EOQ

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EOQ

• Answers the Question How Much to Order?
• Assumptions
• Instantaneous production
• Immediate delivery
• Deterministic demand
• Constant demand D units/year
• Constant setup cost A /setup
• Independent products

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EOQ view of Inventory
Order Quantity Q
Inventory
Time
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Costs

• Setup Costs
• A /setup
• How many setups if we make Q each time?
• Why not just make D units in one setup?

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Inventory Cost

• Usually billed as a holding cost
• Essentially interest on the money tied up in
  inventory
• h /unit/year
• Example Holding 100 units for 6 months costs ?
• Inventory holding Cost
• hAverage Inventory

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A Model

• Lot Size or Order Quantity Q units
• Average Inventory Level Q/2units
• Annual Demand D units/year
• Order Frequency every D/Q times per year
• Average Variable Cost/Year
• TVC hQ/2 AD/Q

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The EOQ

• Use Calculus to find the value of Q that
  minimizes TVC(Q)
• Or...

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The Economic Order Quantity

• h Q/2 A D/Q
• Q2 2 A D/h
• Q SQRT(2 A D/h)
• CAVEAT Make sure you use
• commensurate units!

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An Example

• Raw Material X
• Quarterly demand 6,000 units
• Cost per unit 25/unit
• Holding Cost say 10 per year
• Transaction Cost 100/order
• EOQ SQRT(2 CT D/ CI)
• SQRT(2 100 6,000/(0.02525))
• 1,385 units per shipment

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Robustness of the EOQ
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Robustness
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EPQ

• Answers the Question How Much to Produce?
• Assumptions
• Instantaneous production
• Constant production rate P gt D units/year
• Immediate delivery
• Deterministic demand
• Constant demand D units/year
• Constant setup cost A/setup
• Independent products

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EPQ view of Inventory
Inventory
Production Quantity Q
Max Inv. Level
Length of Prod. Run
Time
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A Model

• Lot Size or Production Quantity Q units
• Average Inventory Level
• Production run lasts Q/P
• Inventory grows at rate (P-Q)
• So, max inventory is (P-D)Q/P (1-D/P)Q
• Average inventory is (1-D/P)Q/2
• Order Frequency every D/Q times per year
• Average Variable Cost/Year
• TVC h(1-D/P)Q/2 AD/Q

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The EPQ

• Use Calculus to find the value of Q that
  minimizes TVC(Q)
• Or use the previous answer...
• TVC h(1-D/P)Q/2 AD/Q
• hQ/2 AD/Q
• So, Q SQRT(2 A D/h)
• SQRT(2AD/h(1-D/P))

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An Example

• Raw Material X
• Quarterly demand 6,000 units
• Cost per unit 25/unit
• Holding Cost say 10 per year
• Transaction Cost 100/order
• Quarterly Production Rate 8,000 units
• EOQ SQRT(2 CT D/ CI)
• SQRT(21006,000/(0.02525(1-6/8)))
• 2,771 units per run

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A Model

• Divide the planning horizon into time buckets t
  1, 2, ..., T
• Dt units of demand in period t
• ct unit production cost in period t
• At setup cost in period t
• ht inventory holding cost in period t
• Qt the lot size in period t
• It units in inventory at the end of period t

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Heuristics

• Lot-for-lot Make what is required each period.
• Fixed Order Quantity Order the EOQ
• Period Order Quantity Calculate the EOQ, Q.
  Convert to order frequency T Q/D. Orders sized
  to last for time T.