Inventory
Control Systems 1
BM317 Warehousing and
Inventory Management
Lecture 10
Inventory System – Defined
Inventory is the stock of any item or resource
used in an organization and can include: raw
materials, finished products, component parts,
supplies, and work-in-process
An inventory system is the set of policies and
controls that monitor levels of inventory and
determines what levels should be maintained,
when stock should be replenished, and how
large orders should be
Cost trade-offs in Marketing
s
LOGISTICS
MARKETING
Cost Trade-offs Required in a
Logistics System
Relationship Between Customer
Service and Inventory Investment
0
400
800
1200
1600
2000
75 80 85 90 95 100
Service %
Inventory Investment in units
Selected Financial Data for Manufacturers,
Wholesalers, and Retailers for 1997 ($Millions)
Companies Sales Net Profits Net Profits as a Total Assets Inventory Investment Inventories as a
Percent of Sales Percent of Assets
Manufacturers
Abbott Laboratories ,883 ,094 18% ,061 ,280 11%
Borden, Inc. 1,488 221 15% 2,206 302 14%
The Clorox Company 2,741 298 11% 3,030 212 7%
Dresser Industries, Inc. 7,458 318 4% 5,099 972 19%
Ford Motor Company 153,627 6,920 5% 279,097 5,468 2%
General Electric Company 90,840 8,203 9% 304,012 5,895 2%
General Mills 6,033 422 7% 3,861 389 10%
Goodyear Tire & Rubber Co. 13,065 559 4% 9,917 1,835 19%
Harris Corp. 3,939 133 3% 3,784 604 16%
Honeywell Co. 8,028 471 6% 6,411 1,028 16%
NCR Corp. 6,598 7 0.11% 5,293 489 9%
Newell Co. 3,234 290 9% 3,944 625 16%
Pfizer, Inc. 12,188 2,213 18% 15,336 1,773 12%
Sara Lee Corp. 20,011 ( 523) -3% 10,989 2,882 26%
Xerox Corp. 18,166 1,452 8% 27,732 2,792 10%
Wholesalers and Retailers
Baxter International 6,138 300 5% 8,707 1,208 14%
Bergen Brunswig Corp. 11,661 8 2 1% 2,707 1,309 48%
Dayton Hudson Corp. 27,757 751 3% 14,191 3,251 23%
Fleming Companies, Inc. 15,372 2 5 0.16% 3,924 1,019 26%
Kmart Corporation 32,183 249 1% 13,558 6,367 47%
Nordstrom 4,852 186 4% 2,865 826 29%
Sears, Roebuck & Company 41,296 1,188 3% 38,700 5,044 13%
Supervalu Inc. 17,201 231 1% 4,093 1,116 27%
Wal-Mart Stores, Inc. 117,958 3,526 3% 45,384 16,497 36%
Winn-Dixie 13,219 204 2% 2,921 1,249 43%
Note: Ending inventory figures are used for inventory investment. All figures are for 1997.
Purposes of Inventory
1.
To maintain independence of operations
2.
To meet variation in product demand
3.
To allow flexibility in production scheduling
4.
To provide a safeguard for variation in raw
material delivery time
5.
To take advantage of economic purchase-order
size
6.
To act as a buffer between critical interfaces
within the supply chain
Finished goods
inventory
in field
Finished goods
inventory
at plant
Raw
materials
inventory
In-process
inventory
Purposes of Holding Different Types
of Inventory
Types of Inventory Purpose of holding inventory
Raw material inventory /
Component Parts
Reducing ordering costs or setup costs
Work-in-process
Reducing setup costs, reducing inter-dependencies
between operations
Finished products
Reducing ordering costs or setup costs, allowing
flexibility in production scheduling, protecting
against uncertainites in demand
Facilitating goods in
service systems
Reducing ordering costs or setup costs, protecting
against uncertainites in supply & demand
Independent vs. Dependent Demand
Independent Demand (Demand for the final endproduct
or demand not related to other items)
Dependent
Demand
(Derived demand
items for
component
parts,
subassemblies,
raw materials,
etc)
Finished
product
Component parts
Inventory Costs
Holding (or carrying) costs
Costs for storage, handling, insurance, etc
Setup (or production change) costs
Costs for arranging specific equipment setups, etc
Ordering costs
Costs of someone placing an order, etc
Shortage costs
Costs of canceling an order, etc
Components of Inventory Carrying Costs
Capital
Inventory service
Storage space
Inventory risk
Inventory
carrying
costs
Inventory investment
Insurance
Taxes
Obsolescence
Pilferage
Storage
space costs
Capital
costs
Inventory
service
costs
Inventory
risk costs
Plant warehouses
Public warehouses
Rented warehouses
Company-owned
warehouses
Damage
Relocation costs
Inventory Carrying Costs
Two Major Decisions
1.
When to place an order for an item?
2.
How many to order or to produce of this
item?
Six Types of Inventory
1.
Cycle Stock
is inventory required to meet demand under certainty
2.
In-Transit Inventories
are items that are move from one location to another
3.
Safety or Buffer Stock
is held in excess of cycle stock because of uncertainty in demand or
lead time
4.
Speculative Stock
is inventory held for reasons other than satisfying current demand (e.g.
quantities discounts)
5.
Seasonal Stock
is a form of speculative stock that involves the accumulation of
inventory before a season begins
6.
Dead Stock
is the set of items for which no demand had been registered for some
specified period of time
Inventory Systems
Fixed-Order Quantity Model
Event triggered (Example: running out of stock)
Fixed-Time Period Model
Time triggered (Example: Monthly sales call by
sales representative)
Fixed-Order Quantity Model
Demand for the product is constant and uniform
throughout the period
Lead time (time from ordering to receipt) is constant
Price per unit of product is constant
Inventory holding cost is based on average inventory
Ordering or setup costs are constant
All demands for the product will be satisfied (No back
orders are allowed)
Assumptions
Basic Fixed-Order Quantity Model
and Reorder Point Behavior
R = Reorder point
Q = Economic order quantity
L = Lead time
L L
Q Q Q
R
Time
Number
of units
on hand
1. You receive an order quantity Q.
2. Your start using
them up over time. 3. When you reach down to
a level of inventory of R,
you place your next Q
sized order.
4. The cycle then repeats.
200
400
0
Days 10 20 30 40 50 60
Inventory
Order
placed
Order
arrival
Order
placed Average
cycle
inventory
A. Orderquantity of 400 units
Order
arrival
The Effect of Reorder Quantity on
Average Inventory Investment
With Constant Demand and Lead Time
Inventory
Order
placed
Order
arrival
Average
cycle
inventory
Days 10 20 30 40 50 60
0
100
200
B. Orderquantity of 200 units
The Effect of Reorder Quantity on
Average Inventory Investment
With Constant Demand and Lead Time
Average
cycle
inventory
Order
arrival
Order
placed
C. Orderquantity of 600 units
Days 10 20 30 40 50 60
Inventory
0
300
600
The Effect of Reorder Quantity on
Average Inventory Investment
With Constant Demand and Lead Time
Cost Minimization
Ordering Costs
Holding
Costs
Order Quantity (Q)
C
OST
Annual Cost of
Items (DC)
Total Cost
QOPT
By adding the item, holding, and ordering costs together, we
determine the total cost curve, which in turn is used to find
the Q
opt inventory order point that minimizes total costs
By adding the item, holding, and ordering costs together, we
determine the total cost curve, which in turn is used to find
the Q
opt inventory order point that minimizes total costs
Basic Fixed-Order Quantity
(EOQ) Model Formula
H
2
Q
S +
Q
D
TC = DC +
Total
Annual =
Cost
Annual
Purchase
Cost
Annual
Ordering
Cost
Annual
Holding
Cost
+ +
TC=Total annual cost
D =Demand
C =Cost per unit
Q =Order quantity
S =Cost of placing an
order or setup cost
R =Reorder point
L =Lead time
H=Annual holding and
storage cost per unit
of inventory
TC=Total annual cost
D =Demand
C =Cost per unit
Q =Order quantity
S =Cost of placing an
order or setup cost
R =Reorder point
L =Lead time
H=Annual holding and
storage cost per unit
of inventory
Source: Chase, Aquilano, Jacobs, “Operations Management – For Competitive Advantage” Iran McGraw-Hill
Order
Quantity
Number
of Orders
(D/Q)
Ordering
Cost
S * (D/Q)
Inventory
Carrying
Cost
1/2 Q * H
Total
Cost
40
60
80
100
120
140
160
200
300
400
120
80
60
48
40
35
30
24
18
12
$ 4,800
3,200
2,400
1,920
1,600
1,400
1,200
960
720
480
$ 500
750
1,000
1,250
1,500
1,750
2,000
2,500
3,750
5,000
$ 5,300
3,950
3,400
3,170
3,100
3,150
3,200
4,460
4,470
5,480
Cost Trade-offs Required to Determine
the Most Economic Order Quantity
Deriving the EOQ
Using calculus, we take the first derivative of the
total cost function with respect to Q, and set the
derivative (slope) equal to zero, solving for the
optimized (cost minimized) value of Q
opt
Using calculus, we take the first derivative of the
total cost function with respect to Q, and set the
derivative (slope) equal to zero, solving for the
optimized (cost minimized) value of Q
opt
Q =
2DS
H
=
2(Annual Demand)(Order or Setup Cost)
Annual Holding Cost
OPT
Q =
2DS
H
=
2(Annual Demand)(Order or Setup Cost)
Annual Holding Cost
OPT
Reorder point, R = d L
_
Reorder point, R = d L
_
d = average daily demand (constant)
L = Lead time (constant)
_
We also need a
reorder point to
tell us when to
place an order
We also need a
reorder point to
tell us when to
place an order
EOQ Example
Annual Demand = 1,000 units
Days per year considered in average
daily demand = 365
Cost to place an order =
Holding cost per unit per year = .50
Lead time = 7 days
Cost per unit =
Given the information below, what are the EOQ and
reorder point?
Given the information below, what are the EOQ and
reorder point?
EOQ Example – Solution
Q =
2DS
H
=
2(1,000 )(10)
2.50
= 89.443 units or
OPT 90 units
d =
1,000 units / year
365 days / year
= 2.74 units / day
Reorder point, R = d L = 2.74units / day (7days) = 19.18 or
_
20 units
In summary, you place an optimal order of 90 units. In
the course of using the units to meet demand, when
you only have 20 units left, place the next order of 90
units.
In summary, you place an optimal order of 90 units. In
the course of using the units to meet demand, when
you only have 20 units left, place the next order of 90
units.
Price-Break Model Formula
Annual Holding Cost
2(Annual Demand)(Order or Setup Cost)
=
iC
2DS
Q =
OPT
Based on the same assumptions as the EOQ model,
the price-break model has a similar Q
opt formula:
i = percentage of unit cost attributed to carrying inventory
C = cost per unit
Since “C” changes for each price-break, the formula
above will have to be used with each price-break cost
value
Price-Break Example
A company has a chance to reduce their inventory
ordering costs by placing larger quantity orders using
the price-break order quantity schedule below. What
should their optimal order quantity be if this company
purchases this single inventory item with an e-mail
ordering cost of , a carrying cost rate of 2% of the
inventory cost of the item, and an annual demand of
10,000 units?
A company has a chance to reduce their inventory
ordering costs by placing larger quantity orders using
the price-break order quantity schedule below. What
should their optimal order quantity be if this company
purchases this single inventory item with an e-mail
ordering cost of , a carrying cost rate of 2% of the
inventory cost of the item, and an annual demand of
10,000 units?
Order Quantity(units) Price/unit($)
0 to 2,499 .20
2,500 to 3,999 1.00
4,000 or more .98
Price-Break Example Solution
= 1,826 units
0.02(1.20)
2(10,000)( 4)
=
iC
2DS
Q =
OPT
Annual Demand (D)= 10,000 units
Cost to place an order (S)=
First, plug data into formula for each price-break value of “C”
= 2,000 units
0.02(1.00)
2(10,000)( 4)
=
iC
2DS
Q =
OPT
= 2,020 units
0.02(0.98)
2(10,000)( 4)
=
iC
2DS
Q =
OPT
Carrying cost % of total cost (i)= 2%
Cost per unit (C) = .20, .00, .98
Interval from 0 to 2499, the
Qopt value is feasible
Interval from 2500-3999, the
Qopt value is not feasible
Interval from 4000 & more,
the Qopt value is not feasible
Next, determine if the computed Q
opt values are feasible or not
Since the feasible solution occurred in the first pricebreak,
it means that all the other true Q
opt values occur
at the beginnings of each price-break interval. Why?
Since the feasible solution occurred in the first pricebreak,
it means that all the other true Q
opt values occur
at the beginnings of each price-break interval. Why?
0 1826 2500 4000 Order Quantity
Total
annual
costs
So the candidates
for the pricebreaks
are 1826,
2500, and 4000
units
So the candidates
for the pricebreaks
are 1826,
2500, and 4000
units
Because the total annual cost function is
a “u” shaped function
Because the total annual cost function is
a “u” shaped function
Price-Break Example Solution
iC
2
Q
S +
Q
D
TC = DC +
Next, we plug the true Q
opt values into the total cost
annual cost function to determine the total cost under
each price-break
Next, we plug the true Q
opt values into the total cost
annual cost function to determine the total cost under
each price-break
TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20)
= ,043.82
TC(2500-3999)= ,041
TC(4000&more)= ,949.20
TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20)
= ,043.82
TC(2500-3999)= ,041
TC(4000&more)= ,949.20
Finally, we select the least costly Q
opt, which is this
problem occurs in the 4000 & more interval. In summary,
our optimal order quantity is 4000 units
Finally, we select the least costly Q
opt, which is this
problem occurs in the 4000 & more interval. In summary,
our optimal order quantity is 4000 units
Price-Break Example Solution
A.With variable demand
Inventory
Average
cycle
inventory
Ss(
afety
tock
50)
y
Ave ra ge
inve ntor
(150)
200
100
8 10 20 30 40
{ {
Days
Average Inventory Investment
Under Conditions of Uncertainty
B. With variable lead time
Inventory
Average
cycle
inventory
y
Ave ra ge
inve ntor
(140)
200
100
{
10 12 20 30 40
Day
Ss(
afety
tock
40) s
{
Average Inventory Investment
Under Conditions of Uncertainty
C. With variable demand and lead time
Inventory
Average
cycle
inventory
y
Ave ra ge
inve ntor
(200)
200
100
{
10 12 20 30 40
Day
y Ss(
afet
0
tock
10 )
{
s 8
Average Inventory Investment
Under Conditions of Uncertainty
Fixed-Time Period Model with Safety
Stock Formula
I = current inventory level (includes items on order)
= standard deviation of demand over the review and lead time
z = the number of standard deviations for a specified service probabilit y
d = forecast average daily demand
L = lead time in days
T = the number of days between reviews
q = quantitiy to be ordered
Where :
q = d(T + L) + Z – I
T+L
T+L
q
q == Averaee demand ++ Safety stock ––Inventory currently on hand
Fixed-Time Period Model:
Determining the Value of
T+L
( )
T+L d
i 1
T+L
d
T+L d
2
=
Since each day is independent and is constant,
= (T + L)
i
2
=
( )
T+L d
i 1
T+L
d
T+L d
2
=
Since each day is independent and is constant,
= (T + L)
i
2
=
The standard deviation of a sequence of
random events equals the square root of the
sum of the variances
Symptoms of Poor Inventory
Increasing numbers of back orders
Increasing dollar investment in inventory with back
orders remaining constant.
High customer turnover rate.
Increasing number of orders being canceled.
Periodic lack of sufficient storage space.
Wide variance in inventory turnover among
distribution centers and major inventory items.
Deteriorating relationships with intermediaries
Large quantities of obsolete items
Ways to Reduce Inventory Levels
Multi-level inventory planning – ABC analysis
Lead time analysis
Delivery time analysis – This may lead to a change in
carriers
Elimination of low turnover and/or obsolete items
Analysis of pack size and discount structure
Encouragement/automation of product substitution
Analysis of customer demand characteristics
Development of a formal sales plan and source demand
ABC Classification System
•
Items kept in inventory are not of equal
importance in terms of:
dollars invested
profit potential
sales or usage volume
stock-out penalties
0
30
60
30
60
A
B
C
% of
$ Value
% of
Items
So, identify inventory items based on percentage of total
dollar value, where “A” items are roughly top 15 %, “B”
items as next 35 %, and the lower 65% are the “C” items
Relationship Between Customer
Service and Inventory Investment
0
400
800
1200
1600
2000
75 80 85 90 95 100
Service %
Inventory Investment in units
Model of Consumer Reaction
to a Repeated Stockout
Customer
3
Lower
4
Other
size
2
Same
1
Higher
Another
store
6
Ask here
again
5
Special
order
Switch
stores
?
Substitute
?
Switch
brand
?
Substitute
?
Switch
price
?
No
No
Yes
Yes
Yes
Yes
No
No
Inventory Accuracy & Cycle Counting
Inventory accuracy refers to how well the
inventory records agree with physical
count
Cycle Counting is a physical inventory taking
technique in which inventory is
counted on a frequent basis rather than
once or twice a year
Credit:ivythesis.typepad.com
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