EOQ: How much to order; ROP: When to order

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When to re-order with EOQ Ordering

• EOQ How much to order ROP When to order
• Re-Order Point (ROP) in periodic inventory system
  is the start of the period. Where is ROP in a
  perpetual system?
• ROP in Perpetual System Quantity on hand drops
  to a predetermined amount.
• If there were no variations in demand, and demand
  was really constant ROP is when inventory on
  hand is equal to the average demand during lead
  time.
• Lead Time is the time interval from placing an
  order until receiving the order.

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When to re-order with EOQ Ordering

• The greater the variability of demand during lead
  time, the greater the need for additional
  inventory to reduce the risk of shortage (i.e.,
  the greater the safety stock).
• When variability exists in demand or lead time,
  actual demand during lead time may exceed average
  demand during lead time.
• If ROP is equal to average demand during lead
  time, there is 50 probability of satisfying all
  the demand.
• But we want this probability to be greater than
  50. We prefer 90, 95, or 99.
• Safety Stock (SS) serves to reduce the
  probability of a stockout during the lead time.
• ROP in perpetual inventory control is the
  inventory level equal to the average demand
  during the lead time a safety stock (to cover
  demand variability)

3
Example 1
Average demand for an inventory item is 200
units per day, lead time is three days, there is
no variation in demand and lead time and
therefore, safety stock is zero. What is the
reorder point? In a perpetual inventory system,
the ROP is the point at which inventory on hand
is equal to the average demand in lead time
plus safety stock. ROP 3(200) Whenever
inventory level drops to 600 units we place an
order. We receive the order in 3 days. Because
there is no variations in demand, there is no
stock out.
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Example 2
Average demand for an inventory item is 200 units
per day, lead time is three days, and safety
stock is 100 units. What is the reorder point
In a perpetual inventory system, the ROP is the
point at which inventory on hand is equal to the
average demand in lead time plus safety
stock. ROP 3(200)100 Whenever inventory level
drops to 700 units we place an order. Since
there is variation in demand, during the next
three days, we may have a demand of 500, 600,
700, or even more.
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Demand During Lead Time
Inventory
Time
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ROP when demand during lead time is fixed
LT
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Demand During Lead Time
Inventory
Time
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Demand During Lead Time is Variable
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Demand During Lead Time is Variable
Inventory
Time
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Safety Stock
Safety stock reduces risk of stockout during lead
time
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Safety Stock
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When to re-order (ROP)
Demand during lead time has Normal distribution.
If we order when the inventory on hand is equal
to the average demand during the lead time then
there is 50 chance that the demand during lead
time is less than our inventory.
However, there is also 50 chance that the demand
during lead time is greater than our inventory,
and we will be out of stock for a while. We
usually do not like 50 probability of stock out
We can accept some risk of being out of stock,
but we usually like a risk of less than 50.
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Safety Stock and ROP
Service level
Probability of no stockout
ROP
Quantity
0
z
Each Normal variable x is associated with a
standard Normal Variable z x is Normal (Average
x , Standard Deviation x) ? z is Normal (0,1)
There is a table for z which tells us Given
any probability of not exceeding z. What is the
value of z Given any value for z. What is the
probability of not exceeding z
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Common z Values
Risk Service level z value 0.1 0.9
1.28 0.05 0.95 1.65 0.01 0.99
2.33
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Relationship between z and Normal Variable x
z (x-Average x)/(Standard Deviation of x) x
Average x z (Standard Deviation of x) µ
Average x s Standard Deviation of x
Risk Service z value
level 0.1 0.9 1.28 0.05 0.95
1.65 0.01 0.99 2.33
? x µ z s
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Relationship between z and Normal Variable ROP
LTD Lead Time Demand ROP Average LTD z
(Standard Deviation of LTD) ROP Average LTD
ss ss z (Standard Deviation of LTD)
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Safety Stock and ROP
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