13
Inventory Chapter Control
McGraw-Hill/Irwin
Copyright 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Learning Objectives
Explain the different purposes for keeping
inventory.
Understand that the type of inventory system
logic that is appropriate for an item depends on
the type of demand for that item.
Calculate the appropriate order size when a onetime purchase must be made.
Describe what the economic order quantity is
and how to calculate it.
Summarize fixedorder quantity and fixedtime
period models, including ways to determine
safety stock when there is variability in demand.
Discuss why inventory turn is directly related to
order quantity and safety stock.
13-2
Inventory
You should visualize inventory as stacks of
money sitting on forklifts, on shelves, and in
trucks and planes while in transit
For many businesses, inventory is the largest
asset on the balance sheet at any given time
Inventory is often not very liquid
It is a good idea to try to get your inventory
down as far as possible
The average cost of inventory in the United States
is 30 to 35 percent of its value
13-3
Supply Chain InventoriesMake-to-Stock
Environment
13-4
Models Discussed
1. The single-period model
Used when we are making a one-time
purchase of an item
1. Fixedorder quantity model
Used when we want to maintain an item
in-stock, and when we restock, a certain
number of units must be ordered
1. Fixedtime period model
The item is ordered at certain intervals of
time
13-5
Definition of Inventory
Inventory: 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
Manufacturing inventory: refers to items that
contribute to or become part of a firms product
Inventory system: 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
13-6
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
13-7
Inventory Costs
1. Holding (or carrying) costs
Costs for storage, handling, insurance,
and so on
1. Setup (or production change) costs
Costs for arranging specific equipment
setups, and so on
1. Ordering costs
Costs of placing an order
1. Shortage costs
Costs of running out
13-8
Independent Versus Dependent Demand
Independent demand: the demands
for various items are unrelated to each
other
For example, a workstation may produce
many parts that are unrelated but meet
some external demand requirement
Dependent demand: the need for any
one item is a direct result of the need
for some other item
Usually a higher-level item of which it is
part
13-9
Inventory Control-System Design Matrix:
Framework Describing Inventory Control Logic
13-10
Inventory Systems
Single-period inventory model
One time purchasing decision (Example:
vendor selling t-shirts at a football game)
Seeks to balance the costs of inventory
overstock and under stock
Multi-period inventory models
Fixed-order quantity models
Event triggered (Example: running out of stock)
Fixed-time period models
Time triggered (Example: Monthly sales call by
sales representative)
13-11
A Single-Period Inventory Model
Consider the problem of deciding how
many newspapers to put in a hotel
lobby
Too few papers and some customers
will not be able to purchase a paper
and they will lose the profit associated
with these sales
Too many papers and will have paid for
papers that were not sold during the
day, lowering profit
13-12
A Simple View of the Problem
Consider how much risk we are willing
to take for running out of inventory
Assume a mean of 90 papers and a
standard deviation of 10 papers
Assume they want an 80 percent
chance of not running out
Assuming that the probability
distribution associated of sales is
normal, stocking 90 papers yields a 50
percent chance of stocking out
13-13
A Simple View of the Problem Continued
To be 80 percent sure of not stocking
out, we need to carry a few more than
90 papers
From the cumulative standard normal
distribution table, we see that we need
approximately 0.85 standard deviation
of extra papers to be 80 percent sure of
not stocking out
With Excel, =NORMSINV(0.8) = 0.84162
13-14
Single-Period Inventory Model Formulas
Cu
P
Co + Cu
Where :
Co = Cost per unit of demand over estimated
Cu = Cost per unit of demand under estimated
P = Probability that the unit will be sold
We should increase the size of the inventory so
long as the probability of selling the last unit added
is equal to or greater than the ratio of Cu/Co+Cu
13-15
Example 13.1
Mean of 5
Standard deviation of 3
Cost $80
Overbook cost is $200
CU
$80
P
=
= 0.2857
CO CU $200 $80
13-16
Calculations
13-17
Multi-Period Models
There are two general types of multiperiod inventory systems
1. Fixedorder quantity models
Also called the economic order quantity, EOQ,
and Q-model
Event triggered
1. Fixedtime period models
Also the called periodic system, periodic
review system, fixed-order interval system,
and P-model
Time triggered
13-18
Key Differences
To use the fixedorder quantity model,
the inventory remaining must be
continually monitored
In a fixedtime period model, counting
takes place only at the review period
The fixedtime period model
Has a larger average inventory
Favors more expensive items
Is more appropriate for important items
Requires more time to maintain
13-19
FixedOrder Quantity and FixedTime
Period Differences
13-20
Comparison for FixedOrder Quantity and
FixedTime Period Inventory Systems
13-21
Fixed-Order Quantity Model Models
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
13-22
Basic FixedOrder Quantity Model
Lead time
Place Order
Receive order
Use inventory
13-23
Basic Fixed-Order Quantity (EOQ) Model
Formula
TC = D C +
D
Q
S+ H
Q
2
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
13-24
Annual Product Costs, Based on Size of
the Order
13-25
Example 13.2
D = 1,000 units
d = 1,000/365
S = $5 per order
H = $1.25 per unit per year
L = 5 days
C = $12.50
2 DS
2(1,000) 5
=
= 8,000 = 89.4 units
H
1.25
1,000
( 5) = 13.7 units
R = dL =
365
D
Q
TC = DC + S + H
Q
2
1,000
( $5) + 89 ( $1.25)
= 1,000( $12.50) +
89
2
= $12,500 + $56.18 + $55.63 = $12,611.81
Qopt =
13-26
Establishing Safety Stock Levels
Safety stock: amount of inventory carried in
addition to expected demand
Safety stock can be determined based on many
different criteria
A common approach is to simply keep a
certain number of weeks of supply
A better approach is to use probability
Assume demand is normally distributed
Assume we know mean and standard deviation
To determine probability, we plot a normal
distribution for expected demand and note where the
amount we have lies on the curve
13-27
FixedOrder Quantity Model with Safety
Stock
13-28
FixedOrder Quantity Model with Safety
Stock
R = d L + z L
R = Reorder point in units
d = Average daily demand
L = Lead time in days
z = Number of standard deviations for a service probability
L = Standard deviation of usage during lead time
13-29
Example 13.4
d = 60
D = 60( 365) = 21,900
d = 7
S = $10
H = $0.50
L=6
Qopt
2 DS
=
H
2( 21,900)10
0.50
= 936 units
=
L =
L
d2 = L d2 = 6( 7 ) = 17.15
2
i =1
R = d L + z L
= 60( 6 ) + 1.64(17.15)
= 388 units
13-30
Fixed-Time Period Models
q = d(T + L) + Z T + L - I
Order quantity Safety stock
Average daily period
Vulnerable
Inventory on hand
Average
demand
demand
Where :
q = quantitiy to be ordered
T = the number of days between reviews
L = lead time in days
d = forecast average daily demand
z = the number of standard deviations for a specified service probability
T + L = standard deviation of demand over the review and lead time
I = current inventory level (includes items on order)
13-31
FixedTime Period Inventory Model
13-32
Example 13.5
Daily demand of 10 units
Daily standard deviation
of 3 units
Review period of 30 days
Lead time of 14 days
Satisfying 98 percent of
demand from items in
stock
150 Units in inventory
q = d ( T + L ) + z T + L I
= 10( 30 + 14) + 2.05 T + L 150
T +L
=
T +L
i =1
=
2
d
( T + L ) d2
=
( 30 + 14) 32
= 19.9
q = 10( 30 + 14) + 2.05(19.9 ) 150
= 331 units
13-33
Inventory Control and Supply Chain
Management
Q
Average inventory = + SS
2
Inventory turn =
D
Q + SS
2
13-34
Price Break Models
Price varies with the order size
To find the lowest-cost, need to calculate the
order quantity for each price and see if the
quantity is feasible
1. Sort prices from lowest to highest and calculate
the order quantity for each price until a feasible
order quantity is found
2. If the first feasible order quantity is the lowest
price, this is best, otherwise, calculate the total
cost for the first feasible quantity and calculate
total cost at each price lower than the first feasible
order quantity
13-35
Curves for Three Separate Order Quantity
Models in a Three-Price-Break Situation
13-36
Example 13.8: The Data and Order
Quantities
D = 10,000
S = $20
i = 20 percent
Cost per unit
1-499 $5.00
500-999 $4.50
1,000 and up $3.90
Q=
2 DS
iC
Q1 499 =
2(10,000 ) 20
= 633
0.20( 5.00)
Q500999 =
2(10,000 ) 20
= 667
0.20( 4.50 )
Q1, 000+ =
2(10,000 ) 20
= 716
0.20( 3.90)
13-37
Example 13.8: The Solution
D
Q
S + iC
Q
2
10,000
667
= 10,000( 4.50 ) +
20 +
0.20( 4.50 )
667
2
= 45,000 + 299.85 + 300.15
TC = DC +
TC500999
= $45,600
TC1,000+
10,000
1,000
= 10,000( 3.90 ) +
20 +
0.20( 3.90 )
1,000
2
= 39,000 + 200 + 390
= $39,590
13-38
ABC Classification
13-39
Inventory Accuracy and Cycle Counting
Inventory accuracy: refers to how well
the inventory records agree with
physical count
Cycle counting: a physical inventorytaking technique in which inventory is
counted on a frequent basis rather than
once or twice a year
13-40