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Chapter 13
Inventory Management
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Copyright 2011 John Wiley & Sons, Inc.
Lecture Outline
• Elements of Inventory Management• Inventory Control Systems• Economic Order Quantity Models• Quantity Discounts• Reorder Point• Order Quantity for a Periodic Inventory System
13-2
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What Is Inventory?
• Stock of items kept to meet future demand• Purpose of inventory management
• how many units to order• when to order
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Supply Chain Management
• Bullwhip effect• demand information is distorted as it moves away
from the end-use customer• higher safety stock inventories to are stored to
compensate• Seasonal or cyclical demand• Inventory provides independence from vendors• Take advantage of price discounts• Inventory provides independence between
stages and avoids work stoppages
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Quality Management in the Supply Chain
• Customers usually perceive quality service as availability of goods they want when they want them
• Inventory must be sufficient to provide high-quality customer service in QM
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Types of Inventory
• Raw materials• Purchased parts and supplies• Work-in-process (partially completed) products
(WIP)• Items being transported• Tools and equipment
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Two Forms of Demand
13-7
• Dependent• Demand for items used to produce final
products • Tires for autos are a dependent demand item
• Independent• Demand for items used by external customers• Cars, appliances, computers, and houses are
examples of independent demand inventory
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Inventory Costs
• Carrying cost• cost of holding an item in inventory
• Ordering cost• cost of replenishing inventory
• Shortage cost• temporary or permanent loss of sales when
demand cannot be met
13-8
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Inventory Control Systems
13-9
• Continuous system (fixed-order-quantity)• constant amount ordered when inventory declines to
predetermined level
• Periodic system (fixed-time-period)• order placed for variable amount after fixed passage
of time
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ABC Classification
• Class A• 5 – 15 % of units• 70 – 80 % of value
• Class B• 30 % of units• 15 % of value
• Class C• 50 – 60 % of units• 5 – 10 % of value
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ABC Classification
13-11
1 $ 60 902 350 403 30 1304 80 605 30 1006 20 1807 10 1708 320 509 510 60
10 20 120
PART UNIT COST ANNUAL USAGE
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ABC Classification
13-12
Example 10.1
9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.02 14,000 16.4 4.0 15.01 5,400 6.3 9.0 24.04 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.05 3,000 3.5 13.0 71.0
10 2,400 2.8 12.0 83.07 1,700 2.0 17.0 100.0
TOTAL % OF TOTAL % OF TOTALPART VALUE VALUE QUANTITY % CUMMULATIVE
A
B
C
$85,400
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ABC Classification
13-13
Example 10.1
% OF TOTAL % OF TOTALCLASS ITEMS VALUE QUANTITY
A 9, 8, 2 71.0 15.0B 1, 4, 3 16.5 25.0C 6, 5, 10, 7 12.5 60.0
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Economic Order Quantity (EOQ) Models
• EOQ• optimal order quantity that will minimize
total inventory costs
• Basic EOQ model• Production quantity model
13-14
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Assumptions of Basic EOQ Model
• Demand is known with certainty and is constant over time
• No shortages are allowed• Lead time for the receipt of orders is constant• Order quantity is received all at once
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Inventory Order Cycle
13-16
Demand rate
TimeLead time
Lead time
Order placed
Order placed
Order receipt
Order receipt
Inve
ntor
y Le
vel
Reorder point, R
Order quantity, Q
0
Average inventory
Q
2
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EOQ Cost Model
13-17
Co - cost of placing order D - annual demand
Cc - annual per-unit carrying cost Q - order quantity
Annual ordering cost =CoD
Q
Annual carrying cost =CcQ
2
Total cost = +CoD
Q
CcQ
2
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EOQ Cost Model
13-18
TC = +CoD
Q
CcQ
2
= – +CoD
Q2
Cc
2
TC
Q
0 = – +C0D
Q2
Cc
2
Qopt =2CoD
Cc
Deriving Qopt Proving equality of costs at optimal point
=CoD
Q
CcQ
2
Q2 =2CoD
Cc
Qopt =2CoD
Cc
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EOQ Cost Model
13-19
Order Quantity, Q
Annual cost ($) Total Cost
Carrying Cost =CcQ
2
Slope = 0
Minimum total cost
Optimal order Qopt
Ordering Cost =CoD
Q
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EOQ Example
13-20
Cc = $0.75 per gallon Co = $150 D = 10,000 gallons
Qopt =2CoD
Cc
Qopt =2(150)(10,000)
(0.75)
Qopt = 2,000 gallons
TCmin = +CoD
Q
CcQ
2
TCmin = +(150)(10,000)
2,000
(0.75)(2,000)
2
TCmin = $750 + $750 = $1,500
Orders per year = D/Qopt
= 10,000/2,000
= 5 orders/year
Order cycle time = 311 days/(D/Qopt)
= 311/5
= 62.2 store days
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Production Quantity Model
• Order is received gradually, as inventory is simultaneously being depleted• AKA non-instantaneous receipt model• assumption that Q is received all at once is relaxed
• p - daily rate at which an order is received over time, a.k.a. production rate
• d - daily rate at which inventory is demanded
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Production Quantity Model
13-22
Q(1-d/p)
Inventorylevel
(1-d/p)Q2
Time0
Orderreceipt period
Beginorder
receipt
Endorder
receipt
Maximuminventory level
Averageinventory level
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Production Quantity Model
13-23
p = production rate d = demand rate
Maximum inventory level = Q - d
= Q 1 -
Qp
dp
Average inventory level = 1 -Q2
dp
TC = + 1 -dp
CoD
Q
CcQ
2
Qopt =2CoD
Cc 1 - dp
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Production Quantity Model
13-24
Cc = $0.75 per gallon Co = $150 D = 10,000 gallons
d = 10,000/311 = 32.2 gallons per day p = 150 gallons per day
Qopt = = = 2,256.8 gallons
2CoD
Cc 1 - dp
2(150)(10,000)
0.75 1 - 32.2150
TC = + 1 - = $1,329dp
CoD
Q
CcQ
2
Production run = = = 15.05 days per orderQp
2,256.8150
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Production Quantity Model
Copyright 2011 John Wiley & Sons, Inc. 13-25
Number of production runs = = = 4.43 runs/yearDQ
10,0002,256.8
Maximum inventory level = Q 1 - = 2,256.8 1 -
= 1,772 gallons
dp
32.2150
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Solution of EOQ Models With Excel
13-26
The optimal ordersize, Q, in cell D8
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Solution of EOQ Models With Excel
13-27
The formula for Qin cell D10
=(D4*D5/D10)+(D3*D10/2)*(1-(D7/D8))
=D10*(1-(D7/D8))
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Solution of EOQ Models With OM Tools
13-28
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Quantity Discounts
13-29
Price per unit decreases as order quantity increases
TC = + + PDCoD
Q
CcQ
2
where
P = per unit price of the itemD = annual demand
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Quantity Discount Model
13-30
Qopt
Carrying cost
Ordering cost
Inve
ntor
y co
st (
$)
Q(d1 ) = 100 Q(d2 ) = 200
TC (d2 = $6 )
TC (d1 = $8 )
TC = ($10 ) ORDER SIZE PRICE
0 - 99 $10
100 – 199 8 (d1)
200+ 6 (d2)
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Quantity Discount
13-31
QUANTITY PRICE
1 - 49 $1,400
50 - 89 1,100
90+ 900
Co = $2,500
Cc = $190 per TV
D = 200 TVs per year
Qopt = = = 72.5 TVs2CoD
Cc
2(2500)(200)190
TC = + + PD = $233,784 CoD
Qopt
CcQopt
2
For Q = 72.5
TC = + + PD = $194,105CoD
Q
CcQ
2
For Q = 90
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Quantity Discount Model With Excel
13-32
=(D4*D5/E10)+(D3*E10/2)+C10*D5=IF(D10>B10,D10,B10)
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Reorder Point
13-33
• Inventory level at which a new order is placed
R = dLwhere
d = demand rate per periodL = lead time
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Reorder Point
13-34
Demand = 10,000 gallons/year
Store open 311 days/year
Daily demand = 10,000 / 311 = 32.154 gallons/day
Lead time = L = 10 days
R = dL = (32.154)(10) = 321.54 gallons
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Safety Stock
• Safety stock• buffer added to on hand inventory during lead time
• Stockout • an inventory shortage
• Service level • probability that the inventory available during lead
time will meet demand• P(Demand during lead time <= Reorder Point)
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Variable Demand With Reorder Point
13-36
Reorderpoint, R
Q
LT
Time
LT
Inve
nto
ry le
vel
0
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Reorder Point With Safety Stock
13-37
Reorderpoint, R
Q
LTTime
LT
Inve
nto
ry le
vel
0
Safety Stock
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Reorder Point With Variable Demand
13-38
R = dL + zd L
where
d = average daily demandL = lead timed = the standard deviation of daily demand
z = number of standard deviationscorresponding to the service levelprobability
zd L = safety stock
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Reorder Point For a Service Level
13-39
Probability of meeting demand during lead time = service level
Probability of a stockout
R
Safety stock
dLDemand
zd L
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Reorder Point For Variable Demand
13-40
The paint store wants a reorder point with a 95% service level and a 5% stockout probability
d = 30 gallons per dayL = 10 daysd = 5 gallons per day
For a 95% service level, z = 1.65
R = dL + z d L
= 30(10) + (1.65)(5)( 10)
= 326.1 gallons
Safety stock = z d L
= (1.65)(5)( 10)
= 26.1 gallons
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Determining Reorder Point with Excel
13-41
The reorder pointformula in cell E7
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Order Quantity for a Periodic Inventory System
13-42
Q = d(tb + L) + zd tb + L - I
where
d = average demand ratetb = the fixed time between ordersL = lead timesd = standard deviation of demand
zd tb + L = safety stockI = inventory level
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Periodic Inventory System
13-43
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Fixed-Period Model With Variable Demand
13-44
d = 6 packages per daysd = 1.2 packagestb = 60 daysL = 5 daysI = 8 packagesz = 1.65 (for a 95% service level)
Q = d(tb + L) + zd tb + L - I
= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8
= 397.96 packages
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Fixed-Period Model with Excel
13-45
Formula for ordersize, Q, in cell D10
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