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Item Withdrawn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

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
Units on Hand Q Q
Time D

9. Annual Costs For EOQ Model

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

11. Annual Costs for Quantity Discount Model
22,000
21000
20000
2000
1000
C = $20.00
C = $19.50
C = $18.75
Annual Cost, $
Order quantity, Q

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

13. Formulas for Special Models
Quantity Discount Total Cost Model
Model with Planned Shortages

14. Values for Q* and K* as A Function of Backorder Cost
B Q* K* Inventory Levels
undefined Q*

15. Demand During Lead Time Example+ + + =
u=3
u=3
u=3
u=3
ROP
s s
Four Days Lead Time
Demand During Lead time

16. Safety Stock (SS)
Demand During Lead Time (LT) has Normal Distribution with - -
SS with r% service level
Reorder Point

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

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

19. Inventory Control Systems
Continuous Review System
Periodic Review System

20. ABC Classification of Inventory Items

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 , A
Entertainment center ,000
Television sets ,000
Refrigerators , B
Monitors ,000
Stereos ,000
Cameras ,000
Software , C
Computer disks ,000
CDs ,000
Totals ,

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
Expected Profit $ $ $ $ $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)
(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
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)

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?