Inventory
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Overview of inventory
• Inventory functionality and
definitions
• Inventory carrying cost
• Planning inventory
• Managing uncertainty
• Inventory management
policies
• Inventory management
practices
7-2
Why do we have inventories?
Because the customer usually
isn’t sitting at the plant exit!
Queen Elizabeth research station in Antarctica
7-3
Risks associated with holding inventory
• Typical measures of exposure to investments in inventory
– Time duration
– Depth of commitment
– Width of commitment
• Supply chain exposure based on location
– Manufacturer’s exposure is typically narrow, but deep and of long
duration
– Wholesaler’s exposure is wider than manufacturers and
somewhat deep
• Duration is medium
– Retailer’s exposure is wide, but not very deep
• Duration is usually short except for specialty retailers
7-4
Functions of Inventory
• Geographical specialization allows us to specialize
production across different locations
• Decoupling allows us to run processes for maximum
economic lot sizes within a single facility
• Supply/Demand balancing accommodates the elapsed
time between inventory availability and consumption
• Buffering uncertainty accommodates uncertainty related
to
– Demand in excess of forecast or
– Unexpected delays in delivery (aka safety stock)
7-5
Inventory policy
• Inventory policy is a firm’s
guidelines concerning
– What to purchase or manufacture
– When to take action
– In what quantity should action be
taken
– Where products should be
located geographically
• Firm’s policy also includes
decisions about which
inventory management
practices to adopt
7-6
Service level
• Service level is a performance target
specified by management and defines
inventory performance objectives
• Common measures of service level include
– Performance cycle is the elapsed time between
release of a purchase order by the buyer to the
receipt of shipment
– Case fill rate is the percent of cases ordered that
are shipped as requested
– Line fill rate is the percent of order lines (items)
that were filled completely
– Order fill is the percent of customer orders filled
completely
7-7
Inventory definitions
•
Inventory includes materials, components, work-inprocess, and finished goods that are stocked in the
company’s logistical system
– The cycle inventory (base stock) is the portion of
average inventory that results from replenishment
– Order quantity is the amount ordered for
replenishment
– Transit inventory represents the amount typically in
transit between facilities or on order but not received
– Obsolete inventory is stock that is out-of-date or is
not in recent demand
– Speculative inventory is bought to hedge a currency
exchange or to take advantage of a discount
– Safety stock is the remainder of inventory in the
logistics system
7-8
Average inventory is the typical amount stocked
over time
• Average inventory equals the maximum inventory plus the minimum
inventory divided by two
– Typically equal to ½ order quantity + safety stock + in-transit stock
Figure 7.1 Inventory Cycle for Typical Product
7-9
Smaller replenishment order quantities
results in lower average inventory
• Policy must decide how much inventory to order at a specified time
– Reorder point defines when a replenishment order is initiated
• However, other factors are important like performance cycle
uncertainty, purchasing discounts, and transportation economies
Figure 7.3 Alternative Order Quantity and Average Inventory
7-10
Inventory carrying cost is the expense associated
with maintaining inventory
• Inventory expense is
– Annual inventory carrying cost percent times average inventory
value
• Cost components
– Cost of capital is specified by senior management
– Taxes on inventory held in warehouses
– Insurance is based on estimated risk or loss over time and
facility characteristics
– Obsolescence results from deterioration of product during
storage
• E.g. food and pharmaceutical sell-by dates
– Storage is facility expense related to product holding rather than
product handling
7-11
Final carrying cost percent used by a firm is
a managerial policy
Table 7.2 Inventory Carrying Cost Components
7-12
Inventory ordering cost components
•
•
•
•
•
Order preparation costs
Order transportation costs
Order receipt processing costs
Material handling costs
Total cost is driven by inventory planning
decisions which establish when and how much to
order
7-13
When to order
• Basic reorder formula if demand and performance are certain
R= D × T
– R = Reorder point in units
– D = Average daily demand in units
– T = Average performance cycle length in days
• If safety stock is needed to accommodate uncertainty the formula is
R = D × T + SS
–
–
–
–
R = Reorder point in units
D = Average daily demand in units
T = Average performance cycle length in days
SS = Safety stock in units
7-14
How much to order
• Economic order quantity
is the amount that
balances the cost of
ordering with the cost of
maintaining average
inventory
– Assumes demand and
costs are relatively stable
for the year
– Does not consider impact of
joint ordering of multiple
products
Figure 7.4 Economic Order Quantity
7-15
Standard mathematical solution for EOQ
7-16
Example EOQ solution using Table 7.3
• Total ordering cost is $152 = (2400/300 x $19.00)
• Inventory carrying cost is $150 = [300/2 x (5 x 0.20)]
7-17
Simple EOQ model assumptions
• All demand is satisfied
• Rate of demand is continuous, constant and know
• Replenishment performance cycle time is constant and
known
• Constant price of product that is independent of order
quantity or time
• An infinite planning horizon exists
• No interaction between multiple items of inventory
• No inventory is in transit
• No limit is placed on capital availability
7-18
Relationships useful for guiding inventory
planning
• EOQ is found at the point where annualized order
placement cost and inventory carrying cost are
equal
• Average base inventory equal one-half order
quantity
• Value of the inventory unit, all other things being
equal, will have a direct relationship with
replenishment order frequency
– Higher value products will be ordered more frequently
7-19
Typical adjustments to EOQ
• Volume transportation rates offer a freight-rate discount for larger
shipments
– Compare total cost with each transportation rate option
• Quantity discounts offer a lower per unit cost when larger quantities
are purchased
– If discount is sufficient to offset added inventory carrying cost less the reduced
cost of ordering then it is viable choice
• Other EOQ adjustments
–
–
–
–
–
Production lot size
Multiple-item purchase
Limited capital
Dedicated trucking
Unitization
7-20
Uncertainty in inventory management
• Inventory policy must deal with uncertainty
– Demand uncertainty — when and how much product
will our customers order?
– Performance cycle uncertainty — how long will it take
to replenish inventory with our customers?
• Variations must be considered in both areas to
make effective inventory planning decisions
7-21
Demand uncertainty can be managed using
safety stock
• To protect against stockout when uncertain demand
exceeds forecast we add safety stock to base
inventory
• Planning safety stock requires three steps
– Determine the likelihood of stockout using a probability
distribution
– Estimate demand during a stockout period
– Decide on a policy concerning the desired level of
stockout protection
7-22
Probability theory enables calculation of safety
stock for a target service level
• Service level is equal to 100% minus probability % of
stockout
– E.g. a service level of 99% results in a stockout probability of 1%
• The most common probability distribution for demand is the
normal distribution
– From analysis of historical demand data the safety stock required
to ensure a stock out only 1% of the time is possible
– A one-tailed normal distribution is used because only demand
that is greater than the forecast can create a stockout
7-23
Example of historical demand analysis using
a normal distribution
Figure 7.6 Historical Analysis of Demand History
Figure 7.7 Normal Distribution
7-24
Performance cycle uncertainty means operations
cannot assume consistent delivery
Table 7.10 Calculation of Standard Deviation of Replenishment Cycle Duration
7-25
Demand Uncertainty
Units
0
1
2
3
4
5
6
7
8
9
10
N=28
Frequency(F)
1
2
2
3
4
5
3
3
2
2
1
s=5
Deviation From Mean Deviation Squared
-5
25
-4
16
-3
9
-2
4
-1
1
0
0
+1
1
+2
4
+3
9
+4
16
+5
25
FiDi2
25
32
18
12
4
0
3
12
18
32
25
7-26
Continuation Demand Uncertainty
F D
i
2
 181
2
181

 2.54
28
i
F iDi

n
7-27
Combined Demand and Performance
Uncertainty
c 
TS s  D 2 S t
2
2
Where:
T=average performance cycle time
St =standard deviation of the performance cycle
D=average daily sales
Ss=standard deviation of daily sales, and
c
= standard deviation of the combined uncertainty
7-28
Combined Demand and Performance
Uncertainty
 c  10.00(2.54) 2  5.002 (2) 2  12.83
Round to 13
7-29
Safety stock with combined uncertainty
• Planning for both demand and performance cycle
uncertainty requires combining two independent
variables
• The joint impact of the probability of both demand
and performance cycle variation must be
determined
– Direct method is to combine standard deviations using a
convolution formula
7-30
The fill rate is the magnitude rather than the
probability of a stockout
• Increasing the replenishment order quantity decreases the
relative magnitude of potential stockouts
• The formula for this relationship is
7-31
3 approaches to introduce safety stock into
dependent demand situations
• Put safety time into the requirements plan
– E.g. order a component earlier than needed to assure timely
arrival
• Over-planning top-level demand is a procedure to
increase the requisition by a quantity specified by some
estimate of expected plan error
– E.g. assume plan error will not exceed 5 percent
• Utilize statistical techniques to set safety stocks directly for
a component rather than to the item of top-level demand
7-32
Approaches to implementing inventory
management policies
• Reactive (or pull) approach responds to customer
demand to pull the product through the distribution
channel
• Planning approach proactively allocates inventory
on the basis of forecasted demand and product
availability
• Hybrid approach uses a combination of push and
pull
7-33
Inventory control using reactive approaches
• Inventory control defines how
often inventory levels are
reviewed to determine when
and how much to order
– Perpetual review continuously
monitors inventory levels to
determine inventory
replenishment needs
– Periodic review monitors
inventory status of an item at
regular intervals such as weekly
or monthly
7-34
Reorder point formulas for reactive methods
Perpetual Review
Periodic Review
7-35
Assumptions of classical reactive inventory logic
•
•
•
•
All customers, market areas, and product contribute equally to profits
Infinite capacity exists at the production facility
Infinite inventory availability at the supply location
Performance cycle time can be predicted and that cycle lengths are
independent
• Customer demand patterns are relatively stable and consistent
• Each distribution warehouse’s timing and quantity of replenishment
orders are determined independently of all other sites, including the
supply source
• Performance cycle length cannot be correlated with demand
7-36
Planning approaches coordinate requirements
across multiple locations in the supply chain
• Two planning approaches
– Fair share allocation provides each distribution facility
with an equitable distribution of available inventory
• Limited ability to manage multistage inventories
– Requirements planning integrates across the supply
chain taking into consideration unique requirements
• Materials requirements planning (MRP) is driven by a
production schedule
• Distribution requirements planning (DRP) is driven by supply
chain demand
7-37
Example of fair share allocation method
Figure 7.11 Fair Share Allocation Example
• Allocation of 500 available units from plant
– Warehouse 1 = 47
– Warehouse 2 = 383
– Warehouse 3 = 70
7-38
Integrated planning approach for raw materials,
work-in-process, and finished goods
MRP
system
DRP
system
Figure 7.12 Conceptual Design of Integrated MRP/DRP System
7-39
Limitations to planning approaches
• Requires accurate and
coordinated forecasts for each
warehouse
• Requires consistent and
reliable product movement
between warehouse facilities
• Subject to frequent
rescheduling (system
nervousness) because of
production breakdowns or
delivery delays
7-40
Collaborative inventory replenishment programs
• Replenishment programs are designed to streamline the
flow of goods within the supply chain
– Intent is to reduce reliance on forecasting and position inventory
using actual demand on a just-in-time basis
• Quick response (QR) is a technology-driven cooperative
effort between retailers and suppliers to improve inventory
velocity while matching supply to consumer buying patterns
• Vendor-managed inventory (VMI) is a modified QR that
eliminates the need for replenishment orders
• Profile replenishment (PR) extends QR and VMI by giving
suppliers the right to anticipate future requirements
according to their knowledge of a product category
7-41
Managerial considerations when developing
an inventory policy
Table 7.18 Suggested Inventory Management Logic
7-42
Inventory management practices
• Product/market classification groups products, markets, or
customers with similar characteristics to facilitate inventory
management
– E.g. classify by sales, profit contribution, inventory value, usage rate or item
category
• Segment strategy definition specifies all aspects of inventory
management process for each segment of inventory
– E.g. service objectives, forecasting method, management technique, and
review cycle
• Policies and parameters must be defined at a detailed level
– E.g. data requirements, software applications, performance objectives, and
decision guidelines
7-43
Example of product classification by sales
Table 7.19 Product Market Classification (Sales)
7-44
Sample illustrating segment strategy
definitions
Table 7.20 Integrated Strategy
7-45