Inventory Pooling

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Inventory Pooling
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Distributed versus Pooled Inventory
Distribution center 1
Versus
Assembly factory
Assembly factory
Consolidated distribution center
Distribution center 2
Retailers
Retailers
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Examples of Inventory Pooling

• Centralized warehousing (physical/virtual)
• Common components
• Delayed differentiation
• Product/component substitution
• E-tailing

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The Impact of Inventory Pooling

• Impact on safety stocks
• Impact on cycle stocks

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Impact on Safety Stocks
The distributed system A system with N different
inventory locations, each facing independent
demand Xi (i1,, N), normally distributed with
mean m and standard deviation s and each with
similar shortage and overage costs cs and co.
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Impact on Safety Stocks
The distributed system A system with N different
inventory locations, each facing independent
demand Xi (i1,, N), normally distributed with
mean m and standard deviation s and each with
similar shortage and overage costs cs and co.
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Impact on Safety Stocks (continued)
The pooled system A system with a single
inventory location from which all demand is
satisfied
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Impact on Safety Stocks (continued)
The pooled system A system with a single
inventory location from which all demand is
satisfied,
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Impact on Safety Stocks (continued)
Inventory pooling reduces both the optimal cost
and the optimal amount of safety stock by a
factor of ?N.
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What Happens if the Demands are Correlated?
Consider two locations with demand X1 and X2 with
mean m1 and m2, standard deviation s1 and s2. Then
Let Then
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What Happens if the Demands are Correlated?
(Continued)

• If Cov(X1, X2) gt 0, X1 and X2 are positively
  correlated
• If Cov(X1, X2) lt 0, X1 and X2 are negatively
  correlated
• If Cov(X1, X2) 0, X1 and X2 are uncorrelated

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What Happens if the Demands are Correlated?
Let
Then
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What Happens if the Demands are Correlated?
If the demands X1 and X2 are pooled in a single
location, then
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What Happens if the Demands are Correlated?
If the demands X1 and X2 are pooled in a single
location, then
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What Happens if the Demands are Correlated?
If the demands X1 and X2 are pooled in a single
location, then
If the demands X1 and X2 are satisfied from
separate locations, then
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What Happens if the Demands are Correlated?
If the demands X1 and X2 are pooled in a single
location, then
If the demands X1 and X2 are satisfied from
separate locations, then
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What Happens if the Demands are Correlated?
(Continued)
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What Happens if the Demands are Correlated?
(Continued)
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What Happens if the Demands are Correlated?
(Continued)
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The Case of Identical demands (m1m2m s1s2s)
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The Case of Identical demands (m1m2m s1s2s)
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The Case of Identical demands (m1m2m s1s2s)
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The Case of Identical demands (m1m2m s1s2s)
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Inventory pooling is most beneficial when the
demands have perfect negative correlation. On the
other hand, there is no value to pooling when the
demands have perfect positive correlation.
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Impact on Cycle Stocks
The distributed system A system with N
different inventory locations, each facing a
deterministic demand rate D and each with
ordering cost A and holding cost h
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Impact on Cycle Stocks
The pooled system A system with a single
location, facing a deterministic demand rate ND,
ordering cost A and holding cost h
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Example
N 2 Total cost is reduced by 29. N4 N
5 N 10
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The Square Root Law
Average inventory increases proportionally to the
square root of the number of locations in which
inventory is held.
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The Square Root Law (Continued)
There is a diminishing effect to pooling. Most of
the benefits of pooling occur by consolidating
few locations. In most cases, total pooling may
not be necessary.