Admission in India 2015
By:
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Managing Facilitating Goods
Factory Wholesaler Distributor Retailer Customer
Replenishment order
Replenishment order
Replenishment order
Customer order
Production Delay
WholesalerInventory
Shipping Delay
Shipping Delay
DistributorInventory
RetailerInventory
Item Withdrawn
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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.• 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.
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Role of Inventory in Services
• Decoupling inventories
• Seasonal inventories
• Speculative inventories
• Cyclical inventories
• In-transit inventories
• Safety stocks
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Considerations in Inventory Systems
• Type of customer demand
• Planning time horizon
• Replenishment lead time
• Constraints and relevant costs
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Relevant Inventory Costs
• Ordering costs
• Receiving and inspections costs
• Holding or carrying costs
• Shortage costs
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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?
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Inventory Models• Economic Order Quantity (EOQ)• Special Inventory Models
With Quantity DiscountsPlanned 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
0
Un
its o
n H
an
d
Q
Q
D
Time
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Annual Costs For EOQ Model
0
100
200
300
400
500
600
700
800
9000 20 40 60 80 100
120
140
Order Quantity, Q
An
nu
al C
ost
, $
Holding CostOrdering CostTotal Cost
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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 TCp S D Q H Q ( / ) ( / )2
EOQDS
H
2
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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
An
nua
l Co
st, $
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Inventory Levels For Planned Shortages Model
Q
Q-K
0
-KT1 T2
TIME
T
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Formulas for Special Models
• Quantity Discount Total Cost Model
• Model with Planned Shortages
TC CD S D Q I CQqd ( / ) ( / )2
TC SD
QH
Q K
QB
K
Qb
( )2 2
2 2
QDS
H
H B
B*
2
K QH
H B* *
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Values for Q* and K* as AFunction of Backorder CostB Q* K* Inventory Levels
B
0 B
B 0
2DS
H
2DS
H
H B
B
undefined
QH
H B*
Q*
00
0
0
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Demand During Lead Time Example
++ + =
u=3
15.
u=3 u=3 u=3
15. 15.
L 3
dL
12 ROP
s s
Four Days Lead Time Demand During Lead time
15.
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Safety Stock (SS)
• Demand During Lead Time (LT) has Normal Distribution with - -
• SS with r% service level
• Reorder Point
Mean d LTL( ) ( )Std Dev LTL. .( )
SS z LTr
ROP SS dL admission.edhole.com
Continuous Review System (Q,r)
Average lead time usage, dL
Reorder point, ROP
Safety stock, SS
Inventory on hand
Ord
er q
uant
ity, E
OQ
EOQ
EOQ
d1 d2
d3
Amount used during first lead time
First leadtime, LT1
Order 1 placed
LT2 LT3
Order 2 placed Order 3 placed
Shipment 1 received Shipment 2 received Shipment 3 received
Time
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Periodic Review System(order-up-to)
RP RP RP
Review period
First order quantity, Q1
d1
Q2Q3
d2
d3
Target inventory level, TIL
Amount used duringfirst 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
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Inventory Control Systems• Continuous Review System
• Periodic Review System
EOQDS
HROP SS LT
SS z LTr
2
RP EOQ
TIL SS RP LT
SS z RP LTr
/
( )
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ABC Classification of Inventory Items
0102030405060708090
100
0 10 20 30 40 50 60 70 80 90 100
Percentage of inventory items (SKUs)
Perc
enta
ge o
f dol
lar v
olum
e
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 AEntertainment center 2500 30 75,000
Television sets 400 60 24,000Refrigerators 1000 15 15,000 16 30 BMonitors 200 50 10,000
Stereos 150 60 9,000Cameras 200 40 8,000Software 50 100 5,000 10 50 CComputer disks 5 1000 5,000CDs 20 200 4,000
Totals 305,000 100 100
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Single Period Inventory ModelNewsvendor Problem ExampleD = 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 = $2admission.edhole.com
Single Period Inventory Model Expected Value Analysis
Stock Qp(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)
P D Q C P D Q Cu o( ) ( )
1 P D Q C P D Q Cu o( ) ( )
P D QC
C Cu
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 stockedadmission.edhole.com
Critical fractile for the newsvendor problem
0 2 4 6 8 10 12 14
Newspaper demand, Q
Pro
bab
ility
P(D<Q)(Co applies)
P(D>Q)(Cu applies)
0.722
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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 revenueS – D = D(PNY)
)1( PNY
SD
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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?
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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?
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