Inventory Review

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Inventory Review

• ISQA 459

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Basic EOQ Model
Important assumptions

• Demand is known, constant, and independent
• Lead time is known and constant
• Receipt of inventory is instantaneous and
  complete
• Quantity discounts are not possible
• Only variable costs are setup and holding
• Stockouts can be completely avoided

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Inventory Usage Over Time
Order quantity Q (maximum inventory level)
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Minimizing Costs
Objective is to minimize total costs
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The EOQ Model
Q Number of pieces per order Q Optimal
number of pieces per order (EOQ) D Annual
demand in units for the Inventory item S Setup
or ordering cost for each order H Holding or
carrying cost per unit per year
Annual setup cost (Number of orders placed per
year) x (Setup or order cost per order)
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The EOQ Model
Q Number of pieces per order Q Optimal
number of pieces per order (EOQ) D Annual
demand in units for the Inventory item S Setup
or ordering cost for each order H Holding or
carrying cost per unit per year
Annual holding cost (Average inventory level)
x (Holding cost per unit per year)
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The EOQ Model
Q Number of pieces per order Q Optimal
number of pieces per order (EOQ) D Annual
demand in units for the Inventory item S Setup
or ordering cost for each order H Holding or
carrying cost per unit per year
Optimal order quantity is found when annual setup
cost equals annual holding cost
Solving for Q
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An EOQ Example
Determine optimal number of needles to order D
1,000 units S 10 per order H .50 per unit
per year
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An EOQ Example
Determine optimal number of needles to order D
1,000 units Q 200 units S 10 per order H
.50 per unit per year
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An EOQ Example
Determine optimal number of needles to order D
1,000 units Q 200 units S 10 per order N
5 orders per year H .50 per unit per year T
50 days
Total annual cost Setup cost Holding cost
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Variable Demand

• Requires Safety Stock to achieve a desired
  service level and avoid stock-outs.
• As illustrated in the Game.

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Reorder Point Safety Stock

• At what point (number of items left in stock)
  should we place another order so that
• New product arrives before we run out (lead time
  for product to get to us)
• Add in safety stock to insure not running out.
• Reorder Point ROP d x L safety stock
• Where
• d average daily (weekly) demand
• L lead time in days (weeks)

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Safety Stock

• Safety stock Z sdlt
• Where
• Z number standard deviations required to meet
  service level
• sdlt standard deviation of demand during lead
  time
• sd standard deviation of demand (daily or
  weekly)
• Or

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Example

• Average daily demand 15 units
• Standard deviation of daily demand 5 units
• Lead Time is 4 days
• 90 Service Level Required
• Z ?
• Reorder Point
• ROP d x L