This document discusses inventory management. It defines inventory inputs like raw materials and outputs like finished goods. It provides an analogy comparing inventory levels to the relationship between supply, demand, and buffers. It outlines typical inventory carrying costs and gives examples. It also discusses inventory management systems and approaches, including ABC analysis to prioritize items. The Economic Order Quantity model is explained in detail, including how to calculate optimal order quantity and reorder point to minimize total inventory costs.

1. INVENTORY
MANAGEMENT
2 Feb 2010 Arif Mahmood

2. Inventory
Inputs
Raw material
Purchased Parts
Maintenance and Repair
Material
Out Puts
Finished Goods
Scrap, Waste
In Process
Partially completed
Subassemblies

3. Analogy for Inventory
Supply Rate
Inventory Level
Demand Rate
Inventory Level
Buffers Demand Rate
from Supply Rate

4. Inventory Cost Structures
 Ordering (or setup) cost
 Carrying (or holding) cost:
 Cost of capital
 Cost of storage
 Cost of obsolescence, deterioration, and loss
 Stock out cost
 Item costs, shipping costs and other cost subject
to volume discounts

5. Typical Inventory Carrying Costs
Housing cost:
 Building rent or depreciation
 Building operating cost
 Taxes on building
 Insurance
Material handling costs:
 Equipment, lease, or depreciation
 Power
 Equipment operating cost
Manpower cost from extra handling and supervision
 Borrowing costs
 Taxes on inventory
 Insurance on inventory
Pilferage, scrap, and obsolescence
Overall carrying cost
Costs as % of
Inventory Value

6. Inventory Management Systems
 Functions of Inventory Management
– Track inventory
– How much to order
– When to order
 Prioritization
 Inventory Management Approach
– EOQ
– Continuous / Periodic

7. ABC Prioritization
 „A‟ items: 20% of SKUs, 80% of Rupee
 „B‟ items: 30 % of SKUs, 15% of Rupee
 „C‟ items: 50 % of SKUs, 5% of Rupee
 Three classes is arbitrary; could be any
number.
 Percents are approximate.
 Danger: Rs use may not reflect importance
of any given SKU!

8. ABC ANALYSIS
EXAMPLE
10 20 30 40 50 60 70 80 90 100
Percentage of items
PercentageofRsvalue
100 —
90 —
80 —
70 —
60 —
50 —
40 —
30 —
20 —
10 —
0 —
+Class C
Class A
+Class B

9. Annual Usage of Items by Rs Value
Annual Usage
in Units Unit Cost RsUsage
%of Total
Rs 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%
254,725.00 100.0%

10. Inventory Management Approaches
 A-items
– Track carefully (e.g. continuous review)
– Sophisticated forecasting to assure
correct levels
 C-items
– Track less frequently (e.g. periodic
review)
– Accept risks of too much or too little
(depending on the item)

11. Economic Order Quantity (EOQ)
Model
 Demand rate D is constant, recurring, and known
 Amount in inventory is known at all times
 Ordering (setup) cost S per order is fixed
 Lead time L is constant and known.
 Unit cost C is constant (no quantity discounts)
 Annual carrying cost is i time the average RS value of
the inventory
 No stockouts allowed.
 Material is ordered or produced in a lot or batch and
the lot is received all at once

12. EOQ Lot Size Choice
 There is a trade-off between lot size and
inventory level.
 Frequent orders (small lot size): higher
ordering cost and lower holding cost.
 Fewer orders (large lot size): lower ordering
cost and higher holding cost.

13. EOQ Inventory Order Cycle
Demand
rate
0 TimeLead
time
Lead
time
Order
Placed
Order
Placed
Order
Received
Order
Received
Inventory
Level
Reorder point, R
Order qty, Q
As Q increases, average
inventory level
increases, but number of
orders placed decreases
ave = Q/2

14. Inventory Management EOQ Model
Keeping track of inventory
 Implied that we track continuously
How much to order?
 Solve for when the derivative of total cost with respect to
Q = 0: -SD/Q^2 + iC/2 = 0
 Q = sqrt ( 2SD/iC)
When to order?
 Order when inventory falls to the “Reorder Point-level” R
so we will just at the last item as the new order comes
in:
 R = DL

15. Re-order Point Example
Demand = 10,000 yds/year
Lead time = L = 10 days
When inventory falls to R, we order so as not to
run out before the new order comes in.
R = ?

16. Re-order Point
Demand = 10,000 yds/year
Daily demand = 10,000 / 365 = 27.4 yds/day
Lead time = L = 10 days
R = D*L = (27.4)(10) = 274 yds
Don’t forget to convert to consistent time units!

17. EOQ Summary
How much to order?
 Q = sqrt(2DS/iC)
When to order?
 R = DL

18. Annual Demand = 1,000 units
Days per year considered in average
daily demand = 365
Cost to place an order = Rs 10
Holding cost per unit per year = Rs 2.50
EOQ and reorder point?
units90orunits89.443=
2.50
)(10)2(1,000
=
H
2DS
=QOPT
units/day2.74=
days/year365
units/year1,000
=d
Lead time = 7 days
Cost per unit = Rs15
units20or19.18=(7days)day2.74units/=Ld=Rpoint,Reorder
_

19. EOQ Example

20. Tug of war between acquisition
costs and inventory carrying costs
 ROP = SSQ + (QUD x ALT)
Where,
ROP = Reorder Point
SSQ = Safety Stock Quantity
QUD = Quantity Used Daily
ALT = Average Lead Time (in days)
 How much to order.
 Acquisition costs and inventory carrying costs:
 when you order bigger quantities less frequently, your aggregate
acquisition costs are low but your inventory costs are high due to
higher inventory levels.
 Conversely, when order smaller quantities more often, your
inventory costs are low but your acquisition costs are higher
because you are expending more resources on ordering.
 The EOQ is the order quantity that minimizes the sum of these two
costs

21. Safety Stock
Formula
order)onitems(includeslevelinventorycurrent=I
timeleadandreviewover thedemandofdeviationstandard=
yprobabilitservicespecifiedafordeviationsstandardofnumberthe=z
demanddailyaverageforecast=d
daysintimelead=L
reviewsbetweendaysofnumberthe=T
orderedbetoquantitiy=q
:Where
I-Z+L)+(Td=q
L+T
L+T


q = Average demand + Safety stock – Inventory currently on hand
17-21

22. Cost
Regular
Fast
Review
Local
Forecast
Inventory

23. Gain Life a
balance

24. Take the Service to the Patient Thanks