Problem 3 (15 points). The local Wal-Mart Store sells party hats to consumers. T
ID: 417154 • Letter: P
Question
Problem 3 (15 points). The local Wal-Mart Store sells party hats to consumers. The department manager of party supplies has analyzed the point of sale data to find that the daily demand for the party hats is normally distributed with mean 40 and standard deviation 13.
a. (5 points) Suppose the manger places replenishment orders to the Wal-Mart distribution center only once a week. What is the weekly demand for party hats?
b. (5 points) How many party hats should be there on the shelf at the beginning of a week to achieve a 95% service level for the week? Assume that no additional receipts of hats are scheduled for the week.
c. (5 points) What is the expected lost sale during a week if the local Wal-Mart has 245 party hats on the shelf at the beginning of the week? Assume that no additional receipts of hats are scheduled for the week.
Explanation / Answer
Given ,
Lead time = o ( i.e. order is received moment it is placed )
Order placement frequency = 7 days ( i.e. 1 week )
Therefore, Protection period = Lead time + Order placement frequency = 7 days
Standard deviation of daily demand = 13
Therefore, Standard deviation of demand during protection period
= Standard deviation of daily demand x Square root ( Protection period )
= 13 x Square root ( 7 )
= 13 x 2.645
= 34.385
Weekly demand for party hats = 40 / day x 7 days = 280 party hats
Z value for 95% service level = NORMSINV ( 0.95 ) = 1.6448
Therefore, safety stock
= Z value x Standard deviation of demand during protection period
= 1.6448 x 34.385
= 56.55 ( 57 rounded to nearest whole number )
Number of hats to be there on shelf at the beginning of a week
= Weekly demand + safety stock
= 280 + 57
= 337 party hats
Expected lost sales if the wal mart store has 245 hats at the beginning of a week = 337 - 245 = 92 hats
WEEKLY DEMAND FOR PARTY HATS = 280 HATS
NUMBER OF PARTY HATS TO BE THERE ON SHELF AT BEGINNING OF THE WEEK = 337
EXPECTED LOST SALES = 92 HATS
WEEKLY DEMAND FOR PARTY HATS = 280 HATS
NUMBER OF PARTY HATS TO BE THERE ON SHELF AT BEGINNING OF THE WEEK = 337
EXPECTED LOST SALES = 92 HATS
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