This document discusses inventory management concepts including reorder point, safety stock, economic order quantity (EOQ) models, ABC classification, and quantity discounts. It provides information on inventory control systems, types of inventory, inventory costs, and supply chain management. Various EOQ models are presented including the basic EOQ model and a production quantity model. Examples are provided to illustrate key concepts.

1. Chapter 13
Inventory Management

2. Lecture Outline
• Elements of Inventory Management
• Inventory Control Systems
• Economic Order Quantity Models
• Quantity Discounts
• Reorder Point
• Order Quantity for a Periodic Inventory System
Copyright 2011 John Wiley & Sons, Inc. 13-2

3. What Is Inventory?
• Stock of items kept to meet future demand
• Purpose of inventory management
• how many units to order
• when to order
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4. Supply Chain Management
• Bullwhip effect
• demand information is distorted as it moves away
from the end-use customer
• higher safety stock inventories to are stored to
compensate
• Seasonal or cyclical demand
• Inventory provides independence from vendors
• Take advantage of price discounts
• Inventory provides independence between
stages and avoids work stoppages
Copyright 2011 John Wiley & Sons, Inc. 13-4

5. Quality Management in the Supply Chain
• Customers usually perceive quality service as
availability of goods they want when they want
them
• Inventory must be sufficient to provide high-
quality customer service in QM
Copyright 2011 John Wiley & Sons, Inc. 13-5

6. Types of Inventory
• Raw materials
• Purchased parts and supplies
• Work-in-process (partially completed) products
(WIP)
• Items being transported
• Tools and equipment
Copyright 2011 John Wiley & Sons, Inc. 13-6

7. Two Forms of Demand
• Dependent
• Demand for items used to produce final
products
• Tires for autos are a dependent demand item
• Independent
• Demand for items used by external customers
• Cars, appliances, computers, and houses are
examples of independent demand inventory
Copyright 2011 John Wiley & Sons, Inc. 13-7

8. 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
Copyright 2011 John Wiley & Sons, Inc. 13-8

9. Inventory Control Systems
• Continuous system (fixed-order-quantity)
• constant amount ordered when inventory declines to
predetermined level
• Periodic system (fixed-time-period)
• order placed for variable amount after fixed passage
of time
Copyright 2011 John Wiley & Sons, Inc. 13-9

10. ABC Classification
• Class A
• 5 – 15 % of units
• 70 – 80 % of value
• Class B
• 30 % of units
• 15 % of value
• Class C
• 50 – 60 % of units
• 5 – 10 % of value
Copyright 2011 John Wiley & Sons, Inc. 13-10

11. ABC Classification
PART UNIT COST ANNUAL USAGE
1 $ 60 90
2 350 40
3 30 130
4 80 60
5 30 100
6 20 180
7 10 170
8 320 50
9 510 60
10 20 120
Copyright 2011 John Wiley & Sons, Inc. 13-11

12. ABC Classification
TOTAL % OF TOTAL % OF TOTAL
PART VALUE VALUE QUANTITY % CUMMULATIVE
9 $30,600 35.9 6.0 6.0
8 16,000 18.7 5.0 11.0
2 14,000 16.4 4.0
A 15.0
1 5,400 6.3 9.0 24.0
4 4,800 5.6 6.0 B 30.0
3 3,900 4.6 10.0 40.0
6 3,600 4.2 18.0 58.0
5 3,000 3.5 13.0 71.0
10 2,400 2.8 12.0 C 83.0
7 1,700 2.0 17.0 100.0
$85,400
Example 10.1
Copyright 2011 John Wiley & Sons, Inc. 13-12

13. ABC Classification
% OF TOTAL % OF TOTAL
CLASS ITEMS VALUE QUANTITY
A 9, 8, 2 71.0 15.0
B 1, 4, 3 16.5 25.0
C 6, 5, 10, 7 12.5 60.0
Example 10.1
Copyright 2011 John Wiley & Sons, Inc. 13-13

14. Economic Order Quantity
(EOQ) Models
• EOQ
• optimal order quantity that will minimize
total inventory costs
• Basic EOQ model
• Production quantity model
Copyright 2011 John Wiley & Sons, Inc. 13-14

15. Assumptions of Basic EOQ Model
• Demand is known with certainty and is constant
over time
• No shortages are allowed
• Lead time for the receipt of orders is constant
• Order quantity is received all at once
Copyright 2011 John Wiley & Sons, Inc. 13-15

16. Inventory Order Cycle
Order quantity, Q
Demand Average
rate inventory
Inventory Level
Q
2
Reorder point, R
0 Lead Lead Time
time time
Order Order Order Order
placed receipt placed receipt
Copyright 2011 John Wiley & Sons, Inc. 13-16

17. EOQ Cost Model
Co - cost of placing order D - annual demand
Cc - annual per-unit carrying cost Q - order quantity
Co D
Annual ordering cost =
Q
CcQ
Annual carrying cost =
2
CoD CcQ
Total cost = +
Q 2
Copyright 2011 John Wiley & Sons, Inc. 13-17

18. EOQ Cost Model
Deriving Qopt Proving equality of
costs at optimal point
CoD CcQ
TC = +
Q 2 CoD CcQ
=
TC CoD Cc Q 2
= – Q2 +
Q 2
2CoD
C0D Cc Q2 =
Cc
0 = – Q2 +
2
2CoD
2CoD Qopt =
Qopt = Cc
Cc
Copyright 2011 John Wiley & Sons, Inc. 13-18

19. EOQ Cost Model
Annual
cost ($) Total Cost
Slope = 0
CcQ
Minimum Carrying Cost =
2
total cost
CoD
Ordering Cost = Q
Optimal order Order Quantity, Q
Qopt
Copyright 2011 John Wiley & Sons, Inc. 13-19

20. EOQ Example
Cc = $0.75 per gallon Co = $150 D = 10,000 gallons
2CoD CoD CcQ
Qopt = TCmin = +
Cc Q 2
2(150)(10,000) (150)(10,000) (0.75)(2,000)
Qopt = (0.75) TCmin = 2,000 + 2
Qopt = 2,000 gallons TCmin = $750 + $750 = $1,500
Orders per year = D/Qopt Order cycle time = 311 days/(D/Qopt)
= 10,000/2,000 = 311/5
= 5 orders/year = 62.2 store days
Copyright 2011 John Wiley & Sons, Inc. 13-20

21. Production Quantity Model
• Order is received gradually, as inventory is
simultaneously being depleted
• AKA non-instantaneous receipt model
• assumption that Q is received all at once is relaxed
• p - daily rate at which an order is received over
time, a.k.a. production rate
• d - daily rate at which inventory is demanded
Copyright 2011 John Wiley & Sons, Inc. 13-21

22. Production Quantity Model
Inventory
level
Maximum
Q(1-d/p) inventory
level
Average
Q inventory
(1-d/p)
2 level
0
Begin End Time
order order
Order
receipt receipt
receipt period
Copyright 2011 John Wiley & Sons, Inc. 13-22

23. Production Quantity Model
p = production rate d = demand rate
Maximum inventory level = Q - Q d
p
=Q1- d 2CoD
p
Qopt = d
Q d Cc 1 -
Average inventory level = 1- p
2 p
CoD CcQ d
TC = Q + 2 1 - p
Copyright 2011 John Wiley & Sons, Inc. 13-23

24. Production Quantity Model
Cc = $0.75 per gallon Co = $150 D = 10,000 gallons
d = 10,000/311 = 32.2 gallons per day p = 150 gallons per day
2CoD 2(150)(10,000)
Qopt = = = 2,256.8 gallons
Cc 1 - d 0.75 1 -
32.2
p 150
CoD CcQ d
TC = Q + 2 1 - p = $1,329
Q 2,256.8
Production run = = = 15.05 days per order
p 150
Copyright 2011 John Wiley & Sons, Inc. 13-24

25. Production Quantity Model
D 10,000
Number of production runs = = = 4.43 runs/year
Q 2,256.8
d 32.2
Maximum inventory level = Q 1 - = 2,256.8 1 -
p 150
= 1,772 gallons
Copyright 2011 John Wiley & Sons, Inc. 13-25

26. Solution of EOQ Models With Excel
The optimal order
size, Q, in cell D8
Copyright 2011 John Wiley & Sons, Inc. 13-26

27. Solution of EOQ Models With Excel
The formula for Q
in cell D10
=(D4*D5/D10)+(D3*D10/2)*(1-(D7/D8))
=D10*(1-(D7/D8))
Copyright 2011 John Wiley & Sons, Inc. 13-27

28. Solution of EOQ Models With OM Tools
Copyright 2011 John Wiley & Sons, Inc. 13-28

29. Quantity Discounts
Price per unit decreases as order
quantity increases
CoD CcQ
TC = + + PD
Q 2
where
P = per unit price of the item
D = annual demand
Copyright 2011 John Wiley & Sons, Inc. 13-29

30. Quantity Discount Model
ORDER SIZE PRICE
0 - 99 $10 TC = ($10 )
100 – 199 8 (d1)
200+ 6 (d2) TC (d1 = $8 )
TC (d2 = $6 )
Inventory cost ($)
Carrying cost
Ordering cost
Q(d1 ) = 100 Qopt Q(d2 ) = 200
Copyright 2011 John Wiley & Sons, Inc. 13-30

31. Quantity Discount
QUANTITY PRICE
Co = $2,500
1 - 49 $1,400 Cc = $190 per TV
50 - 89 1,100 D = 200 TVs per year
90+ 900
2CoD 2(2500)(200)
Qopt = = = 72.5 TVs
Cc 190
For Q = 72.5 CoD CcQopt
TC = + 2 + PD = $233,784
Qopt
For Q = 90 Co D CcQ
TC = + 2 + PD = $194,105
Q
Copyright 2011 John Wiley & Sons, Inc. 13-31

32. Quantity Discount Model With Excel
=IF(D10>B10,D10,B10) =(D4*D5/E10)+(D3*E10/2)+C10*D5
Copyright 2011 John Wiley & Sons, Inc. 13-32

33. Reorder Point
• Inventory level at which a new order is placed
R = dL
where
d = demand rate per period
L = lead time
Copyright 2011 John Wiley & Sons, Inc. 13-33

34. Reorder Point
Demand = 10,000 gallons/year
Store open 311 days/year
Daily demand = 10,000 / 311 = 32.154
gallons/day
Lead time = L = 10 days
R = dL = (32.154)(10) = 321.54 gallons
Copyright 2011 John Wiley & Sons, Inc. 13-34

35. Safety Stock
• Safety stock
• buffer added to on hand inventory during lead time
• Stockout
• an inventory shortage
• Service level
• probability that the inventory available during lead
time will meet demand
• P(Demand during lead time <= Reorder Point)
Copyright 2011 John Wiley & Sons, Inc. 13-35

36. Variable Demand With Reorder Point
Q
Inventory level
Reorder
point, R
0
LT LT
Time
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37. Reorder Point With Safety Stock
Inventory level
Q
Reorder
point, R
Safety Stock
0
LT LT
Time
Copyright 2011 John Wiley & Sons, Inc. 13-37

38. Reorder Point With Variable Demand
R = dL + z d L
where
d = average daily demand
L = lead time
d = the standard deviation of daily demand
z = number of standard deviations
corresponding to the service level
probability
z d L = safety stock
Copyright 2011 John Wiley & Sons, Inc. 13-38

39. Reorder Point For a Service Level
Probability of
meeting demand during
lead time = service level
Probability of
a stockout
Safety stock
z d L
dL R
Demand
Copyright 2011 John Wiley & Sons, Inc. 13-39

40. Reorder Point For Variable Demand
The paint store wants a reorder point with a 95%
service level and a 5% stockout probability
d = 30 gallons per day
L = 10 days
d = 5 gallons per day
For a 95% service level, z = 1.65
R = dL + z d L Safety stock = z d L
= 30(10) + (1.65)(5)( 10) = (1.65)(5)( 10)
= 326.1 gallons = 26.1 gallons
Copyright 2011 John Wiley & Sons, Inc. 13-40

41. Determining Reorder Point with Excel
The reorder point
formula in cell E7
Copyright 2011 John Wiley & Sons, Inc. 13-41

42. Order Quantity for a
Periodic Inventory System
Q = d(tb + L) + z d tb + L - I
where
d = average demand rate
tb = the fixed time between orders
L = lead time
d = standard deviation of demand
z d tb + L = safety stock
I = inventory level
Copyright 2011 John Wiley & Sons, Inc. 13-42

43. Periodic Inventory System
Copyright 2011 John Wiley & Sons, Inc. 13-43

44. Fixed-Period Model With
Variable Demand
d = 6 packages per day
d = 1.2 packages
tb = 60 days
L = 5 days
I = 8 packages
z = 1.65 (for a 95% service level)
Q = d(tb + L) + z d tb + L - I
= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8
= 397.96 packages
Copyright 2011 John Wiley & Sons, Inc. 13-44

45. Fixed-Period Model with Excel
Formula for order
size, Q, in cell D10
Copyright 2011 John Wiley & Sons, Inc. 13-45

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