Question

. A store that sells healthy food has an annual demand for a specific item 810 units. The cost of placing an order is $20, while holding cost per unit per year is $4.

1. How many orders per year should they have
2. What is the minimum total cost of inventory (ordering and holding)

Answer 1

Assume Ordering Quantity=Q

N=Number of orders in a year=810/Q

Annual ordering Cost =N*$20=(810/Q)*20=16200/Q

Average Inventory=Q/2

Annual holding cost=(Q/2)*$4=2*Q

For Economic Order Quantity,

The total cost of Ordering and holding will be minimum if,

Annual ordering Cost=Annual holding cost

(16200/Q)=2*Q

(Q^2)=(16200/2)=8100

Q=Square Root (8100)=90

Economic Order Quantity=90

a. Number of Orders per year=N=810/90=9

b.Minimum total cost (ordering and holding)=(16200/Q)+(2*Q)=(16200/90)+(2*90)=180+180=360

Minimum total Cost =$360