7 inventory analysis

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?

7 inventory analysis

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