Problem 1 20 points Sprit Halloween sells various Halloweenr

Problem 1 (20 points). Sprit Halloween sells various Halloween-related seasonal merchandise during the fall season throughout the US. It often rented spaces at any location for a few months in fall to sell its merchandise. Consider the problem of a specific merchandise, the Elvis wig, at the local Spirit Halloween store. The store manager estimates the weekly demand for the wig to be normally distributed with mean 74 and standard deviation 22.

a. (5 points) Suppose that the local store has 98 Elvis wigs in stock at the beginning of a week, and that no additional receipts are scheduled for the week. What then is the chance of a stock out during the week?

b. (5 points) How much inventory of the Elvis wig does the store need for the week if it wants the stock-out probability to be 2% or less?

c. (5 points) What is the chance that the weekly demand is within 20% of the average/man value?

d. (5 points) Consider a second wig, “2099: the wig of the future” that is also sold by the local Sprit Halloween store. The weekly demand for this wig is identical to that of the Elvis wig (i.e., normally distributed with mean 74 and standard deviation 22). Furthermore, the demand for the two wigs are perfectly substitutable, implying, any customer looking for the Elvis wig will buy the wig of the future if the former is out-of-stock, and the vice versa. As a result, the store manager is thinking of managing the inventory of these two items together. How much total inventory (i.e., Elvis plus the wig of the future) wigs does the store need for the week if it wants the stock-out probability to be 2% or less?

Solution

Mean demand 74.00 Std deviation 22.00 a Inventory beginning 98.00 Prob(Demand>98) 0.14 Using norm.dist function in excel If demnad is more than 98 there will be stockout b Stockout probablity 0.02 Inventory level 119.18 So for a stock out probablity of 2%,98% of the time there should be stock So using norm.inv function in excel wil probablity of 98% will give the desired inventory level c Probablity of being within 20% of average Average+20% 88.80 Average-20% 59.2 Probablity(88.8>demand<59.2) 0.50 Using norm dist function for finding probablity between above two values d second wig Mean 74 Std dev 22 Combined mean 148 Combined Std dev 31.11 It is std dev*sqrt(2), as there are two types Stock out probablity 2% Inventory level 211.90 Using the Norm.inv function and combined mean and combined std dev