Teddy bower is an outdoor clothing and accessories chain that purchases a line of parkas at $10 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 2,100 and standard deviation of 1,200. teddy bower sells these parkas at $22 each. unsold parkas have little salvage value; teddy bower simply gives them away to a charity.

a) how many parkas should teddy bower buy from teddysports to maximize expected profit?

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?

e)evaluate teddy bower's stockout probability.

Following is the analysis of Teddy Bower expected profits, stock-in and stock-out profitability.

Explanation:

Answer a)

To determine how much teddy bowers should buy to maximize the expected profits  

=22 - 10 = 12, and the overage cost, =10 - 0 = 10. The critical ratio is 12/ (10 + 12) = 0.5455. We see from the Standard Normal Distribution Function Table that    (0.11) =0.5438 and (0.12) =0.5478,  

We choose z= 0.12. Convert that z-statistic back into an order quantity, Q = μ+z* = 2100 +  

0.12*1200= 2,244.

Answer b)

We assume that they wish to target in stock probability of 90%, we need to find the z-statistic such that.  We have chosen 2.10 from normal distribution table to find to analyse what should be the target of teddy bower’s if they wish to get 90% in-stock probability = 2100 + 2.10 * 1200 = 4522

They need to produce 4522 to reach 90% stock-in probability.

Answer c)

C) Teddy bowers has a limited supply of parkas and, in order to fulfill the demand, If they don’t buy parkas from teddy sports, they expect to turn away almost 18.9% of their buyers because there is a shortage of product they produce. Because according to the above calculation if they produce almost 4522 parkas, they have a 90% stock-in chance.

Answer d)

We are assuming 3000 parkas, if 3000 parkas are ordered then the corresponding z-statistic is (3000 -  2100) /1200 = 0.75.

Now look up expected lost sales with the Standard Normal distribution in the Standard Normal Loss Function  

Table: L(0.75)  =  0.1312 . Convert that lost sales into the expected lost sales with the actual demand distribution= 1200* 0.1312 = 157.4.

Expected sales = expected demand – expected lost sales

                         = 2100-157.4 = 1942.6.

Expected left over inventory = 3000 –1942.6 = 1057.4.

Finally,

Expected profit = (22-10)*1942.6-(10-0)*1057.4

                         = 12,737

Answer e)

Teddy Bower is a chain that buys a line of parkas at $10 each from its Asian provider, Teddy Sports. Similarly, the demand for their product is still uncertain, and there is a chance that some customers might not be able to get the product due to stock out. According to the given data, there is a 22.7% probability of stock out which is not suitable for their business.  

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