Annual demand for an item is 40,000 units. The holding cost rate is 30% of the item cost. Ordering costs are $60/ order. Quantity discounts are available according to the schedule below: Quantity Price per Unit ($) 1-99 90.00 100-299 85.00 300-399 80.00 400+ 78.00 a. What is the optimal order quantity? b. What is the total annual inventory cost of your policy? c. Assume 52 five-day weeks per year. If the lead-time is 5 weeks, what should the reorder point be? Solution Hi, a) optimal order quantity = sqroot(2*40000*60/(30%*78)) = 452.91 =453 units b) total annual inventory cost = Annual demand * unit cost + ordering cost*annual demand/ordered quantity + Carrying cost per unit * unit cost * average inventory per cycle =40000*78+60*40000/453+78*(453/2)*60 =$4185318 c) Reorder Point = (Lead Time + Safety Stock + Basic Stock) * Unit Sales Per Day Please provide the safety stock to calulate the re order point.

1. Annual demand for an item is 40,000 units. The holding cost rate is 30% of the item cost.
Ordering costs are $60/ order. Quantity discounts are available according to the schedule below:
Quantity Price per Unit ($)
1-99 90.00
100-299 85.00
300-399 80.00
400+ 78.00
a. What is the optimal order quantity?
b. What is the total annual inventory cost of your policy?
c. Assume 52 five-day weeks per year. If the lead-time is 5 weeks, what should the reorder point
be?
Solution
Hi,
a) optimal order quantity = sqroot(2*40000*60/(30%*78))
= 452.91
=453 units
b) total annual inventory cost = Annual demand * unit cost + ordering cost*annual
demand/ordered quantity + Carrying cost per unit * unit cost * average inventory per cycle
=40000*78+60*40000/453+78*(453/2)*60
=$4185318
c) Reorder Point = (Lead Time + Safety Stock + Basic Stock) * Unit Sales Per Day
Please provide the safety stock to calulate the re order point