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8/13/2019 7 Inventory Analysis
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Inventory Analysis
Deterministic Models
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EOQ Model
K = fixed charge for a single order
h= holding cost ($/item/unit time)
D = constant demand per unit time (unit)Q*= economic order quantity
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The EOQ Model
with Non-zero Lead Time
Lead Time Less than inventory Cycle Time
C: the length of the inventory cycle
L: the deterministic lead time
R*: reorder point
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C = Q*/D
Each time the inventory level reach R*, an
order must be placed so that it arrives when
an inventory is depleted
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Lead Time Greater than inventory Cycle Time
The order must be placed in a previousinventory cycle in order to satisfy demand
at least one order will arrive during the lead
time
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L/C represents the lead time in terms of a
number of inventory cyclesfractional part =
F(L/C)
Example:
C = 0.2 years
L = 90 days
F(L/C) = F((90/365)/0.2) = F(1.23) = 0.23
Reorder point:
R* = (F(L/C)Q*
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Example:
A department store carpet division sells
30,000 yards of carpet of of a particular type
and color per year. Every time the division
places an order to the manufacturer, there is afixed charge of $1,000 independent of the size
of the order. At the same time the estimated
costs of holding a yard of carpet in inventoryfor a year is $2. How many yards of carpet
should be ordered each time an order is
placed?
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Example:
The length of the inventory cycle was
approximately 67 days and lead time was 30
days. The order must be placed when the
inventory level reach how many yards?
If the lead time was 75 days, the order must
be placed when the inventory level reach how
many yards
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The EOQ Model
with A Uniform Replenishment Rate
Inventory is received gradually over a period
of a time
Important for an organization that produces
and inventories the same end itemEPQ /
EMQ
Works only if items are being produced at a
rate greater than the demand rate
The ordering cost is not affected, but the
holding cost does change
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p = uniform replenishment rate = production rate
tp= the production time
td= the time that inventory is being depleted andnot replenished
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Total order cost per unit time = K(D/Q) Length of production run = Q/p
Demand during production = (Q/p)D
The inventory will be maximized preciselywhen production stops and when total
production reaches the order quantity Q
maximum inventory level = Q-(Q/p)D
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Total number of production runs (or orders) per year
= D/Q
The time during which the inventory is being depleted
= Q/pQ/d
Economic order quantity:
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Example:
year
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EOQ?
Total annual inventory cost?
Total number of production runs (or
orders) per year?
The length of production run? The time during which the inventory is
being depleted?
Maximum inventory level?