BUAD306
Chapter 13 - Inventory Management
Everyday Inventory
Food
 Gasoline
 Clean clothes…

What else?
Inventory


Stock or quantity of items kept to meet
demand
Takes on different forms






Final goods
Raw materials
Purchased/component parts
Labor
In-process materials
Working capital
Inventory
Static – only one opportunity to buy
and sell units
 Dynamic – ongoing need for units;
reordering must take place

Demand

Dependent Demand


Items are used internally to produce a
final product
Independent Demand

Items are final products demanded by
external customers
Reasons To Hold Inventory







To meet anticipated demand
To smooth production requirements
To decouple components of the productiondistribution system
To protect against stock-outs
To take advantage of order cycles
To hedge against price increases or to take
advantage of quantity discounts
To permit operations
Inventory Costs

Carrying Costs


Ordering Costs


Costs of holding an item in inventory
Costs of replenishing inventory
Shortage (stockout) Costs

Temporary or permanent loss of sales
when demand cannot be met
Inventory Management
How much and when to order inventory?
Objective: To keep enough inventory
to meet customer demand and also
be cost-effective
 Purpose: To determine the amount of
inventory to keep in stock - how much
to order and when to order

Inventory Management
Requirements
A system to keep track of the inventory
on hand and on order
 A reliable forecast of demand
 Knowledge of lead times
 Reasonable estimates of inventory
costs
 A classification system for inventory
items (ABC)

Inventory Control Systems

Control the level of inventory by
determining how much to order and
when
Continuous (Perpetual) Inventory
System - a continual record of the
inventory level for every item is
maintained
 Periodic Inventory System - inventory
on hand is counted at specific time
intervals

Other Control Systems/Tools
Two-Bin System - two containers of
inventory; reorder when the first is
empty
 Universal Product Code (UPC) - Bar
code printed on a label that has
information about the item to which it
is attached
0
 RFID Tags

214800
232087768
Considerations

Lead Time


Cycle Counting


Time interval between ordering and
receiving the order
Physical count of items in inventory
Usage Rate

Rate at which amount of inventory is
depleted
Inventory Cycle
Profile of Inventory Level Over Time
Q
Usage
rate
Quantity
on hand
Reorder
point
Receive
order
Place Receive
order order
Lead time
Place
order
Receive
order
Time
Economic Order Quantity

The EOQ Model determines the
optimal order size that minimizes total
inventory costs
Inventory Costs

Carrying Costs – cost associated with
keeping an item in stock


Includes: storage, warehousing,
insurance, security, taxes, opportunity
cost, depreciation, etc.
Ordering Costs – cost associated with
ordering and receiving inventory

Determining quantities needed,
preparing documentation, shipping,
inspection of goods, etc.
Optimal Order Quantity
Q
o
=
2DS = 2 (Annual Demand) (Order Cost)
H
Annual Holding Cost per unit
Length of order cycle =
Qo
D
# Orders / Year =
D
Qo
Basic EOQ Model
Annual
Annual
Total cost = carrying + ordering
cost
cost
TC =
Where:
Qo
H
2
+
DS
Qo
Qo = Economic order quantity in units
H = Holding (carrying) cost per unit
D = Demand, usually in units per year
S = Ordering cost
Cost Minimization Goal
Annual Cost
The Total-Cost Curve is U-Shaped
TC 
Qo
D
H
S
2
Qo
Carrying Costs
Ordering Costs
QO (optimal order quantity)
Order Quantity
(Q)
EOQ Example 1
A local office supply store expects to sell
2400 printers next year. Annual carrying
cost is $50 per printer, and ordering cost is
$30. The company operates 300 days a
year.
A) What is the EOQ?
B) How many times per year does the store reorder?
C) What is the length of an order cycle?
D) What is the total annual cost if the EOQ quantity is
ordered?
Given:
Demand = D = 2400
Holding Cost = H = $50 per unit per year
Ordering Cost = S = $30
A. What is the EOQ?
B. How many times per year does the store reorder?
C. What is the length of an order cycle?
Given:
Demand = D = 2400
Holding Cost = H = $50 per unit per year
Ordering Cost = S = $30
D. What is the total annual cost if the EOQ quantity is
ordered?
TC = Carrying cost + Ordering cost
EOQ Example 2
A local electronics store expects to sell 500
flat-screen TVs each month during next
year. Annual carrying cost is $60 per TV,
and ordering cost is $50. The company
operates 364 days a year.
A) What is the EOQ?
B) How many times per year does the store reorder?
C) What is the length of an order cycle?
D) What is the total annual cost if the EOQ quantity is
ordered?
Given:
Demand = D = 6,000
Holding Cost = H = $60 per unit per year
Ordering Cost = S = $50
A. What is the EOQ?
B. How many times per year does the store reorder?
C. What is the length of an order cycle?
Given:
Demand = D = 6,000
Holding Cost = H = $60 per unit per year
Ordering Cost = S = $50
D. What is the total annual cost if the EOQ quantity is
ordered?
TC = Carrying cost + Ordering cost
Other Considerations
Safety Stock
 Reorder Point
 Seasonality

Quantity Discounts
A
price discount on an item if
predetermined numbers of units
are ordered
TC =
Carrying cost + Ordering cost + Purchasing cost =
(Q / 2) H + (D / Q) S + PD
where P = Unit Price
Quantity Discount Example
Campus Computers 2Go Inc. wants to reduce a large
stock of laptops it is discontinuing. It has offered the
University Bookstore a quantity discount pricing
schedule as shown below. Given the discount
schedule and its known costs, the bookstore wants to
determine if it should take advantage of this discount
or order the basic EOQ order size.
Quantity
Price
Carrying Cost:
$200
1 – 49
$1,500
Ordering Cost
$1,000
50 – 89
$1,000
Annual Demand
400 units
90 +
$800

First, determine the optimal size and cost with the
basic EOQ model.
 QO =

This order size is eligible for the discount price of $1,000…
now we compute the total cost
 TC =

Compare this cost to an ordering size of 90 @ $800:
 TC = (Q / 2) H + (D / Q) S + PD =

What if a new discount was offered where they would
receive a price of $790 if they were to order 150 or
more?
HW #13
A mail-order house
uses 18,000 boxes
a year. Carrying
costs are $.60 per
box per year and
ordering costs are
$96. The following
price schedule is
offered. Determine
the EOQ and the #
of orders per year.
# Boxes
Unit Price
1000-1999
$1.25
2000-4999
$1.20
5000-9999
$1.15
10000+
$1.10
EOQ with Incremental
Replenishment (EPQ)
Used when company makes its own
product
 Considers a variety of costs/terms:

Carrying Cost
 Setup Cost (analogous to ordering costs)
 Maximum and Average Inventory Levels
 Economic Run Quantity
 Cycle Time
 Run Time

EOQ with Incremental
Replenishment (EPQ)

Definitions
S = Setup Cost
 H = Holding Cost
 Imax = Maximum Inventory
 Iavg = Average Inventory
 D = Demand/Year
 p = Production or Delivery Rate
 u = Usage Rate

EOQ with Incremental
Replenishment
Total Cost = Carrying
Cost + Setup Cost
Economic run quantity
(Imax/2) H + (D/Qo) S
Qo = 2DS/H * p/(p-u)
Cycle time (time between Qo /u
runs)
Run time (production
Qo /p
phase)
Maximum Inventory Level Imax = (Qo /p)(p-u)
Average Inventory Level
Iaverage = Imax /2
Assumptions
Only one item is involved
 Annual demand is known
 Usage rate is constant
 Usage occurs continually, production
periodically
 Production rate is constant
 Lead time doesn’t vary
 No quantity discounts

EOQ Replenishment Example
A toy manufacturer uses 48,000 rubber wheels per
year for its product. The firm makes its own
wheels, which it can produce at a rate of 800 per
day. The toy trucks are assembled uniformly over
the entire year. Carrying cost is $1 per wheel a
year. Setup cost for a production run of wheels is
$45. The firm operates 240 days per year.
Determine the:
Optimal
run size
Minimum total annual cost for carrying and setup
Cycle time for the optimal run size
Run time




D = 48,000 wheels per year
S = $45
H = $1 per wheel per year
p = 800 wheels per day
u = 48,000 wheels per 240 days, or 200 wheels per day
Qo = 2DS/H *
p/(p-u) =
Imax = (Qo /p)(p-u) =
TCmin = (Imax/2) H + (D/Qo) S =
Cycle time = Qo /u =
Run time = Qo /p =
1
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1000
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800
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START ALL OVER
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