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Inventory Definitions
 Inventory
vs. Inventory system
 Dependent vs. Independent
environments
 Types
 Safety Stock
 Anticipation Inventory
 Hedge inventory (unusual events)
 Transportation or Pipeline Inventory

3

Purposes of Inventory

1. Independence of operations.
2. Variation
 Product demand
 Material Delivery Time
3. Scheduling flexibility
4. Volume Discounts
5. Material price fluctuations
4

Inventory Costs
 Holding (or carrying) costs

 Setup (or production change) costs

 Ordering costs.

 Shortage costs.

5

Inventory Systems

 Rules to manage inventory, specifically:
 timing (when to order)

 sizing (how much to order)

 Continuous Review or Fixed-Order Quantity
Models (Q)
 Event triggered (Example: running out of
stock)
 Periodic Review or Fixed-Time Period Models (P)
 Time triggered (Example: Monthly sales call
by sales representative)

6

Comparison of Periodic and
Continuous Review Systems
Periodic Review Continuous Review
 Fixed order intervals  Varying order intervals
 Variable order sizes
 Fixed order sizes (Q)
 Allows individual review
 Convenient to
frequencies
administer
 Possible quantity discounts
 Inventory position only  Lower, less-expensive
required at review safety stocks

7

Inventory costs
C = Unit cost or production cost: the
additional cost for each unit purchased or
produced.
 H = Holding costs: cost of keeping items in
inventory(cost of lost capital, taxes and
insurance for storage, breakage, etc.,
handling and storing)
 S = Setup or ordering costs: a fixed cost
incurred every time you place an order or a
batch is produced.

8

Total costs of carrying inventory
 Assumptions
 demand is constant and uniform throughout the
period for your products (5 cases per day)
 Price per unit is constant for the period ($16/case)

 Inventory holding cost is based on an average cost.

 TotalInventory Policy Cost annually
= annual purchase cost
+ annual order cost
+ annual holding cost

9

Cost Minimization Goal

C
O Total Cost
S
T Holding
Costs
Annual Cost of
Items (DC)

Ordering Costs

QOPT
Order Quantity (Q)

Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

10

Total cost of Inventory Policy

= annual purchase cost (annual demand *
Cost/item)
+ annual order cost (annual # orders * Cost to
order)
+ annual holding cost (average units held*cost
to carry one unit)

11

Total Inventory Cost Equation
D Q
TC = D * C + S + H
Q 2
D = yearly demand of units
C = cost of each unit
Q = quantity ordered
S = cost to place order
H = average yearly holding cost for each unit
= storage+interest*C
D/Q = number of orders per year
Q/2 = average inventory held during a given period
assuming with start with Q and drop to zero
before next order arrives (cycle inventory).
12

Deriving the EOQ :
Economic Order Quantity

 Using calculus, we take the derivative of
the total cost function and set the
derivative (slope) equal to zero

2DS 2(Annual Demand)(Order or Setup Cost)
Q = EOQ = =
H Annual Holding Cost

13

EOQ Model--Basic Fixed-Order
Quantity Model (Q)

Number
of units
on hand Q Q Q

R
L L

Time
R = Reorder point
Q = Economic order quantity
L = Lead time
14

The Reorder Point

Reorder point = (average period demand)*Lead Time periods
= d*L

15

Another EOQ Example

Annual Demand = 1,000 units
Days per year considered in average daily demand = 365
Cost to place an order = $10
Holding cost per unit per year = $2.50
ead time = 7 days
Cost per unit = $15

Determine the economic order quantity & reorder point.

16

Minor Deviations Here

 What causes minor deviations from the
ideal order size?
 Assumptions behind the regular EOQ
Model?

17

Variations in lead time
 If we have variations in lead time, how should we
change the reorder point so we rarely run out?
Reorder Point = Average demand during lead time(d*L) +
safety stock (Z* σL)

σL =σD L
 where:
d = average daily (or weekly) demand
L = Lead time (matching days or weeks)
σL = standard deviation of demand during lead time.
σD = standard deviation of demand (days or weeks).

18

Service Level or % of time inventory will
meet demand during lead time

Z Value Resulting Service Level

1.28 90%

1.65 95%

2.33 99%

3.08 99.9%

19

Example

 Annual Demand = 1000 units
 250 work days in the year
d=1000/250 = 4 units/day
 Q= 200 units
L=9 days σL = 3 units
 z=2 (97.7% likelihood that we won’t run out during
lead time)

Reorder point= d*L +z*σL
= (4*9) + (2*3) = 42 units
20

P Method (periodic review)
 You have a predetermined time (P) between
orders (sales rep comes by every 10 days) or
the average time between orders from EOQ =
Q/D
 How much should you order to bring inventory
level up to some predetermined level, R where:
 R = restocking level
 Current Inventory position = IP
 Order Quantity= R-IP

21

Restocking Level
 Needs to meet most demand situations
 R= Restocking level
= Average demand during lead time & review
period+ safety stock
= µP+L + z* σP+L
where:
µP+L = average demand during lead time and review
period
z = # of standard dev from mean above the average
demand (higher z is lower probability of running out).
σRP+L = standard deviation of demand during lead time
+ review period

22

ABC Inventory Management

 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.
 SKU: Stock Keeping Unit

23

ABC Inventory Management
 ‘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!
24

Example of SKU list for 10 items
Percentage of
Annual Usage Total Dollar
Item in Units Unit Cost Dollar Usage Usage
1 5,000 $ 1.50 $ 7,500 2.9%
2 1,500 8.00 12,000 4.7%
3 10,000 10.50 105,000 41.2%
4 6,000 2.00 12,000 4.7%
5 7,500 0.50 3,750 1.5%
6 6,000 13.60 81,600 32.0%
7 5,000 0.75 3,750 1.5%
8 4,500 1.25 5,625 2.2%
9 7,000 2.50 17,500 6.9%
10 3,000 2.00 6,000 2.4%
Total �� $ 254,725 100.0% 25

ABC Chart for SKU List
45.0% 120.0%
40.0%
100.0%

Cumulative % Usage
35.0%
A B C
Percent Usage

30.0% 80.0%
25.0%
60.0%
20.0%
15.0% 40.0%
10.0%
20.0%
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

26

ABC Application

 Jewelry Store
 Fine Dining Restaurant
 Outdoor Retailer
 Large Department Store

27

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Inventory

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