6 Why Order Cost Decreases Cost is spread over more unitsExample: You need 1000 microwave ovens1 Order (Postage $ 0.35)1000 Orders (Postage $350)Purchase OrderPurchase OrderPurchase OrderPurchase OrderDescriptionQty.Purchase OrderDescriptionQty.DescriptionQty.DescriptionQty.Microwave1000DescriptionMicrowaveQty.1Microwave1Microwave1Microwave1Order quantity
8 EOQ Model Annual Cost Total Cost Curve Holding Cost Order (Setup) Cost Order Quantity
9 Optimal Order Quantity (Q*) EOQ ModelAnnual CostTotal Cost CurveHolding CostOrder (Setup) CostOrder QuantityOptimal Order Quantity (Q*)
10 EOQ Formula Derivation D = Annual demand (units)C = Cost per unit ($)Q = Order quantity (units)S = Cost per order ($)I = Holding cost (%)H = Holding cost ($) = I x CNumber of Orders = D / QOrdering costs = S x (D / Q)Average inventoryunits = Q / 2$ = (Q / 2) x CCost to carryaverage inventory = (Q / 2) x I x C= (Q /2) x HTotal cost = (Q/2) x I x C + S x (D/Q)inv carry cost order costTake the 1st derivative:d(TC)/d(Q) = (I x C) / (D x S) / Q²To optimize: set d(TC)/d(Q) = 0DS/ Q² = IC / 2Q²/DS = 2 / ICQ²= (DS x 2 )/ ICQ = sqrt (2DS / IC)
11 Economic Order Quantity D = Annual demand (units)S = Cost per order ($)C = Cost per unit ($)I = Holding cost (%)H = Holding cost ($) = I x C
12 EOQ Model Equations D = Demand per year S = Setup (order) cost per orderH = Holding (carrying) costd = Demand per dayL = Lead time in days
13 EOQ Example You’re a buyer for SaveMart. SaveMart needs 1000 coffee makers per year. The cost of each coffee maker is $78. Ordering cost is $100 per order. Carrying cost is 40% of per unit cost. Lead time is 5 days. SaveMart is open 365 days/yr.What is the optimal order quantity & ROP?
14 SaveMart EOQ EOQ = 80 coffeemakers D = 1000 S = $100 C = $ 78 I = 40% H = C x IH = $31.20EOQ = 80 coffeemakers
15 SaveMart ROP ROP = 2.74 x 5 = 13.7 => 14 ROP = demand over lead time= daily demand x lead time (days)= d x lD = annual demand = 1000Days / year = 365Daily demand = 1000 / 365 = 2.74Lead time = 5 daysROP = 2.74 x 5 = 13.7 => 14
16 Average (Cycle Stock) Inventory SaveMartAverage (Cycle Stock) InventoryAvg. CS = OQ / 2= 80 / 2 = 40 coffeemakers= 40 x $78 = $3,120Inv. CC = $3,120 x 40% = $1,248Note: unrelated to reorder point
17 Economic Order Quantity D = Annual demand (units)S = Cost per order ($)C = Cost per unit ($)I = Holding cost (%)H = Holding cost ($) = I x C
18 What if … Interest rates go up ? Order processing is automated ? Warehouse costs drop ?Competitive product is introduced ?Product is cost-reduced ?Lead time gets longer ?Minimum order quantity imposed ?