Operations Management
Contemporary Concepts and Cases
Chapter Fifteen
Independent Demand Inventory
McGraw-Hill/Irwin
Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 15 Outline
Purpose of Inventories
Costs of Inventories
Independent versus Dependent Demand
Economic Order Quantity
Continuous Review System
Periodic Review System
Using P and Q System in Practice
ABC Inventory Management
15-2
Definitions
Inventory: a stock of materials used to facilitate
production or satisfy customer demand
Types of inventory
–
–
–
–
Raw materials, purchased parts (RM)
Work in process (WIP)
Finished goods (FG)
Maintenance, repair & operating supplies (MRO)
15-3
Inventory Management
Technologies
Bar coding
Point of sale (data) (POS)
Radio-frequency Identification (RFID)
15-4
Materials-Flow Process (Fig. 15.1)
Productive Process
Work in
process
Vendors
Raw
Materials
Work in
process
Finished Customer
goods
Work in
process
15-5
Water Tank Analogy for Inventory
Inventory Level
Supply Rate
Inventory Level
Demand Rate
15-6
Purpose of Inventories (1)
To protect against uncertainties (safety stock)
–
–
–
–
demand (FG, MRO)
supply (RM, MRO)
lead times (RM, WIP)
schedule changes (WIP)
To allow economic production and purchase
(discounts for buying RM in bulk)
15-7
Purpose of Inventories (2)
To cover anticipated changes in demand (as
in a level strategy) or supply
– FG
– RM
To provide for transit (pipeline inventories)
– RM
– FG
– WIP (independence of operations)
15-8
Inventory Cost Structures (1)
Item cost
– Expressed as cost per unit or SKU. Gets into
LIFO and FIFO issues.
– Problem can be compounded by quantity
discounts.
Ordering (or setup) cost
– Paperwork, worker time (ordering)
– Worker time, downtime (setup)
– Typically expressed as a fixed cost per order or
setup.
15-9
Inventory Cost Structures (2)
Carrying (or holding) cost:
– Cost of capital (market rate or internal rate of return)
– Cost of storage (building, utilities, insurance, handling)
– Cost of obsolescence, deterioration, and loss
(shrinkage)
– Management cost (record keeping, counting)
Typically expressed as a percentage of SKU cost.
Estimated U.S. average is 35% per year.
Businesses often use only cost of capital
(understatement).
15-10
Inventory Cost Structures (3)
How the 35% carrying cost is distributed:
Cost of Capital—9-20 percent
Obsolescence—2-5 percent
Storage—2-5 percent
Material Handling—1-3 percent
Shrinkage—1-3 percent
Taxes & Insurance—1-3 percent
Source: Mark Williams, APICS Instructor Listserv, 22 January 2001
15-11
Inventory Cost Structures (4)
Shrinkage
– “… ‘shrinkage’…costs U.S. retailers about $41.6
billion last year.” This is more than the combined
total from other crimes such as robberies, auto
theft and larceny.
Source: Wall Street Journal, 11 July 2007, p. B4.
15-12
Inventory Cost Structures (5)
Stock out cost (back order or lost sales)
–
–
–
–
Record maintenance
Lost income
Customer dissatisfaction
Typically expressed as a fixed cost per backorder
or as a function of aging of backorders.
15-13
Two Forms of Demand (1)
Independent demand (this chapter)
–
–
–
–
Finished goods, spare parts, MRO
Based on market demand
Requires forecasting
Managed using ‘replenishment philosophy’, i.e.,
reorder when reach a pre-specified level.
15-14
Two Forms of Demand (2)
Dependent demand (Chapter 16)
–
–
–
–
Parts that go into the finished products, RM or WIP
Demand is a known function of independent demand
Calculate instead of forecast
Managed using a ‘requirements philosophy’, i.e.,
only produced or ordered as needed for higher level
components or products (‘parents’).
15-15
Figure 15.4: Demand Patterns
A pattern plus random influences
‘Lumpy’ because of production lots
15-16
Economic Order Quantity (EOQ)
Developed in 1915 by F.W. Harris
Answers the question ‘How much do I order?’
Used for independent demand items.
Objective is to find order quantity (Q) that minimizes
the total cost (TC) of managing inventory.
Must be calculated separately for each SKU.
Widely used and very robust (i.e., works well in a
variety of situations, even when its assumptions don’t
hold exactly).
15-17
Economic Order Quantity (EOQ)
Basic Model Assumptions
Demand rate is constant, recurring, and known.
Lead time is constant and known.
No stockouts allowed.
Material is ordered or produced in a lot or batch
and the lot is received all at once.
5. Costs are constant:
1.
2.
3.
4.
1. Unit cost is constant (no quantity discounts)
2. Carrying cost is constant per unit (SKU)
3. Ordering (setup) cost per order is fixed
6. Item is a single product or SKU; demand not
influenced by other items.
15-18
EOQ Lot Size Choice
There is a trade-off between frequency of
ordering (or the size of the order) and the
inventory level.
– Frequent orders (small lot sizes) lead to lower
average inventory level, i.e., higher total ordering
costs and lower total holding costs.
– Fewer orders (large lot sizes) lead to higher
average inventory level, i.e., lower total ordering
costs and higher total holding costs.
15-19
Figure 15.5: EOQ Inventory Levels
(‘sawtooth model’)
Order
Interval
Lot size = Q
Average Inventory
Level = Q/2
Time
15-20
Notation in EOQ Calculation
D = Demand rate, units per year
S = Cost per order placed or setup cost,
dollars per order
C = Unit cost, dollars per unit
i = Carrying rate, percent of value per year
Q = Lot size, units
TC= total of ordering cost plus carrying cost
15-21
Cost Equations in EOQ
Ordering cost per year =
(cost per order) x (orders per year) = SD/Q
Carrying cost per year = (annual carrying rate) x
(unit cost) x (average inventory) = iCQ/2
Total annual cost (TC) = ordering cost per year
+ carrying cost per year = SD/Q + iCQ/2
15-22
Total Cost of Inventory (Fig. 15.6)
15-23
TC and EOQ
TC = ordering cost + holding cost
= S*(D/Q) + iC*(Q/2)
EOQ =
2 SD
Q
iC
note: Although we use annual costs, any time period can be used.
Just be consistent! The same is true for currency designations.
15-24
EOQ Example
Sales = 10 cases/week
S = $12/order
i = 30% per year
C = $80/case
_________
EOQ =  (2SD)/iC
=  (2*12*10*52) / (.3*80)
= 22.8 cases/order
TC = ordering cost + holding cost
= S*(D/Q) + iC*(Q/2) = 12*(520/22.8) + .3*80(22.8/2)
= 273.68 + 273.60 = $547.28/year
If order 22 cases instead, TC = $547.64; if 23, TC = $547.30
15-25
EOQ Example
Total Inventory Cost
800
400
200
40
36
32
28
24
21
17
0
13
Dollars
600
Order Size
15-26
Relevant Supply Chain Costs for
Personal Computer Inventories
Component devaluation costs
Price protection costs
Product return costs
Obsolescence costs (end-of-life)
15-27
Continuous Review System
Relax assumption of constant demand.
Demand is assumed to be random.
Check inventory position each time there is
demand (i.e., continuously).
If inventory position drops below the reorder
point, place an order for the EOQ.
Also called fixed-order-quantity or Q system
(the fixed order size is EOQ).
15-28
Continuous Review (Q) System (Fig. 15.7)
R = Reorder Point
Q = Order Quantity
L = Lead time
15-29
Continuous Review (Q) System
Amount to order = EOQ
Order when inventory position = Reorder point
Reorder point (R) = lead time * demand/period
R = lead time demand (when demand is constant)
Reorder point is independent of EOQ!
EOQ tells how much to order.
Reorder point tells when to order.
15-30
Service Level
When demand is random, the reorder point
must take into account the desired service level
or fill rate.
Service level has many definitions:
– Probability that all orders will be refilled while
waiting for an order to arrive.
– Percentage of demand filled from stock in a time
period.
– Percentage of time the system has stock on hand.
15-31
Probability Distribution of Demand over Lead Time
(Fig. 15.8)
m = mean demand
R = Reorder point
s = Safety stock
15-32
Reorder Point
The Reorder point is defined as:
R=m+s
where: R = reorder point
m = mean demand during lead time
s = safety or buffer stock
Using the normal distribution:
s = zσ
where: z = safety factor (from normal table)
σ = standard deviation of lead time demand
Thus:
R = m + zσ
15-33
Periodic Review System (1)
Instead of reviewing continuously, we review
the inventory position at fixed intervals. For
example, the bread truck visits the grocery
store on the same days every week.
Inventory brought up to a ‘target’ level.
Also known as “P system,” “Fixed-orderinterval system” or “Fixed-order-period
system”
15-34
Periodic Review System (2)
Has a target inventory level rather than a
reorder point.
Does not use EOQ (directly) since order
quantity varies according to demand.
The order interval is fixed, the order quantity
varies.
15-35
Periodic Review (P) System (Fig. 15.9)
15-36
Time Between Orders (P) and
Target Level (T) Calculation
2S
P
iC D
T  m'  s '
Where:
T = target inventory level
m’ = average demand over P+L
s’ = safety stock
15-37
Using P and Q System in Practice
Use P system when orders must be placed at
specified intervals.
Use P systems when multiple items are
ordered from the same supplier (jointreplenishment).
Use P system for inexpensive items.
15-38
Using P and Q Systems in Practice
P may be easier to use since levels are
reviewed less often.
P requires more safety stock since may only
order at fixed points.
P is more likely to run out since cannot
respond quickly to increases in demand.
Either may be more costly: P in safety
stock, Q in monitoring cost.
15-39
P and Q Systems at Home
P system: You go to the grocery store on the
same day every week. You ask: “What will
we need for the next week?”
– P is more likely to run out since cannot respond
quickly to increases in demand
– P will carry more inventory (enough to last until
the next trip)
Q system: You go to the grocery store each
time you need something. You ask: “What
do we need?”
– Q may require more ordering and unplanned
order (trips to the store)
15-40
Service Level versus Inventory Level (Fig. 15.10)
105%
Service Level (%)
100%
2.5
95%
90%
1.3
1.4
1.5
1.6
1.7
2.0
1.8 1.9
2.4
2.1 2.2 2.3
1.2
1.1
85%
1.0
z values
80%
75%
150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300
Q  100
  100
Average Inventory Level
15-41
ABC Inventory Management (1)
Based on “Pareto” concept (80/20 rule) and
total usage in dollars of each item.
Classification of items as A, B, or C based on
usage.
Purpose is to set priorities on effort used to
manage different SKUs, i.e., to allocate scarce
management resources.
15-42
ABC Inventory Management (2)
‘A’ items: 20% of SKUs, 80% of dollars
‘B’ items: 30% of SKUs, 15% of dollars
‘C’ items: 50% of SKUs, 5% of dollars
Three classes is arbitrary; could be any number.
Percents are approximate.
Danger: Dollar use may not reflect importance of
any given SKU! Some low value, but critical
items may be classified as ‘A.’
15-43
Annual Usage of Items by Dollar Value (Table 15.4)
Item
1
2
3
4
5
6
7
8
9
10
Total
Percentage of
Annual Usage in
Total Dollar
Units Unit Cost Dollar Usage
Usage
5,000 $
1.50 $
7,500
2.9%
1,500
8.00
12,000
4.7%
10,000
10.50
105,000
41.2%
6,000
2.00
12,000
4.7%
7,500
0.50
3,750
1.5%
6,000
13.60
81,600
32.0%
5,000
0.75
3,750
1.5%
4,500
1.25
5,625
2.2%
7,000
2.50
17,500
6.9%
3,000
2.00
6,000
2.4%
$ 254,725
100.0%
15-44
ABC Chart for Table 15.4
45.0%
120.0%
100.0%
A
Percent Usage
35.0%
B
30.0%
C
80.0%
25.0%
60.0%
20.0%
15.0%
40.0%
10.0%
20.0%
Cumulative % Usage
40.0%
5.0%
0.0%
0.0%
3
6
9
2
4
1
10
8
5
7
Item No.
Percentage of Total Dollar Usage
Cumulative Percentage
15-45
Summary
Purpose of Inventories
Costs of Inventories
Independent versus Dependent Demand
Economic Order Quantity
Continuous Review System
Periodic Review System
Using P and Q System in Practice
ABC Inventory Management
15-46
End of Chapter Fifteen
15-47