Fly-at-Night Express uses 10,000 #3 envelopes per month. It costs $50 to order a
ID: 346868 • Letter: F
Question
Fly-at-Night Express uses 10,000 #3 envelopes per month. It costs $50 to order and receive a shipment of these envelopes. The envelopes cost $.40 each, and Fly-at-Night uses an inventory carrying cost rate of $.12 per envelope per year. (a) (2 pts) Determine the economic order quantity (EOQ). (b) (2 pts) Determine the time between orders when the EOQ is used if Fly-at-Night operates 307 days per year. (c) (2 pts) Calculate the total cost of managing the inventory when the EOQ is used. (c) (2 pts) What should the reorder point be if the envelope supplier takes ten working days to deliver? (d) (2 pts) If the usage rate given is an average and the standard deviation of daily usage of envelopes is 75, what should the reorder point and safety stock be if Fly-at-Night wants to take no more than a 5% chance of running out of stock of envelopes during any given order cycle (i.e., Z = 1.645)?
Explanation / Answer
Given are the following data :
Ordering cost = Co = $50
Demand of envelope for Fly-at-night express = D = 10,000 / month x 12 months = 120,000
Annul unit Inventory carrying cost = Ch = $0.12 per envelope per year
= Square root ( 2 x Co x D / Ch )
= Square root ( 2 x 50 x 120000/ 0.12 )
= 10,000
ECONOMIC ORDER QUANTITY = 10,000
b)Time between orders when EOQ is used ( 1 month = 1/ 12 th of a year )
= 307 days in a year/ 12
= 25.58 days
TIME BETWEEN ORDERS WHEN EOQ IS USED = 25.58 DAYS
c)Annual ordering cost
= Ordering cost per order x Number of orders = Co x Annual demand/ EOQ = 50 x 120,000/10,000 = $ 600
Annual inventory carrying cost
= Annual unit inventory carrying cost x Average Inventory
= Ch x EOQ / 2
= 0.12 x 10,000/2
= $600
Total cost of managing the inventory when EOQ is used
= Annual ordering cost + Annual inventory carrying cost
= $600 + $ 600
= $1200
TOTAL COST OF MANAGING INVENTORY WHEN EOQ IS USED = $1200
d)Reorder point = Average daily demand x 10 working days of lead time
Average daily demand = 120,000 / 307
Therefore , Reorder point = ( 120,000/ 307 ) x 10 = 3908.79 ( 3909 rounded to nearest whole number )
REORDER POINT = 3909ENVELOPES
e)Standard deviation of daily usage of envelope = Sd = 75
Z value corresponding to 5% stock out probability = 1.645
Lead time = 10 days
Therefore, standard deviation of demand during lead time
= Sd x Square root ( Lead time )
= 75 x Square root ( 10 )
= 75 x 3.162
= 237.15
Safety stock = Zvalue x Standard deviation of demand during lead time = 1.645 x 237.15= 390.11 ( 390 rounded to nearest whole number )
Revised reorder point
= Reorder point ( without safety stock ) + Safety stock
= 3909 + 390
= 4299
SAFETY STOCK = 390 ENVELOPES
REORDER POINT = 4299 ENVELOPES
ECONOMIC ORDER QUANTITY = 10,000