Inventory Management
Inventory refers to idle goods or materials
that are held by an organization for use
sometime in the future.
Inventory Models
„
The study of inventory models is
concerned with two basic questions:
•How much should be ordered each
time
•When should the reordering occur
„
The objective is to minimize total
inventory cost over a specified time
period (assumed to be annual in our
examples).
Inventory Costs
„
Ordering cost -- salaries and expenses of
processing an order, regardless of the order
quantity
„
Holding cost -- usually a percentage of the
value of the item assessed for keeping an item
in inventory (including finance costs,
insurance, security costs, taxes, warehouse
overhead, and other related variable expenses)
„
Purchase cost -- the actual price of the items
Deterministic Models
„
The simplest inventory models assume
demand and the other parameters of the
problem to be deterministic and constant.
„
The models we will cover are:
• Economic order quantity (EOQ)
• Economic production lot size (PLS)
„
Variations of these and more complex
models will be covered in upper level
business classes.
Economic Order Quantity (EOQ)
„
The most basic of the deterministic
inventory models is the economic order
quantity (EOQ).
„
The variable costs in this model are annual
holding cost and annual ordering cost.
„
Using the EOQ, annual holding and
ordering costs are equal at the optimal
point.
Inventory Costs
Cost
$
Annual Ordering
Cost
Order Quantity
Inventory Costs
Cost
$
Annual
Holding Cost
Order Quantity
Inventory Costs
Cost
$
Annual
Holding Cost
Annual Ordering
Cost
Q*
Order Quantity
Inventory Costs
Annual Total Cost
Cost
$
Annual
Holding Cost
Annual Ordering
Cost
Q*
Order Quantity
Economic Order Quantity
Assumptions
„ Demand is constant throughout the year.
„
Purchase cost per unit is constant
regardless of the quantity or time of
purchase.
„
Delivery time (lead time) is constant.
„
The entire order is received at the same
time.
Economic Order Quantity
Notation
„
D= annual demand in units.
„
Q=Quantity per order
„
$C=unit purchase cost of each item.
„
Ordering cost is $Co per order.
„
I= annual holding cost rate as a % of $ value.
„
Holding cost is $Ch per item in inventory per
year
• Ch = C*I
Inventory cycle
Inventory Level
Inventory is used at a constant rate
and replenished all at once.
Q
Average
Inventory
Level
Q
2
Time
Inventory Costs
Q
Average units in stock =
2
QC
$ value of average inventory =
2
Annual Holding Cost =
QCI orQCh
2
2
Number of annual orders =
D
Q
Annual Ordering Cost = DCo
Q
Total Inventory Costs
Total Annual Inventory Cost =
Holding Cost
QCh
2
+
+
Ordering Cost
DCo
Q
Economic Order Quantity
Formulas
„
Optimal order quantity: Q* =
„
Number of orders per year: D
2DCO
Ch
Q*
„
Time between orders (cycle time):
Q*
years
D
Q * Ch
„ Total annual cost:
2
DCO
+
Q*
(holding + ordering)
„
(at Q*)
Reorder point: r = dm
(daily demand) * (lead time)
Example: Bart’s Barometer Business
Bart's Barometer Business (BBB) is a retail
outlet which deals exclusively with weather
equipment. Currently BBB is trying to decide on an
inventory and reorder policy for home barometers.
Barometers cost BBB $50 each and demand is
about 500 per year distributed fairly evenly
throughout the year. Reordering costs are $80 per
order and holding costs are figured at 20% of the
cost of the item.
BBB is open 300 days a year (6 days a week and
closed two weeks in August). Lead time is 60
working days.
Example: Bart’s Barometer Business
Barometers cost BBB $50 each = C
Demand is about 500 per year = D
Reordering costs are $80 per order = CO
Holding costs are figured at 20% = I
BBB is open 300 days a year so 500/300 = d
Lead time is 60 working days = m
Ch = C * I = ($50)(.2) = $10
Example: Bart’s Barometer Business
„
Optimal Order Quantity
Q* = 2DCO
Ch
„
=
2(500)(80)
= 89.44 ≈ 90
10
Optimal Reorder Point
Lead time is m = 60 days and daily demand is
d = 500/300 or 1.667.
Thus the reorder point r = (1.667)(60) = 100.
Bart should reorder 90 barometers when his
inventory position reaches 100 (that is 10 on hand
and one outstanding order).
Example: Bart’s Barometer Business
„
Number of Orders Per Year
Number of reorder times per year = (500/90) = 5.56
or once every (300/5.56) = 54 working days (about
every 9 weeks).
„
Total Annual Variable Cost
TC= (1/2)(Q)(Ch) + (DCo)/Q
= (1/2)(90)(10) + (500)(80)/90
= 450 + 444 = $894.
^
^
(Why aren’t these equal?)