# Chapter 10

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```					Inventory
Management

Chapter 10—Inventory Management
Learning Objectives
 Be Able To Apply Concepts Listed In
Learning Goals
 Be Able To Use Formulas Listed In
The Equation Summary of Chapter

Chapter 14—Inventory Management   1
Inventory Costs
 Interest or
Opportunity Costs
   Storage and
Handling Costs
   Taxes, Insurance, and
Shrinkage Costs
   Ordering and Setup Costs
   Transportation Costs
Chapter 10—Inventory Management
Types of Inventory
Cycle Inventory
Q+0
Average cycle inventory =
2

Chapter 10—Inventory Management
Types of Inventory
Cycle Inventory
Q
Average cycle inventory =
2

Safety Stock Inventory

Chapter 10—Inventory Management
Types of Inventory
Cycle Inventory
Q
Average cycle inventory =
2

Safety Stock Inventory
Anticipation Inventory

Chapter 10—Inventory Management
Types of Inventory
Cycle Inventory
Q
Average cycle inventory =
2

Safety Stock Inventory
Anticipation Inventory
Pipeline Inventory

Pipeline inventory = DL = dL

Chapter 10—Inventory Management
ABC Classification

 Start With Inventoried Items Ranked by
Dollar Value in Inventory in Descending
Order
 Plot Cumulative Dollar Value in Inventory
Versus Cumulative Items in Inventory
 . . . more

Chapter 14—Inventory Management   7
ABC Classification
   Typical Observations
   A Small Percentage of Items (Class A) Make up
a Large Percentage of Inventory Value
   A Large Percentage of Items (Class C) Make up
a Small Percentage of Inventory Value
   These Classifications Determine How
Much Attention Should Be Given to
Controlling Inventory of Different Items

Chapter 14—Inventory Management   8
ABC Analysis
100 —

90 —
Percentage of dollar value
80 —

70 —

60 —

50 —

40 —

30 —

20 —

10 —

0—
10   20   30   40   50   60   70   80   90 100
Percentage of items
Chapter 10—Inventory Management
ABC Analysis
Class C
100 —             Class B
90 —
Percentage of dollar value      Class A
80 —

70 —

60 —

50 —

40 —

30 —

20 —

10 —

0—
10   20   30   40   50   60   70   80   90 100
Percentage of items
Chapter 10—Inventory Management
ABC Analysis
Class C
100 —             Class B
90 —
Percentage of dollar value      Class A
80 —

70 —

60 —

50 —

40 —

30 —

20 —

10 —

0—
10   20   30   40   50   60   70   80   90 100
Percentage of items
Chapter 10—Inventory Management
How
Much?
When!

Chapter 10—Inventory Management
Economic
Order
Quantity

Chapter 10—Inventory Management
Economic Order Quantity

Assumptions
1. Demand rate is constant
2. No constraints on lot size
3. Only relevant costs are holding and
ordering/setup
4. Decisions for items are independent
from other items
5. No uncertainty in lead time or
supply
Chapter 10—Inventory Management
Economic Order Quantity
On-hand inventory (units)

Time
Chapter 10—Inventory Management
Economic Order Quantity

Receive
order
On-hand inventory (units)

Q

Time
Chapter 10—Inventory Management
Economic Order Quantity

Receive
order
On-hand inventory (units)

Q

1 cycle
Time
Chapter 10—Inventory Management
Economic Order Quantity

Receive
order
On-hand inventory (units)

Q

1 cycle
Time
Chapter 10—Inventory Management
Economic Order Quantity

Receive         Inventory depletion
order           (demand rate)
On-hand inventory (units)

Q

1 cycle
Time
Chapter 10—Inventory Management
Economic Order Quantity

Receive         Inventory depletion
order           (demand rate)
On-hand inventory (units)

Q

1 cycle
Time
Chapter 10—Inventory Management
Economic Order Quantity

Receive         Inventory depletion
order           (demand rate)
On-hand inventory (units)

Q

Q                                     Average
—                                     cycle
2
inventory

1 cycle
Time
Chapter 10—Inventory Management
Economic Order Quantity
Annual cost (dollars)

Holding cost (HC)

Lot Size (Q)
Chapter 10—Inventory Management
Economic Order Quantity
Annual cost (dollars)

Holding cost (HC)

Ordering cost (OC)

Lot Size (Q)
Chapter 10—Inventory Management
Economic Order Quantity

Total cost = HC + OC
Annual cost (dollars)

Holding cost (HC)

Ordering cost (OC)

Lot Size (Q)
Chapter 10—Inventory Management
Economic Order Quantity
Current
cost
3000 —
Q       D
Annual cost (dollars)

Total cost =     (H) +   (S)
2       Q

2000 —
Q
Holding cost =       (H)
2

1000 —
D
Ordering cost =          (S)
Q

0—       |    |        |     |      |       |         |     |
50   100      150   200    250     300       350   400
Current
Lot Size (Q)
Chapter 10—Inventory Management            Q
Economic Order Quantity
Current
cost
3000 —                              Bird feeder costs
Q      D
Annual cost (dollars)

= + Q (S)
Total cost = D(H)(18 /week)(52 weeks) = 936 units
2
H = 0.25 (\$60/unit) = \$15
2000 —
S = \$45                   Q = EOQ
Q
Holding cost =
Q         (H)
EOQ =
2DS
C=     (H) + 2 D (S)
H                 2           Q
1000 —
D
Ordering cost =          (S)
Q

0—       |    |      |       |      |       |         |     |
50   100    150     200    250     300       350   400
Current
Lot Size (Q)
Chapter 10—Inventory Management            Q
Economic Order Quantity
Current
cost
3000 —                              Bird feeder costs
Q      D
Annual cost (dollars)

= + Q (S)
Total cost = D(H)(18 /week)(52 weeks) = 936 units
2
H = 0.25 (\$60/unit) = \$15
2000 —
S = \$45                   Q = 75 units
Q
Holding cost =
Q         (H)
EOQ =
2DS
C=     (H) + 2 D (S)
H                 2           Q
1000 —
D
Ordering cost =          (S)
Q

0—       |    |      |       |      |       |         |     |
50   100    150     200    250     300       350   400
Current
Lot Size (Q)
Chapter 10—Inventory Management            Q
Economic Order Quantity
Current
cost
3000 —                              Bird feeder costs
Q      D
Annual cost (dollars)

= + Q (S)
Total cost = D(H)(18 /week)(52 weeks) = 936 units
2
H = 0.25 (\$60/unit) = \$15
2000 —
S = \$45                   Q = 75 units
Q
Holding cost =
Q         (H)
EOQ =
2DS
C=     (H) + 2 D (S)
H                 2           Q
1000 —
C = \$562 + \$562 = \$1124
D
Ordering cost =          (S)
Q

0—       |    |      |       |      |       |         |     |
50   100    150     200    250     300       350   400
Current
Lot Size (Q)
Chapter 10—Inventory Management            Q
Economic Order Quantity
Current
cost
3000 —                              Bird feeder costs
Q      D
Annual cost (dollars)

= + Q (S)
Total cost = D(H)(18 /week)(52 weeks) = 936 units
2
H = 0.25 (\$60/unit) = \$15
2000 —
S = \$45                   Q = 75 units
Q
Holding cost =
Q         (H)
EOQ =
2DS
C=     (H) + 2 D (S)
H                 2           Q
1000 —
C = \$562 + \$562 = \$1124
D
Ordering cost =          (S)
Q

0—       |    |      |       |      |       |         |     |
50   100    150     200    250     300       350   400
Current
Lot Size (Q)
Chapter 10—Inventory Management            Q
Economic Order Quantity
Current
cost
3000 —                                 Bird feeder costs
Q      D
Annual cost (dollars)

= + Q (S)
Total cost = D(H)(18 /week)(52 weeks) = 936 units
2
H = 0.25 (\$60/unit) = \$15
2000 —
S = \$45                   Q = 75 units
Q
Holding cost =
Q         (H)
EOQ =
2DS
C=     (H) + 2 D (S)
H                 2           Q
1000 —
C = \$562 + \$562 = \$1124
D
Lowest                                                                  Ordering cost =          (S)
Q
cost
0—         |     |      |       |      |       |         |     |
50    100    150     200    250     300       350   400
Best Q                                                  Current
Lot Size (Q)
(EOQ)          Chapter 10—Inventory Management            Q
Economic Order Quantity
Current
cost
3000 —                                 Bird feeder costs
Q      D
Annual cost (dollars)

= + Q (S)
Total cost = D(H)(18 /week)(52 weeks) = 936 units
2
H = 0.25 (\$60/unit) = \$15
2000 —
S = \$45                   Q = 75 units

2DS                D       Q
EOQ =                   C=        (H) +   (S)
H                 Q       2
1000 —
C = \$562 + \$562 = \$1124
Lowest
cost
0—         |     |      |       |      |       |         |     |
50    100    150     200    250     300       350   400
Best Q                                                  Current
Lot Size (Q)
(EOQ)          Chapter 10—Inventory Management            Q
Economic Order Quantity
Current
cost
3000 —                            Birdfeeder costs
Time between orders
Q      D
Annual cost (dollars)

= + Q (S)
Total cost = D(H)(18 /week)(52 weeks) = 936 units
2
= 0.25 = EOQ= 75/936
HTBO (\$60/unit) = \$15 = 0.080 year
EOQ
S = \$45        D        Q = 75 units
2000 —

2DS                D       Q
EOQ =                   C=        (H) +   (S)
H                 Q       2
1000 —
C = \$562 + \$562 = \$1124
Lowest
cost
0—         |     |      |       |      |       |         |     |
50    100    150     200    250     300       350   400
Best Q                                                  Current
Lot Size (Q)
(EOQ)          Chapter 10—Inventory Management            Q
Economic Order Quantity
Current
cost
3000 —                            Birdfeeder costs
Time between orders
Q      D
Annual cost (dollars)

= + Q (S)
Total cost = D(H)(18 /week)(52 weeks) = 936 units
2
= 0.25 = EOQ= 75/936
HTBO (\$60/unit) = \$15 = 0.080 year
EOQ
S = \$45        D        Q = 75 units
2000 —

TBOEOQ = (75/936)(12) = 0.96 months

TBOEOQ = (75/936)(52) = 4.17 weeks
1000 —
TBOEOQ = (75/936)(365) = 29.25 days
Lowest
cost
0—         |     |      |       |      |       |         |     |
50    100    150     200    250     300       350   400
Best Q                                                  Current
Lot Size (Q)
(EOQ)          Chapter 10—Inventory Management            Q
Economic Order Quantity
Current
cost
3000 —
Q       D
Annual cost (dollars)

Total cost =     (H) +   (S)
2       Q

2000 —
Q
Holding cost =       (H)
2

1000 —
D
Lowest                                                                  Ordering cost =          (S)
Q
cost
0—         |     |       |      |      |       |         |     |
50    100     150    200    250     300       350   400
Best Q                                                  Current
Lot Size (Q)
(EOQ)          Chapter 10—Inventory Management            Q
How
Much?
When!

Chapter 10—Inventory Management
Continuous Review

Order
received
On-hand inventory

Q

OH

R

Time

Chapter 10—Inventory Management
Continuous Review

IP

Order
received
On-hand inventory

Q

OH

R
Order
placed

L
TBO
Chapter 10—Inventory Management
Continuous Review

IP                     IP                   IP

Order                Order                  Order                Order
received             received               received             received
On-hand inventory

Q                     Q                     Q

OH                   OH                     OH

R
Order                 Order                  Order
placed                placed                 placed

L                      L                    L             Time
TBO                  TBO                    TBO
Chapter 10—Inventory Management
Uncertain Demand
On-hand inventory

R

Time

Chapter 10—Inventory Management
Uncertain Demand
IP
IP
Order
Order
Order             received
received
received                                 Order
On-hand inventory

received
Q
Q                     Q
OH

R
Order              Order                         Order
placed             placed                        placed

L1                    L2                        L3      Time
TBO1                  TBO2                      TBO3
Chapter 10—Inventory Management
Reorder Point / Safety Stock

Average
demand
during
lead time

Chapter 10—Inventory Management
Reorder Point / Safety Stock

Cycle-service level = 99%

Probability of stockout
(1.0 – 0.99 = 0.01)
Average
demand
during
lead time                      R

zL

Chapter 10—Inventory Management
Reorder Point / Safety Stock
Safety Stock/R
dL = 250
L = 22
Cycle-service level = 99%
SL = 99%
z = 2.33

Probability of stockout
(1.0 – 0.99 = 0.015)
Average
demand
during
lead time                       R

zL

Chapter 10—Inventory Management
Reorder Point / Safety Stock
Safety Stock/R
Safety stock   = zL
= 2.33(22) = 51.3
Cycle-service level = 99%
= 51 boxes

Probability of stockout
(1.0 – 0.99 = 0.01)
Average
demand
during
lead time                      R

zL

Chapter 10—Inventory Management
Reorder Point / Safety Stock
Safety Stock/R
Safety stock   = zL
= 2.33(22) = 51.3
Cycle-service level = 99%
= 51 boxes

Reorder point = dL + SS
= 250 + 51
= 301 boxes                      Probability of stockout
(1.0 – 0.99 = 0.01)
Average
demand
during
lead time                      R

zL

Chapter 10—Inventory Management
Lead Time Distributions
t = 15

+
75
Demand for week 1

Chapter 10—Inventory Management
Lead Time Distributions
t = 15

+
75
Demand for week 1
t = 15

+
75
Demand for week 2

Chapter 10—Inventory Management
Lead Time Distributions
t = 15

+
75
Demand for week 1
t = 15

+
75
Demand for week 2
t = 15

=
75
Demand for week 310—Inventory Management
Chapter
L  t L

Lead Time Distributions                                            L  15 3
 L  26
t = 15
L = 26

+
75
Demand for week 1
t = 15

+                               225
Demand for
75
Demand for week 2                           three-week lead time
t = 15

=
75
Demand for week 310—Inventory Management
Chapter
Lead Time Distributions
t = 15
t = 26

+       Bird feeder Lead Time Distribution
75
Demand for week 1
t
t = 15 = 1 week       d = 18       L=2
t = 5          SL = 90%

+                               225
Demand for
75
Demand for week 2                           three-week lead time
t = 15

=
75
Demand for week 310—Inventory Management
Chapter
Lead Time Distributions
t = 15
t = 26

+       Bird feeder Lead Time Distribution
75
Demand for week 1
t
t = 15 = 1 week       d = 18       L=2
t = 5          SL = 90%

+   L = t     L =5      2   = 7.1
225
Demand for
75
Demand for week 2                           three-week lead time
t = 15

=
75
Demand for week 310—Inventory Management
Chapter
Lead Time Distributions
t = 15
t = 26

+       Bird feeder Lead Time Distribution
75
Demand for week 1
t
t = 15 = 1 week       d = 18       L=2
t = 5          SL = 90%

+    L = t     L =5      2   = 7.1
225
75 Safety      stock = zL =               = 9.1 or 9
1.28(7.1)Demand for units
Demand for week 2                          three-week lead time
t = 15
Reorder point = dL + SS

=
= 2(18) + 9 = 45 units

75
Demand for week 310—Inventory Management
Chapter
Lead Time Distributions
t = 15
t = 26

+       Bird feeder Lead Time Distribution
75
Demand for week 1
t
t = 15 = 1 week  d = 18     L=2
Reorder point = 2(18) + 9 = 45 units

+                               225
Demand for
75
Demand for week 2                           three-week lead time
t = 15

=
75
Demand for week 310—Inventory Management
Chapter
Lead Time Distributions
t = 15
t = 26

+       Bird feeder Lead Time Distribution
75
Demand for week 1
t
t = 15 = 1 week  d = 18     L=2
Reorder point = 2(18) + 9 = 45 units

+
When stock drops to 45, order 75

C=
75
(\$15) +
936        225
(\$45) + 9(\$15)
Demand for
75            2          75 three-week lead time
Demand for week 2
t = 15
C = \$562.50 + \$561.60 + \$135 = \$1259.10

=
75
Demand for week 310—Inventory Management
Chapter
Periodic Review Systems
T
On-hand inventory

Time
P                      P

Chapter 10—Inventory Management
Periodic Review Systems
T
On-hand inventory

Q1

Order
placed

Time
P                      P

Chapter 10—Inventory Management
Periodic Review Systems
T
On-hand inventory

Q1

Order
placed

L                                            Time
P                      P

Chapter 10—Inventory Management
Periodic Review Systems
T
Order
received
On-hand inventory

Q1

Order
placed

L                                            Time
P                      P

Chapter 10—Inventory Management
Periodic Review Systems
T
Order                  Order               Order
received               received            received
On-hand inventory

Q3
Q1
Q2

Order                         Order
placed                        placed

L                     L                      L      Time
P                      P

Chapter 10—Inventory Management
Periodic Review Systems
T
IP   Order                 IP                      IP Order
Order
received                    received             received
On-hand inventory

Q3
Q1                                            OH
OH          Q2
IP1

IP3
Order                                 Order
placed                                placed
IP2

L                         L                       L         Time
P                           P
Protection interval
Chapter 10—Inventory Management
Periodic Review Systems
T
IP    Order                IP                      IP Order
Order
Bird feeder— Calculating P and T
received                    received             received
On-hand inventory

Q3
Q1                                            OH
OH          Q2
IP1

IP3
Order                                 Order
placed                                placed
IP2

L                         L                       L         Time
P                          P
Protection interval
Chapter 10—Inventory Management
Periodic Review Systems
T
IP    Order               IP                    IP Order
Order
Bird feeder—Calculating P and T
received                   received           received
On-hand inventory

t = 1 units d = 18 L = 2 weeks              Q3
Q5                               cycle/service level = 90%
OH
OH        Q2
EOQ = 75 units     D = (18 units/week)(52 weeks) = 936 units
IP1

IP3
Order                                Order
placed                               placed
IP2

L                         L                     L        Time
P                         P
Protection interval
Chapter 10—Inventory Management
Periodic Review Systems
T
IP    Order               IP                    IP Order
Order
Bird feeder—Calculating P and T
received                  received            received
On-hand inventory

t = 1 units d = 18 L = 2 weeks              Q3
Q5                               cycle/service level = 90%
OH
OH        Q2
EOQ = 75 units     D = (18 units/week)(52 weeks) = 936 units
IP1
EOQ            75
IP3           P=        (52) =     (52) = 4.2 or 4 weeks
D            936
Order                       Order
placed P+L = t P + L = 5 placed 12 units
6 =
IP2

L                         L                     L        Time
P                        P
Protection interval
Chapter 10—Inventory Management
Periodic Review Systems
T
IP    Order            IP                  IP Order
Order
Bird feeder—Calculating P and T
received               received          received
On-hand inventory

t = 1 units d = 18 L = 2 weeks              Q3
Q5                                cycle/service level = 90%
OH
OH        Q2
EOQ = 75 units     D = (18 units/week)(52 weeks) = 936 units
IP1
EOQ            75
IP3              P=        (52) =     (52) = 4.2 or 4 weeks
D            936
Order                       Order
placed P+L = t P + L = 5 placed 12 units
6 =
IP2
T = Average demand during the protection interval + Safety stock
= d (P + L) + zP + L
L                     L                   L       Time
= (18 units/week)(6 weeks) + 1.28(12 units) = 123 units
P                   P
Protection interval
Chapter 10—Inventory Management
Periodic Review Systems
T
IP    Order               IP                    IP Order
Order
Bird feeder—Calculating P and T
received                   received           received
On-hand inventory

t = 1 units d = 18 L = 2 weeks              Q3
Q5                                cycle/service level = 90%
OH
OH        Q2
EOQ = 75 units     D = (18 units/week)(52 weeks) = 936 units
IP1
P = 4 weeks          T = 123 units
IP3
Order                                Order
placed                               placed
IP2

L                         L                     L        Time
P                         P
Protection interval
Chapter 10—Inventory Management
Periodic Review Systems
T
IP    Order                IP                   IP Order
Order
Bird feeder—Calculating P and T
received                   received           received
On-hand inventory

t = 1 units d = 18 L = 2 weeks              Q3
Q5                               cycle/service level = 90%
OH
OH        Q2
EOQ = 75 units     D = (18 units/week)(52 weeks) = 936 units
IP1
P = 4 weeks           T = 123 units
IP3
Order                              Order
placed   4(18)                  936placed
IP2            C=       (\$15) +       (\$45) + 15(\$15)
2           4(18)

C = \$540 + \$585 + \$225 = \$1350
L                         L                     L        Time
P                         P
Protection interval
Chapter 10—Inventory Management
Comparison of Q and P Systems

P Systems
 Convenient to administer
 Orders may be combined
 IP only required at review
Q Systems
 Individual review frequencies
 Possible quantity discounts
 Lower, less-expensive safety stocks
Chapter 10—Inventory Management

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