1
INVENTORY
MANAGEMENT
Chapter 13
MIS 373: Basic Operations Management
Additional content from L. Beril Toktay
LEARNING OBJECTIVES
• After this lecture, students will be able to
1.
2.
3.
4.
5.
6.
Define the term inventory
List the different types of inventory
Describe the main functions of inventory
Discuss the main requirements for effective inventory management
Describe the A-B-C approach and explain how it is useful
Describe the basic EOQ model and its assumptions and solve typical
problems.
7. Describe reorder point models and solve typical problems.
8. Describe situations in which the fixed-order interval model is
appropriate, and solve typical problems.
9. Describe service level and risk of stockout and use Z table to identify
the z value for a service level or a risk of stockout
MIS 373: Basic Operations Management
2
INVENTORY MANAGEMENT
AT COX HARDWARE
• From the video, what are the elements relevant to inventory management?
INVENTORY
• An inventory is a stock or store of goods.
• Inventories are a vital part of business:
• necessary for operations
• contribute to customer satisfaction
• A “typical” firm has roughly 30% of its current assets and as
much as 90% of its working capital invested in inventory
• But
• Costly
• May have limited shelf-life
• Carrier may have limited space
MIS 373: Basic Operations Management
4
TYPES OF INVENTORY
•
•
•
•
•
•
Raw materials and purchased parts
Work-in-process (WIP)
Finished goods inventories or merchandise
Tools and supplies
Maintenance and repairs (MRO) inventory
Goods-in-transit to warehouses or customers (pipeline
inventory)
MIS 373: Basic Operations Management
5
COSTS OF INVENTORY
• Physical holding costs:
• out of pocket expenses for storing inventory (insurance,
security, warehouse rental, cooling)
• All costs that may be entailed before you sell it
(obsolescence, spoilage, rework...)
• Opportunity cost of inventory: foregone return on the
funds invested.
MIS 373: Basic Operations Management
6
With all these costs,
why most companies still like to
hold inventories?
INVENTORY FUNCTIONS
• Inventories serve a number of functions such as:
1. To meet anticipated customer demand
2. To smooth production requirements
•
Firms that experience seasonal patterns in demand often build up
inventories during preseason periods to meet overly high requirements
during seasonal periods.
3. To decouple operations
•
Buffers between operations
4. To protect against stockouts
•
Delayed deliveries and unexpected increases in demand increase the
risk of shortages.
MIS 373: Basic Operations Management
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INVENTORY FUNCTIONS
• Inventories serve a number of functions such as:
5. To take advantage of order cycles
•
It is usually economical to produce in large rather than small quantities.
The excess output must be stored for later use.
6. To hedge against price increases
•
Occasionally a firm will suspect that a substantial price increase is
about to occur and purchase larger-than-normal amounts to beat the
increase
7. To permit operations
•
The fact that production operations take a certain amount of time (i.e.,
they are not instantaneous) means that there will generally be some
work-in-process inventory.
8. To take advantage of quantity discounts
•
Suppliers may give discounts on large orders.
MIS 373: Basic Operations Management
9
OBJECTIVES OF INVENTORY
CONTROL
• Inventory management has two main concerns:
1. Level of customer service
• Having the right goods available in the right quantity in the right place at
the right time
2. Costs of ordering and carrying inventories
• The overall objective of inventory management is to achieve satisfactory
levels of customer service while keeping inventory costs within reasonable
bounds
MIS 373: Basic Operations Management
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MEASURES OF PERFORMANCE
• Measures of performance:
• Customer satisfaction
• Number and quantity of backorders
• Customer complaints
• Inventory turnover = a ratio of
(average) cost of goods sold
(average) inventory investment
during a period
MIS 373: Basic Operations Management
11
INVENTORY MANAGEMENT
• Management has two basic functions concerning
inventory:
1. Establish a system for tracking items in inventory
2. Make decisions about
• When to order
• How much to order
MIS 373: Basic Operations Management
12
EFFECTIVE INVENTORY
MANAGEMENT
• Requires:
1.
2.
3.
4.
A system keep track of inventory
A reliable forecast of demand
Knowledge of lead time and lead time variability
Reasonable estimates of
• holding costs
• ordering costs
• shortage costs
5. A classification system for inventory items
MIS 373: Basic Operations Management
13
INVENTORY COUNTING SYSTEMS
• Periodic System
• Physical count of items in inventory made at periodic intervals
• Perpetual Inventory System
• System that keeps track of removals from inventory continuously, thus
monitoring current levels of each item
• Point-of-sale (POS) systems
• A system that electronically records actual sales
• Radio Frequency Identification (RFID)
MIS 373: Basic Operations Management
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ONE-BIND & TWO-BIN
SYSTEMS
• One-Bin System
• Two-Bin System
Bin A
Bin B
MIS 373: Basic Operations Management
15
INVENTORY COSTS
• Purchase cost
• The amount paid to buy the inventory
• Holding (carrying) costs
• Cost to carry an item in inventory for a length of time, usually a year
• Interest, insurance, taxes (in some states), depreciation, obsolescence,
deterioration, spoilage, pilferage, breakage, tracking, picking, and
warehousing costs (heat, light, rent, workers, equipment, security).
• Ordering costs
• Costs of ordering and receiving inventory
• determining how much is needed, preparing invoices, inspecting goods
upon arrival for quality and quantity, and moving the goods to temporary
storage.
• Shortage costs
• Costs resulting when demand exceeds the supply of inventory; often
unrealized profit per unit
MIS 373: Basic Operations Management
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ABC CLASSIFICATION
SYSTEM
• A-B-C approach
• Classifying inventory according to some measure of importance, and
allocating control efforts accordingly
• A items (very important)
• 10 to 20 percent of the number of items in inventory and about 60
to 70 percent of the annual dollar value
• B items (moderately important)
• C items (least important)
• 50 to 60 percent of the number
of items in inventory but only
about 10 to 15 percent of the
annual dollar value
MIS 373: Basic Operations Management
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ABC CLASSIFICATION
• How to classify?
1. For each item, multiply
annual volume by unit
price to get the annual
dollar value.
2. Arrange annual values
in descending order.
3. A items: the few with
the highest annual
dollar value
C items: the most with
the lowest dollar value.
B items: those in
between
MIS 373: Basic Operations Management
#
Annual
demand
Unit
price
Annual
value
Class
% of
items
% of
value
8
1,000
4,000
4,000,000
A
5.3
52.7
3
2,400
500
1,200,000
B
6
1,000
1,000
1,000,000
B
31.4
40.8
1
2,500
360
900,000
B
4
1,500
100
150,000
C
10
500
200
100,000
C
9
8,000
10
80,000
C
2
1,000
70
70,000
C
63.3
6.5
5
700
70
49,000
C
7
200
210
42,000
C
100
100
18,800
7,591,000
18
ABC CLASSIFICATION:
CYCLE COUNTING
• Cycle counting
• A physical count of items in inventory
• Cycle counting management
• How much accuracy is needed?
• A items: ± 0.2 percent
• B items: ± 1 percent
• C items: ± 5 percent
• When should cycle counting be performed?
• Who should do it?
MIS 373: Basic Operations Management
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HOW MUCH TO ORDER?
ECONOMIC ORDER QUANTITY MODELS
• Economic Order Quantity (EOQ) models:
• identify the optimal order quantity
• by minimizing total annual costs that vary with order size and frequency
1.
2.
3.
4.
5.
6.
The basic Economic Order Quantity model (EOQ)
The Quantity Discount model
The Economic Production Quantity model (EPQ)
Reorder Point Ordering (uncertainty, when to order)
Fixed-Order-Interval model
Single Period model (perishable items)
MIS 373: Basic Operations Management
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BASIC EOQ MODEL
• The basic EOQ model:
• used to find a fixed order quantity that will minimize total annual
inventory costs
• continuous monitoring system
• Assumptions:
1.
2.
3.
4.
5.
6.
Only one product is involved
Annual demand requirements are known
Demand is even throughout the year
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts
MIS 373: Basic Operations Management
21
THE INVENTORY CYCLE
Profile of Inventory Level Over Time
Q
Usage
rate
Quantity
on hand
Reorder
point
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Time
Lead time
MIS 373: Basic Operations Management
22
TOTAL ANNUAL COST
• Total Cost = Annual Holding Cost + Annual Ordering Cost
(TC)
Q
D
=
H
+
S
2
Q
Average number of
units in inventory
Number
of orders
where
• Q = order quantity in units
• H = holding (carrying) cost per unit, usually per year
• D = demand, usually in units per year
• S = ordering cost per order
MIS 373: Basic Operations Management
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GOAL: TOTAL COST
MINIMIZATION
• The Total-Cost Curve is U-Shaped
Annual
Cost
• There is a tradeoff between holding costs and ordering costs
TC 
Q
2
H 
D
S
Q
Holding Costs
Ordering Costs
Q*(optimal order quantity)
MIS 373: Basic Operations Management
Order Quantity
(Q)
24
DERIVING EOQ
• Using calculus, we take the derivative of the total cost
function and set the derivative (slope) equal to zero and solve
for Q.
• The total cost curve reaches its minimum where the carrying
and ordering costs are equal.
𝑇𝐶 ′
𝐻
−1 𝐷𝑆
= +
=0
2
2
𝑄
𝑄∗
=
2𝐷𝑆
=
𝐻
MIS 373: Basic Operations Management
→
𝐷𝑆 𝐻
=
2
𝑄
2
→
𝐷𝑆 𝐻𝑄
=
𝑄
2
2 𝑎𝑛𝑛𝑢𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡
𝑎𝑛𝑛𝑢𝑎𝑙 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 ℎ𝑜𝑙𝑑𝑖𝑛𝑔 𝑐𝑜𝑠𝑡
25
EXAMPLE: DERIVING EOQ
•
•
•
•
Tire distributer
D (Demand)=9,600 tires per year
H (Holding cost)=$16 per unit per year
S (Ordering cost) = $75 per order
∗
𝑄 =
2𝐷𝑆
=
𝐻
2 ∗ 9,600 ∗ 75
= 300 𝑡𝑖𝑟𝑒𝑠
16
𝑄
𝐷
300
9,600
𝑇𝐶 = 𝐻 + 𝑆 =
∗ 16 +
∗ 75 = 2,400 + 2,400 = 4,800
2
𝑄
2
300
MIS 373: Basic Operations Management
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EXAMPLE: DERIVING EOQ
• D (Demand)=9,600 tires per year
• H (Holding cost)=$16 per unit per year
• S (Ordering cost) = $75 per order
• Q*=300 tires
• TCmin = 4,800
TC
250
Let’s verify whether the Q*
indeed gives the lowest cost.

Q
H 
2
TC
400

Q
D
S 
Q
H 
2
MIS 373: Basic Operations Management
D
Q
250
16 
2
S 
400
2
9 , 600
75  2 , 000  2 ,880  4 ,880
250
16 
9 , 600
75  3 , 200  1,800  5 , 000
400
27
WHEN TO REORDER
• If delivery is not instantaneous, but there is a lead time:
When to order?
Inventory
Order
Quantity
Q
Lead Time
MIS 373: Basic Operations Management
Place
order
Receive
order
Time
28
WHEN TO REORDER
• EOQ answers the “how much” question
• The reorder-point (ROP) tells “when” to order
• Reorder-Point
• When the quantity on hand of an item drops to this amount (quantitytrigger), the item is reordered.
• Determinants of the Reorder-Point
1. The rate of demand
2. The lead time
3. The extent of demand and/or lead time variability
4. The degree of stockout risk acceptable to management
MIS 373: Basic Operations Management
29
REORDER-POINT
ROP
= (Demand per day) * (Lead time for a new order in days)
=
d
*
L
where
d = (Demand per year) / (Number of working days in a year)
Example:
• Demand = 12,000 iPads per year
• 300 working day year
• Lead time for orders is 3 working days
In other words, the
manager should place the
order when only 120 units
left in the inventory.
d = 12,000 / 300 = 40 units
ROP = d * L = 40 units per day * 3 days of leading time = 120 units
MIS 373: Basic Operations Management
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THE INVENTORY CYCLE
Q: When shall we order?
A: When inventory = ROP
Q: How much shall we order?
A: Q = EOQ
Profile of Inventory Level Over Time
Q
Usage
rate
Quantity
on hand
Reorder
point
ROP = LxD
Receive
order
D: demand per period
L: Lead time in periods
MIS 373: Basic Operations Management
Place
order
Receive
order
Place
order
Receive
order
Time
Lead time
31
EXERCISE: EOQ & ROP
• Assume a car dealer that faces demand for 5,000 cars per year, and that it costs
$15,000 to have the cars shipped to the dealership. Holding cost is estimated at
$500 per car per year. How many times should the dealer order, and what
should be the order size? (Assuming that the lead time to receive cars is 10
days and that there are 365 working days in a year)
Recall:
∗
𝑄 =
2𝐷𝑆
=
𝐻
2 𝑎𝑛𝑛𝑢𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡
𝑎𝑛𝑛𝑢𝑎𝑙 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 ℎ𝑜𝑙𝑑𝑖𝑛𝑔 𝑐𝑜𝑠𝑡
EOQ
=
ROP
= (Demand per day) * (Lead time for a new order in days)
=
d
*
L
where
d = (Demand per year) / (Number of working days in a year)
EXERCISE: EOQ & ROP
• Assume a car dealer that faces demand for 5,000 cars per year, and that it costs
$15,000 to have the cars shipped to the dealership. Holding cost is estimated at
$500 per car per year. How many times should the dealer order, and what
should be the order size?
Q 
*
2 (15 , 000 )( 5 , 000 )
 548
500
Since d is given in years, first convert: 5000/365 =13.7 cars per working day
So, ROP = 13.7 * 10 = 137
So, when the number of cars on the lot
reaches 137, order 548 more cars.
BUT DEMAND IS RARELY
PREDICTABLE!
Inventory
Level
Order
Quantity
Demand???
Time
Place
order
MIS 373: Basic Operations Management
Lead Time
Receive
order
34
BUT DEMAND IS RARELY
PREDICTABLE!
Inventory
Level
When Actual Demand < Expected Demand
Order
Quantity
Lead Time Demand
ROP
Inventory at time of receipt
Time
Place
order
MIS 373: Basic Operations Management
Lead Time
Receive
order
35
BUT DEMAND IS RARELY
PREDICTABLE!
Inventory
Level
When Actual Demand > Expected Demand
Order
Quantity
Stockout Point
ROP
Unfilled demand
Place
order
MIS 373: Basic Operations Management
Lead Time
Receive
order
Time
36
BUT DEMAND IS RARELY
PREDICTABLE!
Inventory
Level
Order
Quantity
If ROP = expected demand,
inventory left 50% of the time, stock outs 50% of the time.
ROP = Expected Demand
Average
Uncertain Demand
Time
MIS 373: Basic Operations Management
37
SAFETY STOCK
Inventory
Level
To reduce stockouts we add safety stock
Order
Quantity
ROP =
Safety
Stock +
Expected
LT
Demand
Order Quantity
Q = EOQ
Expected
LT Demand
Safety Stock
Place
order
MIS 373: Basic Operations Management
Lead Time
Receive
order
Time
38
HOW MUCH SAFETY STOCK?
• The amount of safety stock that is appropriate for a given
situation depends upon:
1. The average demand rate and average lead time
2. Demand and lead time variability
3. The desired service level
•
Service level = probability of NOT stocking out
• Reorder point (ROP) =
Expected demand during lead time + z*σdLT
Where
z = number of standard deviations
σdLT = the standard deviation of lead time demand
MIS 373: Basic Operations Management
39
REORDER POINT
• The ROP based on a normal distribution of lead time demand
Risk of stockout
Service
level
(probability of
not stockout)
Safety
Stock
Expected
ROP
demand
MIS 373: Basic Operations Management
0
Z
Quantity
Z scale
40
Z TABLE
• http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf
• Other variations of Z table
• http://2.bp.blogspot.com/afjxDroAfuY/UNIjs9kL_YI/AAAAAAAAASY/3gBDkp7r_H8/s1600/normTab.jpeg
• https://onlinecourses.science.psu.edu/stat414/sites/onlinecourses.science.psu.edu.stat414/file
s/lesson17/TopOfNormalBTable.gif
• How to use Z table:
1.
2.
3.
4.
Decide the desired service level
Look up the smallest number in the Z table that is greater than the service level
Use the row of the number to identify the first two digits of the z
Use the column of the number to identify the second decimal point
• Q1: what is the z for a 99% service level?
• Q2: what is the z for a 10% risk of stockout?
FIXED-ORDER-INTERVAL
MODEL
• The fixed-order-interval (FOI) model is used when orders
must be placed at fixed time intervals (weekly, twice a month,
etc.): The timing of orders is set. The question, then, at each
order point, is how much to order.
• Fixed-interval ordering systems are widely used by retail businesses.
• If demand is variable, the order size will tend to vary from cycle to
cycle.
• This is quite different from an EOQ/ROP approach in which the order
size generally remains fixed from cycle to cycle, while the length of
the cycle varies.
MIS 373: Basic Operations Management
42
FIXED-ORDER-INTERVAL
MODEL
• Reasons for Using the Fixed-Order-Interval Model
• A supplier's policy might encourage orders at fixed intervals.
• Grouping orders for items from the same supplier can produce
savings in shipping costs.
• Some situations do not readily lend themselves to continuous
monitoring of inventory levels.
• Many retail operations (e.g., drugstores, small grocery stores) fall into
this category.
• The alternative for them is to use fixed-interval ordering, which requires
only periodic checks of inventory levels.
MIS 373: Basic Operations Management
43
The same quantity
fixed-quantity ordering
LT: Lead Time
Different quantity
fixed-interval ordering
same length same length
MIS 373: Basic Operations Management
LT: Lead Time
OI: Order Interval
44
FIXED-ORDER-INTERVAL
MODEL
• Order size in the fixed-interval model is determined by the
following computation:
Expected demand
Amount
= during protection interval +
to order
Q
=
𝑑 𝑂𝐼 + 𝐿𝑇
Safety
stock
+ 𝑧𝜎𝑑 𝑂𝐼 + 𝐿𝑇
−
−
Amount on hand
at reorder time
A
where
d = demand in a time unit, e.g., 100 units per day
OI = Order interval (length of time between orders), e.g., 10 days
LT = Lead time, e.g., 3 days
𝜎𝑑 = the standard deviation of the demand, e.g., 20 units
z = z score for a desired service level, e.g., 2.33 for a 99% service level
A = Amount on hand at reorder time
MIS 373: Basic Operations Management
45
EXAMPLE: FIXED-ORDERINTERVAL MODEL
• Given the following information, determine the amount to
order.
• d = 30 units per day
• OI = 7 days
• LT = 2 days
• 𝜎𝑑 = 3 units per day
• Service level = 99%  z = 2.33 (by looking up the z table)
• A = 71 units
•
Q
=
𝑑 𝑂𝐼 + 𝐿𝑇
+
𝑧𝜎𝑑 𝑂𝐼 + 𝐿𝑇
−
A
=
30 7 + 2
+
2.33 × 3 × 7 + 2
−
71
= 222 units
MIS 373: Basic Operations Management
46
KEY POINTS
• All businesses carry inventories, which are goods held for future
use or potential future use.
• Inventory represents money that is tied up in goods or materials.
• Effective inventory decisions depend on having good inventory
records, good cost information, and good estimates of demand.
• The decision of how much inventory to have on hand reflects a
trade-off, for example, how much money to tie up in inventory
versus having it available for other uses. Factors related to the
decision include purchase costs, holding costs, ordering costs,
shortage and backlog costs, available space to store the inventory,
and the return that can be had from other uses of the money.
• As with other areas of operations, variations are present and must
be taken into account. Uncertainties can be offset to some degree
by holding safety stock, although that adds to the cost of holding
inventory.
MIS 373: Basic Operations Management
47