Here are the key factors that would explain differences in the cost of a 12-ounce serving of Coke in various situations: - Volume of sales - Locations with higher volume sales like supermarkets can negotiate lower wholesale prices from Coke due to purchasing power. - Overhead costs - Locations with higher fixed costs per unit like convenience stores and restaurants need to mark up prices more to cover overhead like rent. - Inventory carrying costs - Locations that turn inventory faster like supermarkets have lower carrying costs so can offer lower prices. - Competition - Locations with more competition like supermarkets face more pressure to offer lower prices. Monopolistic locations like ballparks can charge a premium. - Perceived value

1. Managing Facilitating Goods
Factory Wholesaler Distributor Retailer Customer
Replenishment
order
Replenishment
order
Replenishment
order
Customer
order
Production
Delay
Wholesaler
Inventory
Shipping
Delay
Shipping
Delay
Distributor
Inventory
Retailer
Inventory
Item Withdrawn

2. Learning Objectives
• Discuss the role of information technology in managing
inventories.
• Describe the functions and costs of an inventory system.
• Determine the order quantity.
• Determine the reorder point and safety stock for inventory
systems with uncertain demand.
• Design a continuous or periodic review inventory-control
system.
• Conduct an ABC analysis of inventory items.
• Determine the order quantity for the single-period inventory
case.
• Describe the rationale behind the retail discounting model.

3. Role of Inventory in Services
• Decoupling inventories
• Seasonal inventories
• Speculative inventories
• Cyclical inventories
• In-transit inventories
• Safety stocks

4. Considerations in Inventory Systems
• Type of customer demand
• Planning time horizon
• Replenishment lead time
• Constraints and relevant costs

5. Relevant Inventory Costs
• Ordering costs
• Receiving and inspections costs
• Holding or carrying costs
• Shortage costs

6. Inventory Management
Questions
• What should be the order quantity
(Q)?
• When should an order be placed,
called a reorder point (ROP)?
• How much safety stock (SS) should
be maintained?

7. Inventory Models
• Economic Order Quantity (EOQ)
• Special Inventory Models
With Quantity Discounts
Planned Shortages
• Demand Uncertainty - Safety Stocks
• Inventory Control Systems
Continuous-Review (Q,r)
Periodic-Review (order-up-to)
• Single Period Inventory Model

8. Inventory Levels For EOQ Model
0
UnitsonHand
Q
Q
D
Time

9. Annual Costs For EOQ Model
0
100
200
300
400
500
600
700
800
900
0
20
40
60
80
100
120
140
Order Quantity, Q
AnnualCost,$
Holding Cost
Ordering Cost
Total Cost

10. EOQ Formula
• Notation
D = demand in units per year
H = holding cost in dollars/unit/year
S = cost of placing an order in dollars
Q = order quantity in units
• Total Annual Cost for Purchase Lots
• EOQ
TCp S D Q H Q= +( / ) ( / )2
EOQ
DS
H
=
2

11. Annual Costs for Quantity
Discount Model
0 100 200 300 400 500 600 700
22,000
21000
20000
2000
1000
C = $20.00 C = $19.50 C = $18.75
Order quantity, Q
AnnualCost,$

12. Inventory Levels For Planned
Shortages Model
Q
Q-K
0
-K
T1 T2
TIME
T

13. Formulas for Special Models
• Quantity Discount Total Cost Model
• Model with Planned Shortages
TC CD S D Q I CQqd = + +( / ) ( / )2
TC S
D
Q
H
Q K
Q
B
K
Qb = +
−
+
( )2 2
2 2
Q
DS
H
H B
B
*
=
+





2
K Q
H
H B
* *
=
+







14. Values for Q* and K* as A
Function of Backorder Cost
B Q* K* Inventory Levels
B → ∞
0 < < ∞B
B 0→
2DS
H
2DS
H
H B
B
+





undefined
Q
H
H B
*
+




Q*
0
0
0
0

15. Demand During Lead Time
Example
++ + =
u=3
σ = 15.
u=3 u=3 u=3
σ = 15. σ = 15.
σ L = 3
dL
−
= 12 ROP
s s
Four Days Lead Time Demand During Lead time
σ = 15.

16. Safety Stock (SS)
• Demand During Lead Time (LT) has
Normal Distribution with
-
-
• SS with r% service level
• Reorder Point
Mean d LTL( ) ( )= µ
Std Dev LTL. .( )σ σ=
SS z LTr= σ
ROP SS dL= +

17. Continuous Review System (Q,r)
Average lead time usage, dL
Reorder point, ROP
Safety stock, SS
Inventory on hand
Orderquantity,EOQ
EOQ
EOQ
d1
d2
d3
Amount used during first lead time
First lead
time, LT1
Order 1 placed
LT2 LT3
Order 2 placed Order 3 placed
Shipment 1 received Shipment 2 received Shipment 3 received
Time

18. Periodic Review System
(order-up-to)
RP RP RP
Review period
First order quantity, Q1
d1
Q2
Q3
d2
d3
Target inventory level, TIL
Amount used during
first lead time
Safety stock, SS First lead time, LT1
LT2 LT3
Order 1 placed Order 2 placed Order 3 placed
Shipment 1 received Shipment 2 received Shipment 3 received
Time
Inventory on Hand

19. Inventory Control Systems
• Continuous Review System
• Periodic Review System
EOQ
DS
H
ROP SS LT
SS z LTr
=
= +
=
2
µ
σ
RP EOQ
TIL SS RP LT
SS z RP LTr
=
= + +
= +
/
( )
µ
µ
σ

20. ABC Classification of Inventory
Items
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
100
Percentage of inventory items (SKUs)
Percentageofdollarvolume
A B C

21. Inventory Items Listed in
Descending Order of Dollar Volume
Monthly Percent of
Unit cost Sales Dollar Dollar Percent of
Inventory Item ($) (units) Volume ($) Volume SKUs Class
Computers 3000 50 150,000 74 20 A
Entertainment center 2500 30 75,000
Television sets 400 60 24,000
Refrigerators 1000 15 15,000 16 30 B
Monitors 200 50 10,000
Stereos 150 60 9,000
Cameras 200 40 8,000
Software 50 100 5,000 10 50 C
Computer disks 5 1000 5,000
CDs 20 200 4,000
Totals 305,000 100 100

22. Single Period Inventory Model
Newsvendor Problem Example
D = newspapers demanded
p(D) = probability of demand
Q = newspapers stocked
P = selling price of newspaper, $10
C = cost of newspaper, $4
S = salvage value of newspaper, $2
Cu = unit contribution: P-C = $6
Co = unit loss: C-S = $2

23. Single Period Inventory Model
Expected Value Analysis
Stock Q
p(D) D 6 7 8 9 10
.028 2 4 2 0 -2 -4
.055 3 12 10 8 6 4
.083 4 20 18 16 14 12
.111 5 28 26 24 22 20
.139 6 36 34 32 30 28
.167 7 36 42 40 38 36
.139 8 36 42 48 46 44
.111 9 36 42 48 54 52
.083 10 36 42 48 54 60
.055 11 36 42 48 54 60
.028 12 36 42 48 54 60
Expected Profit $31.54 $34.43 $35.77 $35.99 $35.33

24. Single Period Inventory Model
Incremental Analysis
E (revenue on last sale) E (loss on last sale)
P ( revenue) (unit revenue) P (loss) (unit loss)
P D Q C P D Q Cu o( ) ( )≥ ≥ <
≥
≥
[ ]1− < ≥ <P D Q C P D Q Cu o( ) ( )
P D Q
C
C C
u
u o
( )< ≤
+
(Critical Fractile)
where:
Cu = unit contribution from newspaper sale ( opportunity cost of underestimating demand)
Co = unit loss from not selling newspaper (cost of overestimating demand)
D = demand
Q = newspaper stocked

25. Critical fractile for the
newsvendor problem
0 2 4 6 8 10 12 14
Newspaper demand, Q
Probability
P(D<Q)
(Co applies)
P(D>Q)
(Cu applies)
0.722

26. Retail Discounting Model
• S = current selling price
• D = discount price
• P = profit margin on cost (% markup as decimal)
• Y = average number of years to sell entire stock of “dogs” at
current price (total years to clear stock divided by 2)
• N = inventory turns (number of times stock turns in one
year)
Loss per item = Gain from revenue
S – D = D(PNY)
)1( PNY
S
D
+
=

27. Topics for Discussion
• Discuss the functions of inventory for different
organizations in the supply chain.
• How would one find values for inventory costs?
• How can information technology create a competitive
advantage through inventory management?
• How valid are the assumptions for the EOQ model?
• How is a service level determined for inventory
items?
• What inventory model would apply to service capacity
such as seats on an aircraft?

28. Interactive Exercise
The class engages in an estimation of the
cost of a 12-ounce serving of Coke in
various situations (e.g., supermarket,
convenience store, fast-food restaurant,
sit-down restaurant, and ballpark).
What explains the differences?