1DSCI 3123
Inventory
• Stock of items held to meet future demand– Tangible goods– Intangible goods
• Inventory management answers two questions– How much to order?– When to order?
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Types of Inventory
• Raw materials• Purchased parts and supplies• Labor• In-process (partially completed) products• Component parts• Working capital• Tools, machinery, and equipment• Finished goods
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Reasons To Hold Inventory
• Meet unexpected demand
• Smooth seasonal or cyclical demand
• Meet variations in customer demand
• Take advantage of price discounts
• Hedge against price increases
• Quantity discounts
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Two Forms Of Demand
• Dependent– items used to produce final products
• Independent– items demanded by external customers
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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
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Inventory Control Systems
• Fixed-order-quantity system (Continuous)– constant amount ordered when inventory declines
to predetermined level
• Fixed-time-period system (Periodic)– order placed for variable amount after fixed
passage of time
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ABC Classification System
• Demand volume & value of items vary• Classify inventory into 3 categories
Class % of Units % of Dollars
A 5 - 15 70 - 80
B 30 1515
C 50 - 60 5 - 10
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ABC Classification ExampleCost Usage Part Value Value Quantity Cumulative
60 90 9 30,600 35.8 6.0 6.0350 40 8 16,000 18.7 5.0 11.0
30 130 2 14,000 16.4 4.0 15.080 60 1 5,400 6.3 9.0 24.030 100 4 4,800 5.6 6.0 30.020 180 3 3,900 4.6 13.0 43.010 170 6 3,600 4.2 18.0 61.0
320 50 5 3,000 3.5 10.0 71.0510 60 10 2,400 2.8 12.0 83.0
20 120 7 1,700 2.0 17.0 100.085,400$
Class Items % Value % UnitsA 9,8,2 71 15B 1, 4, 3 16.5 25C 6, 5, 10, 7 12.5 60
9DSCI 3123
Assumptions Of Basic EOQ Model
• Demand is known with certainty
• Demand is relatively constant over time
• No shortages are allowed
• Lead time for the receipt of orders is constant
• The order quantity is received all at once
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The Inventory Order CycleDemand rate
0 TimeLead time
Lead time
Order Placed
Order Placed
Order Received
Order Received
Inve
ntor
y L
evel
Reorder point, R
Order qty, Q
11DSCI 3123
EOQ Cost Model
CO - cost of placing order D - annual demand
CC - annual per-unit carrying cost Q - order quantity
Annual ordering cost =
Annual carrying cost =
Total cost = +
CoD
QCcQ
2CoD
Q
CcQ
2
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EOQ Model
TC=CoD
Q+CcQ
2
CoD
Q=CcQ
2
∂TC
∂Q=−
CoD
Q2 +Cc
2 Q2 =
2CoD
Cc
0=−CoD
Q2 +Cc
2 Qopt=
2CoD
Cc
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Total Cost at Q*
Qopt=2CoD
Cc
TCmin =CoD
Qopt
+CcQopt
2
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EOQ Model Cost CurvesSlope = 0
Total Cost
Ordering Cost = CoD/Q
Order Quantity, Q
Annualcost ($)
Minimumtotal cost
Optimal order Qopt
Carrying Cost = CcQ/2
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EOQ Example
CC = $0.75 per yard
CO = $150
D = 10,000 yards
Find EOQ, TC at Q*, # of order/year, and cycle time
NOTE: store days = 311
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EOQ Example
Qopt=2CoD
Cc
=2(150)(10,000)
(0.75)=2,000yards
TCmin =CoD
Qopt
+CcQopt
2
=(150)(10,000)
2,000+
(0.75)(2,000)
2=$750+750=$1,500
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Number of orders per year =D
Qopt
=10,000
2,000= 5
Order cycle time =311
D/Qopt
=311
5= 62.2 store days
Orders per/yr and Cycle Time
18DSCI 3123
EOQ With Noninstantaneous Receipt
Q(1-d/p)
Inventorylevel
(1-d/p)Q2
Time0
Orderreceipt period
BeginOrderreceipt
EndOrderreceipt
Maximuminventory level
Averageinventory level
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EOQ With Noninstantaneous Receipt
p = production rate d = demand rate
€
Max inv level = Q -Q
pd = Q 1 -
d
p
⎛
⎝ ⎜
⎞
⎠ ⎟
Avg inv level =1
2Q 1 -
d
p
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢
⎤
⎦ ⎥=Q
21 -
d
p
⎛
⎝ ⎜
⎞
⎠ ⎟
Total carrying cost =CcQ
21 -
d
p
⎛
⎝ ⎜
⎞
⎠ ⎟
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EOQ With Noninstantaneous Receipt
€
TC=CoD
Q+CcQ
21-
d
p
⎛
⎝ ⎜ ⎞
⎠ ⎟
Qopt=2CoD
Cc 1-d
p
⎛
⎝ ⎜ ⎞
⎠ ⎟
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Production Quantity Example
CC = $0.75 per yard
CO = $150
D = 10,000 yards
d = 10,000/311 = 32.2 yards per day
p = 150 yards per day
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Optimum Q - Q*
Qopt=2CoD
Cc 1-d
p
⎛
⎝ ⎜ ⎞
⎠ ⎟
=2(150)(10,000)
0.751-32.2
150
⎛
⎝ ⎜ ⎞
⎠ ⎟
=2,256.8 yards
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Total Cost
€
TCmin=CoD
Q+CcQ
21-
d
p
⎛
⎝ ⎜ ⎞
⎠ ⎟
=(150)(10,000)
2,256.8+
(0.75)2,256.8
21-
32.2
150
⎛
⎝ ⎜ ⎞
⎠ ⎟
=$1,329
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Production Run and Max Inv. Levels
Production run = Q/p
= 2,256.8/150
= 15.05 yards
Number of production runs = D/Q
= 10,000/2,256.8
= 4.43
Max inv level=Q 1-d
p
⎛
⎝ ⎜ ⎞
⎠ ⎟ =2,256.8 1-
32.2
150
⎛
⎝ ⎜ ⎞
⎠ ⎟ =1,722yards
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Safety Stocks
• 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
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Inputs and Outputs to Aggregate Production Planning
AggregateProductionPlanning
CompanyPolicies
FinancialConstraints
StrategicObjectives
Units or dollarssubcontracted,backordered, or
lost
CapacityConstraints
Size ofWorkforce
Productionper month
(in units or $)
InventoryLevels
DemandForecasts
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Hierarchical Planning ProcessItems
Product lines or families
Individual products
Components
Manufacturing operations
Resource level
Plants
Individual machines
Critical work centers
Production Planning Capacity Planning
Resource Requirements Plan
Rough-Cut Capacity Plan
Capacity Requirements Plan
Input/Output Control
Aggregate Production Plan
Master Production Schedule
Material Requirements Plan
Shop Floor Schedule
All work centers