2. 12-2
Learning Objectives
Define the term inventory and list the major
reasons for holding inventories; and list the main
requirements for effective inventory management.
Discuss the nature and importance of service
inventories
Discuss periodic and perpetual review systems.
Discuss the objectives of inventory management.
Describe the A-B-C approach and explain how it
is useful.
3. 12-3
Learning Objectives
Describe the basic Economic Order Quantity
(“EOQ”) model and its assumptions, and solve
typical problems.
Describe the Economic Production Quantity
(“EPQ”) model and solve typical problems.
Describe the quantity discount model and solve
typical problems.
Describe reorder point models and solve typical
problems.
4. 12-4
Inventory Models
Independent demand – finished goods, items
that are ready to be sold
E.g. a computer
Dependent demand – components of
finished products
E.g. parts that make up the computer
6. 12-6
Types of Inventories
Raw materials & purchased parts
Partially completed goods called
work in progress
Finished-goods inventories
(manufacturing firms)
or merchandise
(retail stores)
Replacement parts, tools, & supplies
Goods-in-transit to warehouses or
customers (pipeline inventory)
7. 12-7
Functions of Inventory
To meet anticipated demand
To smooth production requirements
To decouple operations
To protect against stock-outs
8. 12-8
Functions of Inventory (Cont’d)
To take advantage of order cycles
To help hedge against price increases
To permit operations
To take advantage of quantity
discounts
9. 12-9
Objective of Inventory Control
To achieve satisfactory levels of
customer service while keeping
inventory costs within reasonable
bounds
Level of customer service
Costs of ordering and carrying inventory
Inventory turnover is the ratio of average cost
of goods sold to average inventory investment.
10. 12-10
A system to keep track of inventory
A reliable forecast of demand
Knowledge of lead times
Reasonable estimates of
Holding costs
Ordering costs
Shortage costs
A classification system
Effective Inventory Management
11. 12-11
Inventory Counting Systems
Periodic System
Physical count of items made at periodic
intervals
Perpetual Inventory System
System that keeps track of removals from
inventory continuously, thus
monitoring current levels of
each item
12. 12-12
Inventory Counting Systems
(Cont’d)
Two-Bin System - Two containers of
inventory; reorder when the first is
empty
Universal Bar Code - Bar code
printed on a label that has
information about the item
to which it is attached 0
214800 232087768
13. 12-13
Lead time: time interval between
ordering and receiving the order
Holding (carrying) costs: cost to carry
an item in inventory for a length of time,
usually a year
Ordering costs: costs of ordering and
receiving inventory
Shortage costs: costs when demand
exceeds supply
Key Inventory Terms
14. 12-14
ABC Classification System
Classifying inventory according to some
measure of importance and allocating
control efforts accordingly.
A - very important
B - mod. important
C - least important Annual
$ value
of items
A
B
C
High
Low
Low High
Percentage of Items
15. 12-15
Economic order quantity (EOQ) model
The order size that minimizes total annual
cost
Economic production model
Quantity discount model
Economic Order Quantity Models
16. 12-16
Only one product is involved
Annual demand requirements 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
Assumptions of EOQ Model
17. 12-17
The Inventory Cycle
Profile of Inventory Level Over Time
Quantity
on hand
Q
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Lead time
Reorder
point
Usage
rate
Time
20. 12-20
Deriving the EOQ
Using calculus, we take the derivative of
the total cost function and set the
derivative (slope) equal to zero and solve
for Q.
Q =
2DS
H
=
2(Annual Demand )(Order or Setup Cost )
Annual Holding Cost
OPT
21. 12-21
Minimum Total Cost
The total cost curve reaches its
minimum where the carrying and
ordering costs are equal.
Q
2
H
D
Q
S
=
22. EOQ Example
12-22
A local distributor for a national tire company
expects to sell approximately 9,600 steel-belted
radial tires of a certain size and tread design next
year. Annual carrying cost is $16 per tire, and
ordering cost is $75. The distributor operates 288
days a year.
What is the EOQ?
How many times per year does the store reorder?
What is the length of an order cycle (time between
orders)?
What is the total annual cost if the EOQ quantity is
ordered?
24. EOQ Example
Piddling Manufacturing assembles security monitors. It purchases 3,600
black-and-white cathode ray tubes a year at $65 each. Ordering costs are
$31, and annual carrying costs are 20 percent of the purchase price.
Compute the optimal quantity and the total annual cost of ordering and
carrying the inventory.
12-24
25. 12-25
Production done in batches or lots
Capacity to produce a part exceeds the
part’s usage or demand rate
Assumptions of EPQ are similar to EOQ
except orders are received
incrementally during production
Economic Production Quantity (EPQ)
26. 12-26
Only one item is involved
Annual demand is known
Usage rate is constant
Usage occurs continually
Production rate is constant
Lead time does not vary
No quantity discounts
Economic Production Quantity
Assumptions
29. EPQ Example
A toy manufacturer uses 48,000 rubber wheels per year for its
popular dump truck series. The firm makes its own wheels,
which it can produce at a rate of 800 per day. The toy trucks
are assembled uniformly over the entire year. Carrying cost is
$1 per wheel a year. Setup cost for a production run of wheels
is $45. The firm operates 240 days per year. Determine the:
Optimal run size
Minimum total annual cost for carrying and setup
Cycle time for the optimal run size
Run time
12-29
32. 12-32
Total Costs with Purchasing Cost
Annual
carrying
cost
Purchasing
cost
TC = +
Q
2
H
D
Q
S
TC = +
+
Annual
ordering
cost
PD
+
33. 12-33
Total Costs with PD
Cost
EOQ
TC with PD
TC without PD
PD
0 Quantity
Adding Purchasing cost
doesn’t change EOQ
34. Quantity Discount Example
The maintenance department of a large
hospital uses about 816 cases of liquid
cleanser annually. Ordering costs are $12,
carrying costs are $4 per case a year, and the
new price schedule indicates that orders of
less than 50 cases will cost $20 per case, 50 to
79 cases will cost $18 per case, 80 to 99 cases
will cost $17 per case, and larger orders will
cost $16 per case. Determine the optimal order
quantity and the total cost.
12-34
36. Quantity Discount Example
The 70 cases can be bought at $18 per case because 70 falls in the
range of 50 to 79 cases. The total cost to purchase 816 cases a year, at
the rate of 70 cases per order, will be
12-36
Because lower cost ranges exist, each must be checked against the
minimum cost generated by 70 cases at $18 each. In order to buy at $17
per case, at least 80 cases must be purchased. (Because the TC curve
is rising, 80 cases will have the lowest TC for that curve's feasible
region.) The total cost at 80 cases will be
To obtain a cost of $16 per case, at least 100 cases per order are
required, and the total cost at that price break will be
37. Quantity Discount Example
Order Quantity Total Cost
70 14,968
80 14,154
100 13,354
12-37
100 cases per order yields the lowest total
cost, 100 cases is the overall optimal order
quantity.
With Quantity Discounts, purchase quantity
will be equal to or greater optimal
economic quantity.
38. 12-38
When to Reorder with EOQ
Ordering
Reorder Point - When the quantity on hand of
an item drops to this amount, the item is
reordered
Safety Stock - Stock that is held in excess of
expected demand due to variable demand
rate and/or lead time.
Service Level - Probability that demand will
not exceed supply during lead time, (i.e., we
will not have turn customers back during lead
time because we ran out of inventory).
39. 12-39
Determinants of the Reorder
Point
The rate of demand
The lead time
Demand and/or lead time variability
Stockout risk (safety stock)
If demand and lead time are both
constants, then ROP = dxLT
Question: What happens to the EOQ if the
lead time or demand rate changes?
41. Reorder Point Example
Rahim takes Two-a-Day vitamins, which are
delivered to his home seven days after an
order is called in. At what point should Rahim
reorder?
12-41
Rahim should reorder when 14 vitamin tablets are
left, which is equal to a seven-day supply of two
vitamins a day.
42. Safety Stock
When variability is present in demand or lead time, it creates the possibility
that actual demand will exceed expected demand. Consequently, it
becomes necessary to carry additional inventory, called safety stock , to
reduce the risk of running out of inventory (a stockout) during lead time.
The reorder point then increases by the amount of the safety stock:
12-42
For example, if expected demand during lead time is 100 units, and the
desired amount of safety stock is 10 units, the ROP would be 110 units
43. Service Level
Order cycle service level can be defined as the probability
that demand will not exceed supply during lead time (i.e.,
that the amount of stock on hand will be sufficient to meet
demand).
A service level of 95 percent implies a probability of 95
percent that demand will not exceed supply during lead
time.
The risk of a stockout is the complement of service level; a
customer service level of 95 percent implies a stockout risk
of 5 percent.
12-43
44. 12-44
Orders are placed at fixed time intervals
Order quantity for next interval?
Suppliers might encourage fixed
intervals
May require only periodic checks of
inventory levels
Risk of stockout
Fill rate – the percentage of demand
filled by the stock on hand
Fixed-Order-Interval Model
45. 12-45
Tight control of inventory items
Items from same supplier may yield
savings in:
Ordering
Packing
Shipping costs
May be practical when inventories
cannot be closely monitored
Fixed-Interval Benefits
46. 12-46
Requires a larger safety stock
Increases carrying cost
Costs of periodic reviews
Fixed-Interval Disadvantages
47. 12-47
Single period model: model for ordering
of perishables and other items with
limited useful lives
Shortage cost: generally the unrealized
profits per unit
Excess cost: difference between
purchase cost and salvage value of
items left over at the end of a period
Single Period Model
48. 12-48
Optimal Stocking Level
Service Level
So
Quantity
Ce Cs
Balance point
Service level =
Cs
Cs + Ce
Cs = Shortage cost per unit
Ce = Excess cost per unit
49. 12-49
Example
Ce = $0.20 per unit
Cs = $0.60 per unit
Service level = Cs/(Cs+Ce) = .6/(.6+.2)
Service level = .75
Service Level = 75%
Quantity
Ce Cs
Stockout risk = 1.00 – 0.75 = 0.25
50. 12-50
Too much inventory
Tends to hide problems
Easier to live with problems than to
eliminate them
Costly to maintain
Operations Strategy