This document discusses key concepts in inventory management. It covers the purpose of inventory, types of inventory, inventory control systems, economic order quantity models, reorder points, safety stocks, and models for periodic inventory systems. The economic order quantity model is introduced as a way to determine the optimal order quantity to minimize total inventory costs. Reorder point and safety stock concepts are explained for handling variable demand within a periodic inventory system. Examples are provided to illustrate how to apply these inventory management models.

6. Inventory Management
Chapter 13

7. 





Elements of Inventory Management
Inventory Control Systems
Economic Order Quantity Models
Quantity Discounts
Reorder Point
Order Quantity
System
for a Periodic Inventory
Copyright 2006 John Wiley & Sons, Inc. 12-2
Lecture Outline

8.  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. 12-3
What Is Inventory?

9. 


Raw materials
Purchased parts and supplies
Work-in-process (partially
products (WIP)
Items being transported
Tools and equipment
completed)


Copyright 2006 John Wiley & Sons, Inc. 12-4
Types of Inventory

10. Inventory and Supply Chain
 Bullwhip effect
demand information is distorted
from the end-use customer
as it moves away

higher safety stock inventories to are stored
compensate
Seasonal or cyclical demand
to





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. 12-5
Inventory and Supply
Management

11.  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. 12-7
Inventory and Quality
Management

12.  Carrying cost
 cost of holding an item in inventory
 Ordering cost
 cost of replenishing inventory
 Shortage cost
 temporary or permanent loss of
when demand cannot be met
sales
Copyright 2006 John Wiley & Sons, Inc. 12-8
Inventory Costs

13. Inventory Control Systems
 Continuous system (fixed-
order-quantity)
 constant amount ordered
when inventory declines to
predetermined level
 Periodic system (fixed-time-
period)
 order place
amount after fixed passage of
time
Copyright 2006 John Wiley & Sons, Inc. 12-9
d for variable
Inventory Control Syst

14. Economic Order Quantity
 EOQ
optimal order quantity that will
minimize total inventory costs
Basic EOQ model


 Production quantity model
Copyright 2006 John Wiley & Sons, Inc. 12-13
Economic Order Quant
(EOQ) Models

15.  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. 12-14
Assumptions of Basic
EOQ Model

16. time time
placed receipt placed receipt
Copyright 2006 John Wiley & Sons, Inc. 12-15
Inventory
Level
Demand
Inventory Order Cycle
Order quantity, Q
rate
Reorder point, R
0 Lead Lead Time
Order Order Order Order

17. Annual ordering cost =
Annual carrying cost =
Total cost = +
Copyright 2006 John Wiley & Sons, Inc. 12-16
EOQ Cost Model
Co - cost of placing order D - annual demand
Cc - annual per-unit carrying cost Q - order quantity
CoD
Q
CcQ
2
CoD CcQ
Q 2

18. costs at optimal point
TC = +
=
= +
o
Q2 =
c
Q2
2
Qopt =
Cc
Copyright 2006 John Wiley & Sons, Inc. 12-17
Deriving Qopt
CoD CcQ
Q 2
TC CoD Cc
Q Q2
2
C0D Cc
0 = +
2CoD
Qopt =
Proving equality of
CoD CcQ
Q 2
2C D
C
2CoD
Cc
EOQ Cost Model

19. cost ($)
Minimum 2
Qopt
Copyright 2006 John Wiley & Sons, Inc. 12-18
Total Cost
Carrying Cost =
Ordering Cost =
EOQ Cost Model (cont.)
Annual
Slope = 0
CcQ
total cost
CoD
Q
Optimal order Order Quantity, Q

20. Qopt = TCmin = +
Qopt = TCmin = +
(0.75) 2,000 2
Copyright 2006 John Wiley & Sons, Inc. 12-19
EOQ Example
Cc = $0.75 per yard Co = $150 D = 10,000 yards
2CoD CoD CcQ
Cc Q 2
2(150)(10,000) (150)(10,000) (0.75)(2,000)
Qopt = 2,000 yards 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

21.  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. 12-20
Production Quantity
Model

22. Q
inventory
(1-d/p)
receipt receipt
receipt period
Copyright 2006 John Wiley & Sons, Inc. 12-21
invent
Production Quantity Model
(cont.)
Inventory
level
Maximum
Q(1-d/p)
inventory
level
Average
2 level
0
Begin End Time
Order order order

23. Production Quantity Model
p
p o
Q d C 1 -
Average inventory level = 1 -
TC = + 1 - p
Q 2
Copyright 2006 John Wiley & Sons, Inc. 12-22
p = production rate d = demand rate
Maximum inventory level = Q -
Q
d
= Q 1 -
d
2C D
Qopt = d
2 p c p
CoD CcQ d
Production Quantity
(cont.)

24. Production Quantity Model:
2CoD 2(150)(10,000)
Qopt = = = 2,256.8 yards
32.2
d
Cc 1 - 0.75 1 -
150
p
CoD
Q
CcQ
2
d
TC = + 1 - = $1,329
p
2,256.8
150
Q
p
Production run = = = 15.05 days per order
Copyright 2006 John Wiley & Sons, Inc. 12-23
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
Production Quantity M
Example

25. Production Quantity Model:
2,256.8
Q
p 150
Copyright 2006 John Wiley & Sons, Inc. 12-24
Number of production runs =
D
=
10,000
= 4.43 runs/year
Maximum inventory level = Q 1 -
d
= 2,256.8 1 - 32.2
= 1,772 yards
Production Quantity
Example (cont.)

26. Price per unit decreases
quantity increases
as order
CoD
Q
CcQ
2
TC = + + PD
where
P = per unit price of the item
D = annual demand
Copyright 2006 John Wiley & Sons, Inc. 12-25
Quantity Discounts

27. TC (d1 =$8 )
Copyright 2006 John Wiley & Sons, Inc. 12-26
Inventory
cost
($)
ORDERSIZE PRICE
200+ 6 (d )
Quantity Discount Model (cont.)
0 - 99 $10 TC = ($10 )
100 – 199 8 (d1)
2
TC (d2 = $6 )
Carrying cost
Ordering cost
Q(d1 ) = 100 Qopt Q(d2 ) = 200

28. Co = $2,500
$190 per computer
200
Cc
D
=
=
90+ 900
Qopt = = = 72.5 PCs
CcQopt
CoD
2
Qopt
CcQ
CoD
2
Q
Copyright 2006 John Wiley & Sons, Inc. 12-27
Quantity Discount: Example
QUANTITY PRICE
1 - 49 $1,400
50 - 89 1,100
2CoD 2(2500)(200)
Cc
190
For Q = 72.5
TC = + + PD = $233,784
For Q = 90
TC = + + PD = $194,105

29. Level of inventory at which a new order
is placed
R = dL
where
d =
L =
demand rate
lead time
per period
Copyright 2006 John Wiley & Sons, Inc. 12-28
Reorder Point

30. 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
= 32.154
R = dL = (32.154)(10) = 321.54 yards
Copyright 2006 John Wiley & Sons, Inc. 12-29
Reorder Point: Ex

31.  Safety stock
 buffer added to on hand inventory during lead
time
 Stockout
 an inventory shortage
 Service level
 probability that the inventory
lead time will meet demand
available during
Copyright 2006 John Wiley & Sons, Inc. 12-30
Safety Stocks

32. t, R
R
0
Copyright 2006 John Wiley & Sons, Inc. 12-31
Inventory
level
Variable Demand with
a Reorder Point
Reo
poin
n
Q
rder
LT LT
Time

33. Safety Stock
0
Copyright 2006 John Wiley & Sons, Inc. 12-32
Inventory
level Reorder Point with
a Safety Stock
Reorder
point, R
Q
LT LT
Time

34. R = dL + z L
d
where
d
L
d
z
=
=
=
=
average daily demand
lead time
the standard deviation of daily demand
number of standard deviations
corresponding to the service level
probability
safety stock
z L =
d
Copyright 2006 John Wiley & Sons, Inc. 12-33
Reorder Point With
Variable Demand

35. Copyright 2006 John Wiley & Sons, Inc. 12-35
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 Safety stock = z d L
= 30(10) + (1.65)(5)( 10) = (1.65)(5)( 10)
= 326.1 yards = 26.1 yards
Reorder Point for
Variable Demand

36. Periodic Inventory System
Copyright 2006 John Wiley & Sons, Inc. 12-36
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
Order Quantity for a
Periodic Inventory Sy

37. Fixed-Period Model with
Copyright 2006 John Wiley & Sons, Inc. 12-37
d = 6 bottles per day
d = 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) 60 + 5 - 8
= 397.96 bottles
Fixed-Period Model w
Variable Demand