1. Beni Asllani University of Tennessee at Chattanooga
Chapter 12
Inventory Management
Operations Management - 5th Edition
Roberta Russell & Bernard W. Taylor, III
Beni Asllani University of Tennessee at Chattanooga
Copyright 2006 John Wiley & Sons, Inc.

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 2006 John Wiley & Sons, Inc.

3. What Is Inventory? Stock of items kept to meet future demand
Purpose of inventory management
how many units to order
when to order
Copyright 2006 John Wiley & Sons, Inc.

4. Types of Inventory Raw materials Purchased parts and supplies
Work-in-process (partially completed) products (WIP)
Items being transported
Tools and equipment
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5. Inventory and 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 stop-pages
Copyright 2006 John Wiley & Sons, Inc.

6. Two Forms of Demand Dependent Independent
Demand for items used to produce final products
Tires stored at a Goodyear plant are an example of a dependent demand item
Independent
Demand for items used by external customers
Cars, appliances, computers, and houses are examples of independent demand inventory
Copyright 2006 John Wiley & Sons, Inc.

7. Inventory and Quality Management
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 TQM
Copyright 2006 John Wiley & Sons, Inc.

8. Inventory Costs Carrying cost Ordering cost Shortage 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 2006 John Wiley & Sons, Inc.

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 2006 John Wiley & Sons, Inc.

10. ABC Classification Class A Class B Class C 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
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11. ABC Classification: Example
1 $ 60 90
PART UNIT COST ANNUAL USAGE
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12. ABC Classification: Example (cont.)
1 $ 60 90
PART UNIT COST ANNUAL USAGE
TOTAL % OF TOTAL % OF TOTAL
PART VALUE VALUE QUANTITY % CUMMULATIVE
9 $30,
8 16,
2 14,
1 5,
4 4,
3 3,
6 3,
5 3,
10 2,
7 1,
$85,400 A B C
% OF TOTAL % OF TOTAL
CLASS ITEMS VALUE QUANTITY
A 9, 8,
B 1, 4,
C 6, 5, 10,
Example 10.1
Copyright 2006 John Wiley & Sons, Inc.

13. Economic Order Quantity (EOQ) Models
optimal order quantity that will minimize total inventory costs
Basic EOQ model
Production quantity model
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14. 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 2006 John Wiley & Sons, Inc.

15. Inventory Order Cycle Demand rate Time Lead time Order placed
Order receipt
Inventory Level
Reorder point, R
Order quantity, Q
Copyright 2006 John Wiley & Sons, Inc.

16. EOQ Cost Model Co - cost of placing order D - annual demand
Cc - annual per-unit carrying cost Q - order quantity
Annual ordering cost =
CoD Q
Annual carrying cost =
CcQ 2
Total cost =
Copyright 2006 John Wiley & Sons, Inc.

17. EOQ Cost Model TC = + CoD Q CcQ 2 = + Q2 Cc TC Q 0 = + C0D Qopt == Q2 Cc
TC Q
0 =
C0D
Qopt =
2CoD
Deriving Qopt
Proving equality of costs at optimal point =
CoD Q
CcQ 2
Q2 =
2CoD Cc
Qopt =
Copyright 2006 John Wiley & Sons, Inc.

18. EOQ Cost Model (cont.) Order Quantity, Q Annual cost ($) Total Cost
Ordering Cost =
CoD Q
Slope = 0
Minimum total cost
Optimal order
Qopt
Carrying Cost =
CcQ 2
Copyright 2006 John Wiley & Sons, Inc.

19. EOQ Example Cc = $0.75 per yard Co = $150 D = 10,000 yards Qopt = 2CoD
2(150)(10,000)
(0.75)
Qopt = 2,000 yards
TCmin =
CoD Q
CcQ 2
TCmin =
(150)(10,000)
2,000
(0.75)(2,000)
TCmin = $750 + $750 = $1,500
Orders per year = D/Qopt
= 10,000/2,000
= 5 orders/year
Order cycle time = 311 days/(D/Qopt)
= 311/5
= 62.2 store days
Copyright 2006 John Wiley & Sons, Inc.

20. Production Quantity Model
An inventory system in which an 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 2006 John Wiley & Sons, Inc.

21. Production Quantity Model (cont.)
Q(1-d/p)
Inventory
level
(1-d/p) Q 2
Time
Order
receipt period
Begin
order
receipt
End
Maximum
inventory level
Average
Copyright 2006 John Wiley & Sons, Inc.

22. Production Quantity Model (cont.)
p = production rate d = demand rate
Maximum inventory level = Q d
= Q 1 - Q p d
Average inventory level = 2
TC =
CoD
CcQ
Qopt =
2CoD
Cc 1 -
Copyright 2006 John Wiley & Sons, Inc.

23. Production Quantity Model: Example
Cc = $0.75 per yard Co = $150 D = 10,000 yards
d = 10,000/311 = 32.2 yards per day p = 150 yards per day
Qopt = = = 2,256.8 yards
2CoD
Cc 1 - d p
2(150)(10,000)
32.2
150
TC = = $1,329 d p
CoD Q
CcQ 2
Production run = = = days per order Q p
2,256.8
150
Copyright 2006 John Wiley & Sons, Inc.

24. Production Quantity Model: Example (cont.)
Number of production runs = = = 4.43 runs/year D Q
10,000
2,256.8
Maximum inventory level = Q = 2,
= 1,772 yards d p
32.2
150
Copyright 2006 John Wiley & Sons, Inc.

25. P = per unit price of the item
Quantity Discounts
Price per unit decreases as order quantity increases
TC = PD
CoD Q
CcQ 2
where
P = per unit price of the item
D = annual demand
Copyright 2006 John Wiley & Sons, Inc.

26. Quantity Discount Model (cont.)
Qopt
Carrying cost
Ordering cost
Inventory cost ($)
Q(d1 ) = 100
Q(d2 ) = 200
TC (d2 = $6 )
TC (d1 = $8 )
TC = ($10 )
ORDER SIZE PRICE
$10
100 – (d1)
(d2)
Copyright 2006 John Wiley & Sons, Inc.

27. Quantity Discount: Example
QUANTITY PRICE
$1,400
,100
Co = $2,500
Cc = $190 per computer
D = 200
Qopt = = = 72.5 PCs
2CoD Cc
2(2500)(200)
190
TC = PD = $233,784
CoD
Qopt
CcQopt 2
For Q = 72.5
TC = PD = $194,105
CoD Q
CcQ 2
For Q = 90
Copyright 2006 John Wiley & Sons, Inc.

28. Reorder Point Level of inventory at which a new order is placed R = dL
where
d = demand rate per period
L = lead time
Copyright 2006 John Wiley & Sons, Inc.

29. Reorder Point: Example
Demand = 10,000 yards/year
Store open 311 days/year
Daily demand = 10,000 / 311 = yards/day
Lead time = L = 10 days
R = dL = (32.154)(10) = yards
Copyright 2006 John Wiley & Sons, Inc.

30. Safety Stocks Safety stock Stockout Service level
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
Copyright 2006 John Wiley & Sons, Inc.

31. Variable Demand with a Reorder Point
point, R Q LT
Time
Inventory level
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32. Reorder Point with a Safety Stock
point, R Q LT
Time
Inventory level
Safety Stock
Copyright 2006 John Wiley & Sons, Inc.

33. 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 2006 John Wiley & Sons, Inc.

34. Reorder Point for a Service Level
Probability of
meeting demand during
lead time = service level
a stockout R
Safety stock dL
Demand
zd L
Copyright 2006 John Wiley & Sons, Inc.

35. Reorder Point for Variable Demand
The carpet store wants a reorder point with a 95% service level and a 5% stockout probability
d = 30 yards per day
L = 10 days
d = 5 yards per day
For a 95% service level, z = 1.65
R = dL + z d L
= 30(10) + (1.65)(5)( 10)
= yards
Safety stock = z d L
= (1.65)(5)( 10)
= 26.1 yards
Copyright 2006 John Wiley & Sons, Inc.

36. 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
sd = standard deviation of demand
zd tb + L = safety stock
I = inventory level
Copyright 2006 John Wiley & Sons, Inc.

37. Fixed-Period Model with Variable Demand
d = 6 bottles per day
sd = 1.2 bottles
tb = 60 days
L = 5 days
I = 8 bottles
z = 1.65 (for a 95% service level)
Q = d(tb + L) + zd tb + L - I
= (6)(60 + 5) + (1.65)(1.2)
= bottles
Copyright 2006 John Wiley & Sons, Inc.

38. Copyright 2006 John Wiley & Sons, Inc. All rights reserved
Copyright 2006 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein.
Copyright 2006 John Wiley & Sons, Inc.