nventory management , types of inventories , functions of inventory , objective of inventory control , effective inventory management , inventory counting systems , key inventory terms , economic order quantity models , assumptions of eoq model , deriving the eoq , economic production quantity assumptions , single period model , fixed-interval disadvantages , when to reorder with eoq ordering

1. 12-1
Inventory Management

2. 12-2
Types of Inventories
(Nature and importance of inventory)
 Raw materials & purchased parts
 Partially completed goods called work in
progress
 Finished-goods inventories (manufacturing
firms) or merchandise (retail stores)

3. 12-3
Types of Inventories (Cont’d)
 Replacement parts, tools, & supplies
 Goods-in-transit to warehouses or
customers (pipeline inventory)

4. 12-4
Functions of Inventory
 To meet anticipated demand
 To smooth production requirements
 To decouple operations
 To protect against stock-outs

5. 12-5
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

6. 12-6
Objective of Inventory Control
 To achieve satisfactory levels of customer
service while keeping inventory costs within
reasonable bounds
 Level of customer service (to have the right goods,
in sufficient quantities, in the right place, at the right
time)
 Costs of ordering and carrying inventory

7. 12-7
 A system to keep track of inventory
 A reliable forecast of demand
 Knowledge of lead times
 Reasonable estimates of inventory cost
 Holding costs
 Ordering costs
 Shortage costs
 A classification system
Effective Inventory Management

8. 12-8
Inventory Counting Systems
 Periodic System
Physical count of items made at periodic
intervals
 Continuous Inventory System
System that keeps track
of removals from inventory
continuously, thus
monitoring
current levels of
each item

9. 12-9
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
 ABC Classification
0
214800 232087768

10. 12-10
ABC Classification System
Classifying inventory according to some
measure of importance and allocating
control efforts accordingly.
A - very important
B - moderate important
C - least important

11. 12-11
 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 (often unrealized profit per unit)
Key Inventory Terms

12. 12-12
 Economic order quantity (EOQ) model
 The order size that minimizes total annual
cost
 Economic production model
 Quantity discount model
Economic Order Quantity Models

13. 12-13
 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

14. 12-14
The Inventory Cycle
Figure 12.2
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

15. 12-15
Total Cost
Annual
carrying
cost
Annual
ordering
cost
Total cost = +
TC =
Q
2
H
D
Q
S+

16. 12-16
Cost Minimization Goal
Order Quantity
(Q)
The Total-Cost Curve is U-Shaped
Ordering Costs
QO
AnnualCost
(optimal order quantity)
TC
Q
H
D
Q
S 
2
Figure 12.4C

17. 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.
12-17

18. 12-18
Deriving the EOQ
CostHoldingAnnual
Cost)SetuporderDemand)(Or2(Annual
H
2DS
=Q
2
Q2Q
Q2Q2
0
dQ
)Q(
Q
Q
2dQ
dTC
OPT
22
22
-1





H
DS
DSH
DSHDSH
d
DS
d
dH

19. Deriving the EOQ
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.
a. What is the EOQ?
b. How many times per year does the store
reorder?
c. What is the length of an order cycle?
d. What is the total annual cost if the EOQ quantity
is ordered? 12-19

20. Deriving the EOQ
A distributor uses 800 packing crates a
month, which it purchases at a cost of $10
each. The manager has assigned an annual
carrying cost of 35 percent of the purchase
price per crate. Ordering costs are $28.
Currently the manager orders once a month.
How much could the firm save annually in
ordering and carrying costs by using the
EOQ?
12-20

21. Deriving the EOQ
Here annual demand is 800 x 12 = 9600
Annual carrying cost is, H = .35 x $10 = $3.5
So, Total cost = Q/2 . H + D/Q . S
= 400 x 3.5 + 12 x 28 = $1736
EOQ = √ {(2 x 9600 x 28)/3.5} = 391.92 ≈ 392
Using EOQ, TC
= (392/2) x 3.5 + (9600/392) x 28 = $1372
Savings = $1736 - $1372 =$364
12-21

22. 12-22
Minimum Total Cost
The total cost curve reaches its
minimum where the carrying and
ordering costs are equal.
Q
2
H
D
Q
S=

23. 12-23
 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)

24. 12-24
 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

25. 12-25
Economic Run Size
Q
DS
H
p
p u
0
2


Where p = production or delivery rate
u = usage rate

26. 12-26
Total Costs with Purchasing Cost
Annual
carrying
cost
Purchasing
costTC = +
Q
2
H
D
Q
STC = +
+
Annual
ordering
cost
PD+

27. 12-27
Total Costs with PD
Cost
EOQ
TC with PD
TC without PD
PD
0 Quantity
Adding Purchasing cost
doesn’t change EOQ
Figure 12.7

28. 12-28
Total Cost with Constant
Carrying Costs
OC
EOQ Quantity
TotalCost
TCa
TCc
TCb
Decreasing
Price
CC a,b,c
Figure 12.9

29. 12-29
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.

30. 12-30
Determinants of the Reorder
Point
 The rate of demand
 The lead time
 Demand and/or lead time variability
 Stockout risk (safety stock)

31. 12-31
Safety Stock
LT Time
Expected demand
during lead time
Maximum probable demand
during lead time
ROP
Quantity
Safety stock
Figure 12.12
Safety stock reduces risk of
stockout during lead time

32. 12-32
Reorder Point
ROP
Risk of
a stockout
Service level
Probability of
no stockout
Expected
demand Safety
stock
0 z
Quantity
z-scale
Figure 12.13
The ROP based on a normal
Distribution of lead time demand

33. 12-33
 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

34. 12-34
 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

35. 12-35
 Requires a larger safety stock
 Increases carrying cost
 Costs of periodic reviews
Fixed-Interval Disadvantages

36. 12-36
 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

37. 12-37
 Continuous stocking levels
 Identifies optimal stocking levels
 Optimal stocking level balances unit
shortage and excess cost
 Discrete stocking levels
 Service levels are discrete rather than
continuous
 Desired service level is equaled or
exceeded
Single Period Model

38. 12-38
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

39. 12-39
Example 15
 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

40. 12-40
 Too much inventory
 Tends to hide problems
 Easier to live with problems than to
eliminate them
 Costly to maintain
 Wise strategy
 Reduce lot sizes
 Reduce safety stock
Operations Strategy