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
Example #1
Average Inventory
1000
400
0
7-10
Example #1
Average Inventory
1000
(1000+400/ 2)=700
400
0
7-11
Example #2
Order Quantity
2000
1000
0
7-12
Example #2
Order Quantity
2000
1000
1000
0
7-13
Example #3
Average Inventory and Order Quantity
22000
14000
0
7-14
Example #4
Reorder Point
Performance cycle = 4 days
2000
1000
0
0
10
20
7-15
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
7-16
Example #4
Reorder Point
Performance cycle = 4 days
2000
1000
Reorder = 4 x 100 + 1000
Reorder point = 1400
0
0
10
20
7-17
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
7-18
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
7-19
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
7-20
Final carrying cost percent used by a firm is
a managerial policy
Table 7.2 Inventory Carrying Cost Components
7-21
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
7-22
Standard mathematical solution for EOQ
7-23
Example #5- EOQ
•
•
•
•
Annual demand =
Unit value=
Carrying cost %=
Ordering costs =
2400 units
$5.00
20%
$19.00
7-24
Example#5 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)]
7-25
Example #5 - EOQ
Total Ordering cost = (Demand/ EOQ amount) x $ per order
Total ordering cost is $152 = (2400/300 x $19.00)
--------------------------------------------------------------------Inventory carrying cost = (EOQ amount/2) x (Unit price x
Carrying cost %)
Inventory carrying cost is $150 = [300/2 x (5 x 0.20)]
7-26
Example #6- EOQ
•
•
•
•
Annual demand =
Unit value=
Carrying cost %=
Ordering costs =
500 units
$90.00
15%
$35.00
Total Ordering cost = (Demand/ EOQ amount) x $
per order
Inventory carrying cost = (EOQ amount/2) x (Unit
price x Carrying cost %)
7-27
Example #6- EOQ
•
•
•
•
EOQ = √(2x35x500)/(0.15x90)
EOQ = √(35000)/(13.5)
EOQ = √(2592.593)
EOQ = 50.91 ≈ 50
7-28
Example #6 - EOQ
Total Ordering cost = (Demand/ EOQ amount) x $ per order
Total ordering cost is $350 = (500/50 x $35.00)
--------------------------------------------------------------------Inventory carrying cost = (EOQ amount/2) x (Unit price x
Carrying cost %)
Inventory carrying cost is $337.5 = [50/2 x (90 x 0.15)]
7-29
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
7-30
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
7-31
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
7-32
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
7-33
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
7-34
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
7-35
Example of historical demand analysis using
a normal distribution
Figure 7.6 Historical Analysis of Demand History
Figure 7.7 Normal Distribution
7-36
Performance cycle uncertainty means operations
cannot assume consistent delivery
Table 7.10 Calculation of Standard Deviation of Replenishment Cycle Duration
7-37
Example #7 (Standard Deviation)
Days
6
7
8
9
10
11
12
13
14
(F)
2
4
6
8
10
8
6
4
2
7-38
Example #7 (Standard Deviation)
Days
6
7
8
9
10
11
12
13
14
x
(F)
2
4
6
8
10
8
6
4
2
50
12
28
48
72
100
88
72
52
28
500
500/50 = 10
7-39
Performance cycle uncertainty means operations
cannot assume consistent delivery
Table 7.10 Calculation of Standard Deviation of Replenishment Cycle Duration
7-40
Example #7 (Standard Deviation)
Days
6
7
8
9
10
11
12
13
14
--
Mean
10
10
10
10
10
10
10
10
10
(D)
-4
-3
-2
-1
0
1
2
3
4
7-41
Example #7 (Standard Deviation)
Days
6
7
8
9
10
11
12
13
14
Mean
10
10
10
10
10
10
10
10
10
(D)
-4
-3
-2
-1
0
1
2
3
4
(D*D)
16
9
4
1
0
1
4
9
16
7-42
Example #7 (Standard Deviation)
Days
6
7
8
9
10
11
12
13
14
(F)
2
4
6
8
10
8
6
4
2
50
Mean
10
10
10
10
10
10
10
10
10
(D)
-4
-3
-2
-1
0
1
2
3
4
(D*D)
16
9
4
1
0
1
4
9
16
FD2
32
36
24
8
0
8
24
36
32
200
7-43
Performance cycle uncertainty means operations
cannot assume consistent delivery
Table 7.10 Calculation of Standard Deviation of Replenishment Cycle Duration
7-44
Example #8 (Standard Deviation)
Units
3
4
5
6
7
(F)
1
2
4
2
1
7-45
Example #8 (Standard Deviation)
Units
3
4
5
6
7
(F)
1
2
4
2
1
10
Unit*
F Mean (D)
3
5
-2
8
5
-1
20
5
0
12
5
1
7
5
2
50
D2
4
1
0
1
4
FD2
4
2
0
2
4
12
7-46
Example #8 (Standard Deviation)
σ
= √12/10
1.09 units
7-47
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
7-48
Typical situation where both demand and
performance cycle variation exists
Figure 7.8 Combined Demand and Performance Cycle Uncertainty
7-49
Example #9 (Convolution)
Using our previous answers:
• Performance cycle mean (T) =
• Performance cycle standard deviation (St) =
• Demand mean (D)=
• Demand standard deviation (Sd)=
10
2
5
1.09
σ = √((TSd2) + (D2St2))=√ ((10*1.092) + (5222))= 10.58
7-50
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
7-51
Number of stockouts is reduced from two to one
when order quantity is increased
Figure 7.9 Impact of Order Quantity on Stockout Magnitude
7-52
Reorder point formulas for reactive methods
Perpetual Review
Periodic Review
7-53
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
7-54
Example of fair share allocation method
+500
Figure 7.11 Fair Share Allocation Example
Days Supply = (New inventory + sum inventory)/ sum demand
DS = (500 +50 + 100 + 75)/ (10+50+15)
DS = (725/75) = 9.67 days
7-55
Example of fair share allocation method
Figure 7.11 Fair Share Allocation Example
Allocate = (DS – (inventory/demand)) x demand
Allocate = (9.67 – (50/10)) x 10
Allocate = 46.7 or 47.
7-56
Example of fair share allocation method
Figure 7.11 Fair Share Allocation Example
Allocate = (DS – (inventory/demand)) x demand
7-57
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
7-58
Overview of inventory
• Inventory functionality and
definitions
• Inventory carrying cost
• Planning inventory
• Managing uncertainty
• Inventory management
policies
• Inventory management
practices
7-59