Question

1. Lott Manufacturing, Inc. has been ordering parts for its production process in lots of 10,000 units. Each order costs the firm $50 to place, and holding costs per unit average $3. Lott uses 200,000 units every 250 days.

   1. Calculate the EOQ.

   2. Calculate the difference in inventory costs implied by the EOQ and the current order quantity of 10,000 units.

   3. If it takes 2 days to receive an order from suppliers, at what inventory level should another order be placed?

Answer 1

(a) When ordered as per current policy

Order Quantity Q = 10000
Average Inventory = Q/2 =  = 10000/2 = 5000
Annual Inventory Holding cost = average inventory * unit carrying cost = (Q/2)*Cc = (10000/2)*3 = 15000
Number of Orders = D/Q = 200000/10000 = 20
Annual Order cost = Number of orders * cost/order = (D/Q)*Co = (200000/10000)*50 = 1000
Total Annual Cost = Annual Inventory Holding Cost + Annual Order Cost = 15000 + 1000 = $16000

When ordered as per EOQ

Annual Demand = D = 200000/year
Ordering Cost = Co = $50
Holding Cost = Cc = $3
Economic Order Quantity Q* = √(2DCo/Cc) = √(2*200000*50*/3) = 2581.99
Average Inventory = Q*/2 =  = 2581.99/2 = 1291
Annual Inventory Holding cost = average inventory * unit carrying cost = (Q*/2)*Cc = (2581.99/2)*3 = 3872.99
Number of Orders = D/Q* = 200000/2581.99 = 77.46
Annual Order cost = Number of orders * cost/order = (D/Q*)*Co = (200000/2581.99)*50 = 3872.98
Total Annual Cost = Annual Inventory Holding Cost + Annual Order Cost = 3872.99 + 3872.98 = $7745.97

Difference in cost = 16000 - 7745.97 = $8254.03

(b) Order should be placed when the inventory reached the Reorder Point

Reorder Point = dL,

where d = daily = 200000/250 = 800

L = lead time = 2 days

Reorder Point = 800*2 = 1600 units