Inventory Control Guide Page 8
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40EOQ: The Model
This chart shows how the inventory evolves over time. Starting from some value, the inventory
decreases at a constant rate of D items per time unit. When it reaches zero, an order of size
Q is placed and immediately received since the lead time is zero.
Inventory
-D
Q
time
Q / D
C (Q) = Total cost over 1 year with a lot size of Q
Let us review the three cost components.
cost of 1 order × × × × # orders in one year
C (Q)
=
The order/setup cost is O. How often do we order/setup in one year?
We first see that the time between two orders is Q/D. For example, if you order per lots of size
Q=10 items and if the daily demand is D=2 items/day, then you will keep five days (Q/D=5
days) with this order. "5 days" is thus the time between two orders.
The inverse, D/Q is the number of orders per day if D is expressed per day. In this example,
D/Q=0.2/day, that is 0.2 orders per day or 1 order every 5 days. If we express D per year, we
get D/Q=730/10 =73 orders per year.
cost of holding 1 item 1 year × × × ×
+
average # items in inventory during 1 year
The holding cost is H per item per time unit. Here we chose the year as time unit.
How many items do remain in the inventory, on the average? This is given by the area below
the inventory curve. Each triangle can be replaced by a rectangle of half the height, that is
Q/2. The surface is then (Q/2 × one year).
Intuitively, if you order per lot of size Q, an average inventory of Q/2 will remain all the time in
your inventory. Over 1 year, this cost amounts to Q/2 times the holding cost per item per year.
item cost × × × × # items ordered in one year
+
The item costs is just the cost of all the items which are ordered. In one year, we will order
what is needed, that is the demand D over one year. This money is independent of the lot size
Q. Using an abbreviated notation:
C (Q)
=
O D / Q + H Q / 2 + I D
Prod 2100-2110
Inventory Control
7
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