Answer:
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.
