An Economic Order Quantity Example
Q = Number of pieces per order
Q* = Economic Order Quantity (EOQ)
D = Annual demand in units
S = Setup or order cost for each order
H = Holding cost per unit per year
L = Lead time for a new order in days
Annual Setup Cost = (D / Q) S
Annual Holding Cost = (Q / 2) H
2DS
Q* =
H
Expected Number of Orders N = D / Q*
Expected time between orders T = Days per year / N
Total Annual Cost TC = (D / Q) S + (Q / 2) H
Demand per day d = D / Days per year
Reorder Point ROP = dL
Example: Bernard Callebaut operates a chocolate shop in Kensington. The annual
demand for chocolate-covered cherries is 2,500 units. The setup cost is $15 per order.
The holding cost per unit per year is $0.25. What is the optimum number of units per
order? What is the expected number of orders per year? Assuming a 250 day working
year, what is the expected time between orders? What are the total annual inventory
costs? If delivery of the chocolates takes 2 days, at what level of stock should a new
order be placed?
Q* =
2DS
=
H
N = D / Q* =
T = Days per year / N =
TC = (D / Q) S + (Q / 2) H =
ROP = dL =
A Production Order Quantity Example
Q = number of pieces per order
H = holding cost per unit per year
p = Daily production rate
d = Daily demand rate
t = Length of production run in days
Setup Cost = (D / Q) S
Holding Cost = ½ HQ[ 1 – d/p ]
2DS
Q* =
H 1  d / p 
Example: Bernard Callebaut makes peanut clusters. Their forecast for demand is 4,000
units per year, with an average daily demand of 20 units. The production process is
most efficient when 60 units per day are produced. The setup cost is $15, and the
holding cost is $0.25 per unit per year. What is the optimum number of units per order?
Q* =
2DS
=
H 1  d / p 
A Quantity Discount Example
I = Holding cost percentage
P = Unit Price
Q* =
2DS
IP
Example: Chocolate is ordered by the factory from a supplier in Belgium. Normally the
cost for a case of chocolate is $50, but a quantity discount is provided by the
manufacturer, and the cost for quantities of 200 cases or more is $40. Order cost is $25
per order, and the projected annual demand for chocolate is 500 cases of chocolate.
Inventory carrying charge, as a percentage of cost, is 25%. What order quantity will
minimize the inventory cost?