Managing Facilitating Goods

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Item Withdrawn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

• Discuss the role of information technology in
  managing inventories.
• Describe the functions and costs of an inventory
  system.
• Determine the order quantity.
• Calculate the reorder point and safety stock for
  an inventory system.
• Design a continuous or periodic review
  inventory-control system.
• Conduct an ABC analysis of inventory items.
• Determine the order size 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

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

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Inventory Levels For EOQ Model
Units on Hand
Q
0
Q
Time
D
9
Annual Costs For EOQ Model
10
EOQ Formula

• NotationD demand in units per yearH holding
  cost in dollars/unit/yearS cost of placing an
  order in dollarsQ order quantity in units
• Total Annual Cost for Purchase Lots
• EOQ

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Annual Costs for Quantity Discount Model
22,000 21000 20000 2000 1000
C 20.00
C 19.50
C 18.75
Annual Cost,
0 100 200 300
400 500 600
700
Order quantity, Q
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Inventory Levels For Planned Shortages Model
Q-K
Q
TIME
0
-K
T1
T2
T
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Formulas for Special Models

• Quantity Discount Total Cost Model
• Model with Planned Shortages

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Values for Q and K as AFunction of Backorder
Cost
B Q K
Inventory Levels
0
0
0
undefined
Q
0
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Demand During Lead Time Example




u3
u3
u3
u3
ROP
s s
Demand During Lead time
Four Days Lead Time
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Safety Stock (SS)

• Demand During Lead Time (LT) has Normal
  Distribution with - -
• SS with r service level
• Reorder Point

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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 3 placed
Order 2 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
Q3
Q2
d3
d1
Amount used during first lead time
d2
Safety stock, SS
First lead time, LT1
LT2
LT3
Time
Order 2 placed
Order 3 placed
Order 1 placed
Shipment 1 received
Shipment 3 received
Shipment 2 received
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Inventory Control Systems

• Continuous Review System
• Periodic Review System

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ABC Classification of Inventory Items
A
B
C
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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
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Single Period Inventory ModelNewsvendor 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

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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
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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
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Critical fractile for the newsvendor problem
P(DltQ) (Co applies)
P(DgtQ) (Cu applies)
0.722
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Topics for Discussion

• Discuss the functions of inventory for different
  organizations in the distribution system.
• 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?