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INVENTORY

MANAGEMENT

By :

Kuldeep Uttam
Production and Industrial Engineer
Outline
Elements of Inventory Management

Inventory and Supply Chain Management
Inventory Control Systems
Economic Order Quantity Models
Reorder Point
Classification of Inventories: ABC, VED
What is inventory?
A physical resource that a
firm holds in stock with
the intent of selling it or
transforming it into a
more valuable state.

Purpose of inventory
management
• How many units to order?
• when to order? discount
Types of Inventories
Raw materials

Purchased parts and supplies
Finished Goods
Work-in-process (partially completed products )
Items being transported
Tools and equipment
Nature of Inventories
Raw Materials – Basic inputs that are converted into finished product
through the manufacturing process
Work-in-progress – Semi-manufactured products need some more works
before they become finished goods for sale
Finished Goods – Completely manufactured products ready for sale
Supplies – Office and plant materials not directly enter production but are
necessary for production process and do not involve significant investment.
Inventory and Supply Chain Management
Bullwhip effect

• demand information is distorted as it moves away from
the end-use customer(forecast)
• higher safety stock inventories are stored to
compensate

Seasonal or cyclical demand
Sale of umbrella , dominos sale in weekend

Inventory provides independence from vendors
Take advantage of price discounts
Inventory provides independence between stages and avoids work stoppages
WIP inventories
Two Forms of Demand

Dependent
(not used by customer directly)

• Demand for items used to
produce final products
• Tires stored at a plant are
an example of a dependent
demand item

Independent
• Demand for items used by
external customers
• Cars, computers, and
houses are examples of
independent demand
inventory
Inventory and Quality Management

Customers usually perceive quality service as
availability of goods when they want them
Inventory must be sufficient to provide highquality customer service
Inventory Costs
Carrying cost
• cost of holding an item in inventory

Ordering cost
• cost of replenishing inventory
Shortage cost
• temporary or permanent loss of sales when
demand cannot be met
Inventory Control Systems

Continuous system
(fixed-order-quantity)

Periodic system
(fixed-time-period)

• constant amount ordered
when inventory declines
to predetermined level

• order placed for variable
amount after fixed
passage of time
Economic Order Quantity (EOQ) Models

EOQ

• We want to determine the optimal number of
units to order so that we minimize the total cost
associated with the purchase, delivery and
storage of the product.

Basic EOQ model
Production quantity model
Assumptions of Basic EOQ Model
Demand is known, constant, and independent

Lead time is known and constant
Order quantity received is instantaneous and
complete
No shortage is allowed
Inventory Order Cycle
Order quantity, Q
Inventory Level

Demand
rate

Reorder point, R

0

Lead
time
Order Order
placed receipt

Lead
time
Order Order
placed receipt

Time
EOQ Cost Model
Co - cost of placing order
Cc - annual per-unit carrying cost

D - annual demand
Q - order quantity

Annual ordering cost =

CoD
Q

Annual carrying cost =

CcQ
2

Total cost =

CoD
+
Q

CcQ
2
EOQ Cost Model
Proving equality of
costs at optimal point

Deriving Qopt

Co D
CcQ
TC =
+
Q
2
Cc
TC - CoD
=
+
Q2
2
Q

-C0D
0=
2
Q

Qopt =

Cc
+
2

2CoD
Cc

CoD
CcQ
=
Q
2
Q2

2CoD
=
Cc

Qopt =

2CoD
Cc
EOQ Cost Model (cont.)
Annual
cost ($)

Total Cost
Slope = 0
CcQ
Carrying Cost =
2

Minimum
total cost

CoD
Ordering Cost = Q

Optimal order
Qopt

Order Quantity, Q
Production Quantity Model
An inventory system in which an order is received gradually, as
inventory is simultaneously being depleted

Also known as non-instantaneous receipt model
Now replenishment not at once

Assumption
• Q is received all at once is relaxed
• p - daily rate at which an order is received over time, or
production rate
• d - daily rate at which inventory is demanded
Production Quantity Model (cont.)
p = production rate

d = demand rate

Maximum inventory level = Q - Q d
p
=Q1- d
p
Q
d
Average inventory level =
12
p
CoD CcQ
d
TC = Q + 2 1 - p

2CoD
Qopt =

d
Cc 1 p
Quantity Discounts

Price per unit decreases as order quantity
increases

CoD
CcQ
TC =
+
+ PD
Q
2

P = per unit price of the item
where
D = annual demand
Quantity Discount Model (cont.)
ORDER SIZE
0 - 99
100 – 199
200+

PRICE
$10
8 (d1)
6 (d2)

TC = ($10 )
TC (d1 = $8 )

Inventory cost ($)

TC (d2 = $6 )

Carrying cost

Ordering cost
Q(d1 ) = 100 Qopt

Q(d2 ) = 200
Reorder Point
Level of inventory at which a new order is placed

R = dL

where

• d = demand rate per period
• L = lead time
Variable Demand with a Reorder Point

Inventory level

Q

Reorder
point, R

0
LT

LT
Time
Inventory level

Reorder Point with a Safety Stock

Q
Reorder
point, R

Safety Stock

0
LT

LT

Time
Classifying Inventory Items
ABC Classification (Pareto Principle)

In any Retail organization there are large numbers of
inventories to be maintained. It is not practical to have
very stringent inventory control system for each & every
item. So with the modus of having an effective Purchase
& stores control we implement ABC Inventory
Classification model Known as Always Better Control
(ABC) based upon Pareto rule ( 80/20 rule)
ABC Analysis
Divides inventory into three classes based on
Consumption Value
Consumption Value = (Unit price of an item) (No. of units consumed per annum)



Class A - High Consumption Value



Class B - Medium Consumption Value



Class C - Low Consumption Value
ABC Analysis
Item
Stock
Number
#10286

Percent of
Number of
Items
Stocked
20%

Annual
Volume
(units)

x

Unit
Cost

Annual
Consump
= tion value

Percent of
Annual
consumpti
on value

Class

1,000

$ 90.00

$ 90,000

38.8%

#11526

500

154.00

77,000

33.2%

A

#12760

1,550

17.00

26,350

11.3%

B

72%

A

23%
#10867
#10500

30%

350

42.86

15,001

6.4%

B

1,000

12.50

12,500

5.4%

B
ABC Analysis
Item
Stock
Number

Percent of
Number of
Items
Stocked

Annual
Volume
(units)

x

Unit
Cost

=

Annual
cons.
value

Percent of
Annual
cons.
value

Class

#12572

600

$ 14.17

$ 8,502

3.7%

C

#14075

2,000

.60

1,200

.5%

C

100

8.50

850

.4%

5% C

#01307

1,200

.42

504

.2%

C

#10572

250

.60

150

.1%

C

$232,057

100.0%

#01036

50%

8,550
% of Consumption Value

ABC Analysis
A Items

80 –
70 –
60 –
50 –

40 –
30 –
20 –

B Items
C Items

10 –
|

|

|

|

|

|

|

|

10

20

30

40

50

60

70

80

% of inventory items

|

|

90 100
Inventory Management Policy
A Items:
very tight control, complete and accurate records, frequent review via EOQ model.
B Items:
less tightly controlled, good records, regular review
C Items:
simplest controls possible, minimal records, large inventories, periodic review and reorder

Some time with the view of doing Lean inventory management
Within ABC category VED ( Vital , essential & desirable factor) is introduced with the
view of further having effective control of inventory on the basis if its being critical.
V (Vital) is the inventory where neither Substitute nor Variation Gap is allowed .
E (Essential) is the inventory which allows either of the one to be changed
D (Desirable ) is the one which can have variation in both of the parameters
References:
• Cox, James F., III, and John H. Blackstone, Jr. APICS
Dictionary. 9th ed. Falls Church VA: American Production and
Inventory Control Society, 1998.
• Anupindi, Ravi, et al. Managing Business Process Flows:
Principles of Operations Management. 2nd ed. Upper Saddle
River, NJ: Pearson Prentice Hall, 2004.
• Meredith, Jack R., and Scott M. Shafer. Operations
Management for MBAs. 2nd ed. New York: John Wiley & Sons
Inc., 2002.
• Stevenson, William J. Production/Operations
Management. 8th ed. Boston: Irwin/McGraw-Hill, 2005.
Thank You

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Inventory management

  • 2. Outline Elements of Inventory Management Inventory and Supply Chain Management Inventory Control Systems Economic Order Quantity Models Reorder Point Classification of Inventories: ABC, VED
  • 3. What is inventory? A physical resource that a firm holds in stock with the intent of selling it or transforming it into a more valuable state. Purpose of inventory management • How many units to order? • when to order? discount
  • 4. Types of Inventories Raw materials Purchased parts and supplies Finished Goods Work-in-process (partially completed products ) Items being transported Tools and equipment
  • 5. Nature of Inventories Raw Materials – Basic inputs that are converted into finished product through the manufacturing process Work-in-progress – Semi-manufactured products need some more works before they become finished goods for sale Finished Goods – Completely manufactured products ready for sale Supplies – Office and plant materials not directly enter production but are necessary for production process and do not involve significant investment.
  • 6. Inventory and Supply Chain Management Bullwhip effect • demand information is distorted as it moves away from the end-use customer(forecast) • higher safety stock inventories are stored to compensate Seasonal or cyclical demand Sale of umbrella , dominos sale in weekend Inventory provides independence from vendors Take advantage of price discounts Inventory provides independence between stages and avoids work stoppages WIP inventories
  • 7. Two Forms of Demand Dependent (not used by customer directly) • Demand for items used to produce final products • Tires stored at a plant are an example of a dependent demand item Independent • Demand for items used by external customers • Cars, computers, and houses are examples of independent demand inventory
  • 8. Inventory and Quality Management Customers usually perceive quality service as availability of goods when they want them Inventory must be sufficient to provide highquality customer service
  • 9. Inventory Costs Carrying cost • cost of holding an item in inventory Ordering cost • cost of replenishing inventory Shortage cost • temporary or permanent loss of sales when demand cannot be met
  • 10. Inventory Control Systems Continuous system (fixed-order-quantity) Periodic system (fixed-time-period) • constant amount ordered when inventory declines to predetermined level • order placed for variable amount after fixed passage of time
  • 11. Economic Order Quantity (EOQ) Models EOQ • We want to determine the optimal number of units to order so that we minimize the total cost associated with the purchase, delivery and storage of the product. Basic EOQ model Production quantity model
  • 12. Assumptions of Basic EOQ Model Demand is known, constant, and independent Lead time is known and constant Order quantity received is instantaneous and complete No shortage is allowed
  • 13. Inventory Order Cycle Order quantity, Q Inventory Level Demand rate Reorder point, R 0 Lead time Order Order placed receipt Lead time Order Order placed receipt Time
  • 14. EOQ Cost Model Co - cost of placing order Cc - annual per-unit carrying cost D - annual demand Q - order quantity Annual ordering cost = CoD Q Annual carrying cost = CcQ 2 Total cost = CoD + Q CcQ 2
  • 15. EOQ Cost Model Proving equality of costs at optimal point Deriving Qopt Co D CcQ TC = + Q 2 Cc TC - CoD = + Q2 2 Q -C0D 0= 2 Q Qopt = Cc + 2 2CoD Cc CoD CcQ = Q 2 Q2 2CoD = Cc Qopt = 2CoD Cc
  • 16. EOQ Cost Model (cont.) Annual cost ($) Total Cost Slope = 0 CcQ Carrying Cost = 2 Minimum total cost CoD Ordering Cost = Q Optimal order Qopt Order Quantity, Q
  • 17. Production Quantity Model An inventory system in which an order is received gradually, as inventory is simultaneously being depleted Also known as non-instantaneous receipt model Now replenishment not at once Assumption • Q is received all at once is relaxed • p - daily rate at which an order is received over time, or production rate • d - daily rate at which inventory is demanded
  • 18. Production Quantity Model (cont.) p = production rate d = demand rate Maximum inventory level = Q - Q d p =Q1- d p Q d Average inventory level = 12 p CoD CcQ d TC = Q + 2 1 - p 2CoD Qopt = d Cc 1 p
  • 19. Quantity Discounts Price per unit decreases as order quantity increases CoD CcQ TC = + + PD Q 2 P = per unit price of the item where D = annual demand
  • 20. Quantity Discount Model (cont.) ORDER SIZE 0 - 99 100 – 199 200+ PRICE $10 8 (d1) 6 (d2) TC = ($10 ) TC (d1 = $8 ) Inventory cost ($) TC (d2 = $6 ) Carrying cost Ordering cost Q(d1 ) = 100 Qopt Q(d2 ) = 200
  • 21. Reorder Point Level of inventory at which a new order is placed R = dL where • d = demand rate per period • L = lead time
  • 22. Variable Demand with a Reorder Point Inventory level Q Reorder point, R 0 LT LT Time
  • 23. Inventory level Reorder Point with a Safety Stock Q Reorder point, R Safety Stock 0 LT LT Time
  • 24. Classifying Inventory Items ABC Classification (Pareto Principle) In any Retail organization there are large numbers of inventories to be maintained. It is not practical to have very stringent inventory control system for each & every item. So with the modus of having an effective Purchase & stores control we implement ABC Inventory Classification model Known as Always Better Control (ABC) based upon Pareto rule ( 80/20 rule)
  • 25. ABC Analysis Divides inventory into three classes based on Consumption Value Consumption Value = (Unit price of an item) (No. of units consumed per annum)  Class A - High Consumption Value  Class B - Medium Consumption Value  Class C - Low Consumption Value
  • 26. ABC Analysis Item Stock Number #10286 Percent of Number of Items Stocked 20% Annual Volume (units) x Unit Cost Annual Consump = tion value Percent of Annual consumpti on value Class 1,000 $ 90.00 $ 90,000 38.8% #11526 500 154.00 77,000 33.2% A #12760 1,550 17.00 26,350 11.3% B 72% A 23% #10867 #10500 30% 350 42.86 15,001 6.4% B 1,000 12.50 12,500 5.4% B
  • 27. ABC Analysis Item Stock Number Percent of Number of Items Stocked Annual Volume (units) x Unit Cost = Annual cons. value Percent of Annual cons. value Class #12572 600 $ 14.17 $ 8,502 3.7% C #14075 2,000 .60 1,200 .5% C 100 8.50 850 .4% 5% C #01307 1,200 .42 504 .2% C #10572 250 .60 150 .1% C $232,057 100.0% #01036 50% 8,550
  • 28. % of Consumption Value ABC Analysis A Items 80 – 70 – 60 – 50 – 40 – 30 – 20 – B Items C Items 10 – | | | | | | | | 10 20 30 40 50 60 70 80 % of inventory items | | 90 100
  • 29. Inventory Management Policy A Items: very tight control, complete and accurate records, frequent review via EOQ model. B Items: less tightly controlled, good records, regular review C Items: simplest controls possible, minimal records, large inventories, periodic review and reorder Some time with the view of doing Lean inventory management Within ABC category VED ( Vital , essential & desirable factor) is introduced with the view of further having effective control of inventory on the basis if its being critical. V (Vital) is the inventory where neither Substitute nor Variation Gap is allowed . E (Essential) is the inventory which allows either of the one to be changed D (Desirable ) is the one which can have variation in both of the parameters
  • 30. References: • Cox, James F., III, and John H. Blackstone, Jr. APICS Dictionary. 9th ed. Falls Church VA: American Production and Inventory Control Society, 1998. • Anupindi, Ravi, et al. Managing Business Process Flows: Principles of Operations Management. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2004. • Meredith, Jack R., and Scott M. Shafer. Operations Management for MBAs. 2nd ed. New York: John Wiley & Sons Inc., 2002. • Stevenson, William J. Production/Operations Management. 8th ed. Boston: Irwin/McGraw-Hill, 2005.