color.
The UnLimited offers the sweaters to Fashionables at the wholesale price of $45 per sweater, and Fashionables plans to sell each sweater at the retail price of $74 per unit. The UnLimited does not accept any returns of unsold inventory. However, Fashionables can sell all of the unsold sweaters at the end of the season at the fire-sale price of $25 each.
If a part of the question specifies whether to use Table 13.4, or to use Excel, then credit for a correct answer will depend on using the specified method.
A) How many units of each sweater-type should Fashionables order to maximize its expected profit? Use Table 13.4 and round to nearest integer.
B) If Fashionables wishes to ensure a 97.5% in-stock probability, what should its order quantity be for each type of sweater? Use Table 13.4 and round to nearest integer.
C)Say Fashionables orders 650 of each sweater. What is Fashionables’ expected profit? Use Table 13.4.
D) Say Fashionables orders 650 of each sweater. What is the stockout probability for each sweater? Use Excel.
Fashionables is a franchisee of The UnLimited, the well-known retailer of fashionable clothing. Prior to the winter season, The UnLimited offers Fashionables the choice of five different colors of a particular sweater design. The sweaters are knit overseas by hand, and because of th lead times involved, Fashionables will need to order its assortment in advance of the selling season. As per the contracting terms offered by The UnLimited, Fashionables will also not be able to cancel, modify or reorder sweaters during the selling season. Demand for each color during the season is normally distributed with a mean of 500 and a standard deviation of 225. Further, you may assume that the demand for each sweater is independent of the demand for any other color.
The UnLimited offers the sweaters to Fashionables at the wholesale price of $45 per sweater, and Fashionables plans to sell each sweater at the retail price of $74 per unit. The UnLimited does not accept any returns of unsold inventory. However, Fashionables can sell all of the unsold sweaters at the end of the season at the fire-sale price of $25 each.
If a part of the question specifies whether to use Table 13.4, or to use Excel, then credit for a correct answer will depend on using the specified method.
TABLE 13.4 The Distribution, FQ), and Expected Inventory, (Q), Functions for the Standard Normal Distribution Function 9192 9332 9452 9554 0455 0561 0686 0833 1004 1202 1429 1687 1978 2304 2668 3069 3509 3989 4509 5069 5668 6304 6978 7687 8429 9202 1.0004 1.0833 1.1686 1.2561 1.3455 1357 1587 1841 1.5293 1.6232 1.7183 1.8143 -0.9 9713 9772 9821 9861 9893 .0002 0003 0005 0007 0010 0013 0019 0026 0035 0047 0062 .0082 0001 0001 -0.6 2.1 065 0002 2.3037 2.4027 2.5020 2.6015 2.7011 2.8008 2.9005 -0.4 3821 4207 4602 5000 5398 5793 6179 6554 6915 7257 7580 7881 8159 9938 9953 9965 9974 0008 0015 0020 0027 0037 0049 0065 0085 9987 9990 9993 9995 9997 9998 9998 3.1 003 3.2002 3.3001 3.4001 3.5001 2.2 0139 0179 .0228 0287 0359 0446 0548 6 0183 0232 0293 0367 3.7000 8643 8849 9032 3.8000 0808Explanation / Answer
Average Demand = = 500
Standard Deviation = = 225
Retail price = p = 74
Unit Cost = c = 45
Salvage cost = s = 25
1a) How many units of each sweater type should Fashionable order to maximize its expected profit?
Cu = under-stocking cost = cost of shortage (underestimate demand) = Sales price/pair– Cost/pair
Cu = 74 – 45 = $29 per unit
Co = Over-stocking cost = Cost of overage (overestimate demand) = Cost/pair – Salvage value/pair
Co = 45 – 25 = $20 per unit
The service level or probability of not stocking out, is set at,
Service Level = critical ratio = Cu/( Cu + Co) = 29/(29 + 20)
Service Level = 0.59
Company needs to find the z-score for the demand’s normal distribution that yields a probability of 0.6000.
F(0.2) = 0.5793 and F(0.3) = 0.6179
To maximize the profit select higher F(z), z = 0.3
Optimal order quantity = µ + z = 500 + (0.3)225 = 500 + 67.5
Optimal Order quantity = 568 units of each color
Thus, Fashionable should order 568 units of each sweater to maximize its expected profit
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