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Why is Inventory Important?Distribution of Costs in Large Manufacturing
Firms
Payroll17%
Overhead25%
Materials58%
Water Tank Analogy
Flow of Receipts (Raw Materials &
Parts)
Demand Flow (Finished Goods)
Scrap or Reject Flow
Inventory Level
Outflow exceeds Inflow
Flow of Receipts (Raw Materials &
Parts)
Demand Flow (Finished Goods)
Scrap or Reject Flow
Inflows exceed Outflows
Flow of Receipts (Raw Materials &
Parts)
Demand Flow (Finished Goods)
Scrap or Reject Flow
Types of DemandIndependent
• Item’s demand is influenced ONLY by market conditions and is NOT related to production decisions for any other items.
• Only end items
• Demand must be forecast
Examples– Cars, TVs, Bicycles, Number of Seats in a restaurant
Types of DemandDependent
• Item’s demand derives from the production decisions of its parents.
• All intermediate and purchased items in manufacturing
• Demand should be derived
Examples– Car doors, Tv remotes, Bicycle tires, Number of T-
bones for a given night
Pressures for Small Inventories
• Interest/Opportunity Cost
• Storage and handling
• Property Taxes
• Insurance premiums
• Shrinkage
• Spoilage
Pressures for Large Inventories
• Customer Service
• Order/Setup Cost
• Labor/Equipment Utilization
• Transportation Cost
• Cost of Materials/Quantity Discounts
Economic Order QuantityEconomic Order QuantityA
nn
ual
co
st
(do
llars
)
Lot Size (Q)
Holding cost (HC)
Economic Order QuantityEconomic Order QuantityA
nn
ual
co
st
(do
llars
)
Lot Size (Q)
Holding cost (HC)
Ordering cost (OC)
Economic Order QuantityEconomic Order QuantityA
nn
ual
co
st
(do
llars
)
Lot Size (Q)
Ordering cost (OC)
Holding cost (HC)
Total cost = HC + OC
Economic Order QuantityEconomic Order Quantity
| | | | | | | |50 100 150 200 250 300 350 400
An
nu
al c
ost
(d
oll
ars)
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
Economic Order QuantityEconomic Order QuantityA
nn
ual
co
st (
do
llar
s)
| | | | | | | |50 100 150 200 250 300 350 400
3000 —
2000 —
1000 —
0 —
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
Lot Size (Q)
Birdfeeder costs(Current System)
C = (H) + (S)Q2
DQ
D = (18 /week)(52 weeks) = 936 unitsH = 0.25 ($60/unit) = $15S = $45 Q = 390 units
Economic Order QuantityEconomic Order QuantityA
nn
ual
co
st (
do
llar
s)
| | | | | | | |50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
Birdfeeder costs (Current System)
C = (H) + (S)Q2
DQ
D = (18 /week)(52 weeks) = 936 unitsH = 0.25 ($60/unit) = $15S = $45 Q = 390 units
C = $2925 + $108 = $3033
Economic Order QuantityEconomic Order Quantity
| | | | | | | |50 100 150 200 250 300 350 400
An
nu
al c
ost
(d
oll
ars)
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Currentcost
CurrentQ
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
Birdfeeder costs
C = (H) + (S)Q2
DQ
D = (18 /week)(52 weeks) = 936 unitsH = 0.25 ($60/unit) = $15S = $45 Q = 390 units
C = $2925 + $108 = $3033
Economic Order QuantityEconomic Order Quantity
| | | | | | | |50 100 150 200 250 300 350 400
An
nu
al c
ost
(d
oll
ars)
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Currentcost
CurrentQ
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
Economic Order QuantityEconomic Order Quantity
| | | | | | | |50 100 150 200 250 300 350 400
An
nu
al c
ost
(d
oll
ars)
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Currentcost
CurrentQ
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
Birdfeeder costs (Optimal)
D = (18 /week)(52 weeks) = 936 unitsH = 0.25 ($60/unit) = $15S = $45 Q = EOQ
C = (H) + (S)Q2
DQEOQ =
2DSH
Economic Order QuantityEconomic Order Quantity
| | | | | | | |50 100 150 200 250 300 350 400
An
nu
al c
ost
(d
oll
ars)
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Currentcost
CurrentQ
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
Birdfeeder costs (Optimal)
D = (18 /week)(52 weeks) = 936 unitsH = 0.25 ($60/unit) = $15S = $45 Q = 75 units
C = (H) + (S)Q2
DQEOQ =
2DSH
Economic Order QuantityEconomic Order Quantity
| | | | | | | |50 100 150 200 250 300 350 400
An
nu
al c
ost
(d
oll
ars)
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Currentcost
CurrentQ
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
Birdfeeder costs (Optimal)
D = (18 /week)(52 weeks) = 936 unitsH = 0.25 ($60/unit) = $15S = $45 Q = 75 units
C = $562 + $562 = $1124
C = (H) + (S)Q2
DQEOQ =
2DSH
Economic Order QuantityEconomic Order Quantity
| | | | | | | |50 100 150 200 250 300 350 400
An
nu
al c
ost
(d
oll
ars)
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Currentcost
CurrentQ
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
Birdfeeder costs (Optimal)
D = (18 /week)(52 weeks) = 936 unitsH = 0.25 ($60/unit) = $15S = $45 Q = 75 units
C = $562 + $562 = $1124
C = (H) + (S)Q2
DQEOQ =
2DSH
Economic Order QuantityEconomic Order Quantity
| | | | | | | |50 100 150 200 250 300 350 400
An
nu
al c
ost
(d
oll
ars)
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Currentcost
CurrentQ
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
Birdfeeder costs (Optimal)
D = (18 /week)(52 weeks) = 936 unitsH = 0.25 ($60/unit) = $15S = $45 Q = 75 units
C = $562 + $562 = $1124
C = (H) + (S)Q2
DQEOQ =
2DSH
Lowestcost
Best Q(EOQ)
Economic Order QuantityEconomic Order Quantity
| | | | | | | |50 100 150 200 250 300 350 400
An
nu
al c
ost
(d
oll
ars)
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Currentcost
Lowestcost
Best Q(EOQ)
CurrentQ
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
Five Assumptions of the EOQ
• CONSTANT demand rate
• Two relevant COSTS
• Item INDEPENDENCE
• CERTAINTY in demand, lead time and supply
• Whole LOTS
Realistic?• No Way ......
• ................ BUT, since EOQ is relatively insensitive to errors, IT WORKS ANYWAY!
Reorder PointReorder PointO
n-h
and
in
ven
tory
Time
Orderreceived
Orderreceived
Q Q
OH OH
Orderplaced
Orderplaced
IP IP
TBO
L
TBO
L
TBO
L
R
Reorder PointReorder Point
Time
On
-han
d i
nve
nto
ry
Orderreceived
Orderreceived
Q
OH
Orderplaced
Orderplaced
IPIP
R
TBO1 TBO2 TBO3
L1 L2 L3
Reorder Point / Safety StockReorder Point / Safety Stock
Lower Florida Keys Health SystemBasic Surgery Cart
Demand DuringLead Time (units) 100 200 300 400 500 600
Probability 0.10 0.15 0.20 0.25 0.25 0.05
Reorder Point / Safety StockReorder Point / Safety Stock
Lower Florida Keys Health SystemBasic Surgery Cart
Demand DuringLead Time (units) 100 200 300 400 500 600
Probability 0.10 0.15 0.20 0.25 0.25 0.05
CumulativeProbability 0.10 0.25 .045 0.70 0.95 1.00
Reorder Point / Safety StockReorder Point / Safety Stock
Lower Florida Keys Health SystemBasic Surgery Cart
Demand DuringLead Time (units) 100 200 300 400 500 600
Probability 0.10 0.15 0.20 0.25 0.25 0.05
CumulativeProbability 0.10 0.25 .045 0.70 0.95 1.00
Desired Cycle-Service Level = 95%
Reorder Point / Safety StockReorder Point / Safety Stock
Lower Florida Keys Health SystemBasic Surgery Cart
Demand DuringLead Time (units) 100 200 300 400 500 600
Probability 0.10 0.15 0.20 0.25 0.25 0.05
CumulativeProbability 0.10 0.25 .045 0.70 0.95 1.00
Desired Cycle-Service Level = 95%
Reorder Point = 500 units
Reorder Point / Safety StockReorder Point / Safety Stock
Lower Florida Keys Health SystemBasic Surgery Cart
Demand DuringLead Time (units) 100 200 300 400 500 600
Probability 0.10 0.15 0.20 0.25 0.25 0.05
CumulativeProbability 0.10 0.25 .045 0.70 0.95 1.00
Desired Cycle-Service Level = 95%
Reorder Point = 500 units
Reorder Point / Safety StockReorder Point / Safety Stock
Lower Florida Keys Health SystemBasic Surgery Cart
Demand DuringLead Time (units) 100 200 300 400 500 600
Probability 0.10 0.15 0.20 0.25 0.25 0.05
CumulativeProbability 0.10 0.25 .045 0.70 0.95 1.00
Desired Cycle-Service Level = 95%
Reorder Point = 500 units
Safety stock = Reorder point - DDLT
DDLT = 100(0.10) + 200(0.15) ... 600(0.05)= 355 units
Safety stock = 500 - 355 = 145 units
Reorder Point / Safety StockReorder Point / Safety Stock
Probability of stockout(1.0 - 0.85 = 0.15)
Cycle-service level = 85%
Average demand
during lead time
zL
R
Reorder Point / Safety StockReorder Point / Safety Stock
Demand during lead time = 36 units
L = 15 Cycle/service level = 90%
Time
On
-ha
nd
in
ven
toryR
Reorder Point / Safety StockReorder Point / Safety Stock
Demand during lead time = 36 units
L = 15 Cycle/service level = 90%
Time
On
-ha
nd
in
ven
toryR
z = 1.28
Safety stock = zL = 19.2 20
Reorder point = 36 + 20 = 56
Reorder Point / Safety StockReorder Point / Safety Stock
Demand during lead time = 36 units
L = 15 Cycle/service level = 90%
Time
On
-ha
nd
in
ven
tory56
z = 1.28
Safety stock = zL = 19.2 20
Reorder point = 36 + 20 = 56
Reorder Point / Safety StockReorder Point / Safety Stock
Demand during lead time = 36 units
L = 15 Cycle/service level = 90%
Time
On
-ha
nd
in
ven
tory55
z = 1.28
Safety stock = zL = 19.2 19
Reorder point = 36 + 19 = 55
When L not given, but L and t are known:
L = t L
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