EOQ ModelEconomic Order Quantity     Ken Homa
EOQ Assumptions• Known & constant demand• Known & constant lead time• Instantaneous receipt of material• No quantity disco...
Inventory Holding Costs        Reasonably Typical Profile                                 % of   Category                I...
EOQ ModelAnnual Cost                      Order Quantity
EOQ ModelAnnual Cost                          Holding Cost                      Order Quantity
Why Order Cost Decreases  • Cost is spread over more units  Example: You need 1000 microwave ovens1 Order (Postage $ 0.35)...
EOQ ModelAnnual Cost                          Holding Cost                    Order (Setup) Cost                      Orde...
EOQ ModelAnnual Cost         Total Cost Curve                              Holding Cost                        Order (Setu...
EOQ ModelAnnual Cost         Total Cost Curve                                 Holding Cost                            Orde...
EOQ Formula DerivationD=      Annual demand (units)C=      Cost per unit ($)             Total cost =    (Q/2) x I x C + S...
Economic Order Quantity         2× D× S   EOQ =            H   D=    Annual demand (units)   S=    Cost per order ($)   C=...
EOQ Model Equations                               2⋅ D ⋅SOptimal Order Quantity = Q * =                                  H...
EOQ             ExampleYou’re a buyer for SaveMart.SaveMart needs 1000 coffee makers peryear. The cost of each coffee make...
SaveMart EOQ                    2× D× S              EOQ =                       HD=    1000                         2 ×10...
SaveMart ROPROP = demand over lead time    = daily demand x lead time (days)    =dxlD = annual demand = 1000Days / year = ...
SaveMart       Average (Cycle Stock) InventoryAvg. CS = OQ / 2        = 80 / 2 = 40 coffeemakers        = 40 x $78 = $3,12...
Economic Order Quantity         2× D× S   EOQ =            H   D=    Annual demand (units)   S=    Cost per order ($)   C=...
2× D× S      EOQ =               H     What if …2.   Interest rates go up ?3.   Order processing is automated ?4.   Wareho...
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EOQ Ken Homa

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EOQ Ken Homa

  1. 1. EOQ ModelEconomic Order Quantity Ken Homa
  2. 2. EOQ Assumptions• Known & constant demand• Known & constant lead time• Instantaneous receipt of material• No quantity discounts• Only order (setup) cost & holding cost• No stockouts
  3. 3. Inventory Holding Costs Reasonably Typical Profile % of Category Inventory ValueHousing (building) cost 6%Material handling costs 3%Labor cost 3%Inventory investment costs 11%Pilferage, scrap, & obsolescence 3%Total holding cost 26%
  4. 4. EOQ ModelAnnual Cost Order Quantity
  5. 5. EOQ ModelAnnual Cost Holding Cost Order Quantity
  6. 6. Why Order Cost Decreases • Cost is spread over more units Example: You need 1000 microwave ovens1 Order (Postage $ 0.35) 1000 Orders (Postage $350) Purchase Order Purchase Order Purchase Order Purchase Order Description Qty. Purchase OrderQty. Description Qty. Description Qty. Microwave 1000 Description Description Qty.11 Microwave Microwave 1 Microwave 1 Microwave Order quantity
  7. 7. EOQ ModelAnnual Cost Holding Cost Order (Setup) Cost Order Quantity
  8. 8. EOQ ModelAnnual Cost Total Cost Curve Holding Cost Order (Setup) Cost Order Quantity
  9. 9. EOQ ModelAnnual Cost Total Cost Curve Holding Cost Order (Setup) Cost Optimal Order Quantity Order Quantity (Q*)
  10. 10. EOQ Formula DerivationD= Annual demand (units)C= Cost per unit ($) Total cost = (Q/2) x I x C + S x (D/Q)Q= Order quantity (units) inv carry cost order costS= Cost per order ($)I = Holding cost (%) Take the 1st derivative:H= Holding cost ($) = I x C d(TC)/d(Q) = (I x C) / 2 - (D x S) / Q²Number of Orders = D / Q To optimize: set d(TC)/d(Q) = 0Ordering costs = S x (D / Q) DS/ Q² = IC / 2Average inventory units = Q / 2 Q²/DS = 2 / IC $ = (Q / 2) x C Q²= (DS x 2 )/ ICCost to carryaverage inventory = (Q / 2) x I x C Q = sqrt (2DS / IC) = (Q /2) x H
  11. 11. Economic Order Quantity 2× D× S EOQ = H D= Annual demand (units) S= Cost per order ($) C= Cost per unit ($) I = Holding cost (%) H= Holding cost ($) = I x C
  12. 12. EOQ Model Equations 2⋅ D ⋅SOptimal Order Quantity = Q * = H DExpected Number Orders = N = Q* Working Days / YearExpected Time Between Orders = T = N Dd= D = Demand per year Working Days / Year S = Setup (order) cost per order H = Holding (carrying) costROP = d ⋅ L d = Demand per day L = Lead time in days
  13. 13. EOQ ExampleYou’re a buyer for SaveMart.SaveMart needs 1000 coffee makers peryear. The cost of each coffee maker is$78. Ordering cost is $100 per order.Carrying cost is 40% of per unit cost. Leadtime is 5 days. SaveMart is open 365days/yr.What is the optimal order quantity & ROP?
  14. 14. SaveMart EOQ 2× D× S EOQ = HD= 1000 2 ×1000 × $100S= $100 EOQ =C= $ 78 $31.20I= 40%H= CxIH= $31.20 EOQ = 80 coffeemakers
  15. 15. SaveMart ROPROP = demand over lead time = daily demand x lead time (days) =dxlD = annual demand = 1000Days / year = 365Daily demand = 1000 / 365 = 2.74Lead time = 5 daysROP = 2.74 x 5 = 13.7 => 14
  16. 16. SaveMart Average (Cycle Stock) InventoryAvg. CS = OQ / 2 = 80 / 2 = 40 coffeemakers = 40 x $78 = $3,120Inv. CC = $3,120 x 40% = $1,248Note: unrelated to reorder point
  17. 17. Economic Order Quantity 2× D× S EOQ = H D= Annual demand (units) S= Cost per order ($) C= Cost per unit ($) I = Holding cost (%) H= Holding cost ($) = I x C
  18. 18. 2× D× S EOQ = H What if …2. Interest rates go up ?3. Order processing is automated ?4. Warehouse costs drop ?5. Competitive product is introduced ?6. Product is cost-reduced ?7. Lead time gets longer ?8. Minimum order quantity imposed ?
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