(14 pts) Teddy Bower is an outdoor clothing and accessories chain that purchases
ID: 350699 • Letter: #
Question
(14 pts) Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $40 each from its Asian supplier, TeddySports. Unfortunately, at the time of order placement, demand is still uncertain. Teddy Bower forecasts that its demand is normally distributed with mean of 2,800 and standard deviation of 1,000. Teddy Bower sells these parkas at $79 each. Unsold parkas will be sold to a discounter at $15 per unit. 1. a) How many parkas should Teddy Bower buy from TeddySports to maximize expected profit? For parts b) through d), assume Teddy Bower orders 3,250 parkas (0-3,250). b) What is Teddy Bower's CSL (in-stock probability)? c) On average, how many customers does Teddy Bower expect to turn away because of shortage? And on average, how many parkas will Teddy Bower liquidate after each season? d) What is Teddy Bower's expected profit?Explanation / Answer
A) Underage Cost = Cu = 79 - 40 = 39
Overage Cost= Co = 40 - 15 = 25
Critical Ratio = Cu/(Cu+Co)= 39/ (39+25) = 0.6094
(z) = 0.6094; z= 0.28
Q = (µ + z) = 2800 + (0.28 x 1000) = 3080
B) Q = 3250
µ = 2800
= 1000
Z = (Q-µ)/ = (3250-2800)/1000 = 0.450
In-Stock Probability = (z) = (0.450)= 0.6736 = 67.36%
C) L(Z) from L(Z) table = 0.21
Expected Lost Sales = * L(Z) = 210
Expected Sale = Expected Demand - Expected lost Sale = 2800 - 210 = 2590
Expected Left Over Inventory = Actual Order - Expected Sale = 3250 - 2590 = 660
D) Expected Profit = Underage Cost * Expected Sale - Overage Cost * Expected left over Inventory = 39*2590 - 25*660 = 84510
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