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EOQ Assumptions• Known & constant demand• Known & constant lead time• Instantaneous receipt of material• No quantity discounts• Only order (setup) cost & holding cost• No stockouts
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EOQ ModelAnnual Cost Holding Cost Order Quantity
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Why Order Cost Decreases • Cost is spread over more units Example: You need 1000 microwave ovens1 Order (Postage $ 0.35) 1000 Orders (Postage $350) Purchase Order Purchase Order Purchase Order Purchase Order Description Qty. Purchase OrderQty. Description Qty. Description Qty. Microwave 1000 Description Description Qty.11 Microwave Microwave 1 Microwave 1 Microwave Order quantity
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EOQ ModelAnnual Cost Holding Cost Order (Setup) Cost Order Quantity
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EOQ ModelAnnual Cost Total Cost Curve Holding Cost Order (Setup) Cost Order Quantity
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EOQ ModelAnnual Cost Total Cost Curve Holding Cost Order (Setup) Cost Optimal Order Quantity Order Quantity (Q*)
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EOQ Formula DerivationD= Annual demand (units)C= Cost per unit ($) 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
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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
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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
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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?
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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
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SaveMart Average (Cycle Stock) InventoryAvg. CS = OQ / 2 = 80 / 2 = 40 coffeemakers = 40 x $78 = $3,120Inv. CC = $3,120 x 40% = $1,248Note: unrelated to reorder point
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Economic Order Quantity 2× D× S EOQ = H D= Annual demand (units) S= Cost per order ($) C= Cost per unit ($) I = Holding cost (%) H= Holding cost ($) = I x C
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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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