OMSAN LOJİSTİK

Optimum Quantities for Procurement (Replenishment Methods) Procurement and Supplier Relationship Management Latin America Logistics Center Logistics Management Series

EOQ: Efficient Order Quantity Is the Analytical Calculation of Optimum Quantities to Replenish in any point within the Network Suppliers Production Facilities Replenishment to Customers Delivery Quantities

Supuestos Basicos del Modelo EOQ · Constant Demand Rate · No Constraints on Lot Size · Only relevant costs are holding and ordering/setup · Decisions for items are independent from other items · No uncertainty in lead time or supply

Partial Period Balance Is Ordering in a manner so that Costs of Ordering and Inventory Carrying Costs are kept Equal

Y-Axis Order/run Quantity Total Cost = Ordering Cost + Inventory Carrying Cost Inventory Carrying Cost Ordering Cost Economic Order Quantities EOQ Calculation Flat Curve Around Optimum

Economic Production Quantity

Order Quantity Annual Cost Holding Cost EOQ Model

Order Quantity Annual Cost Holding Cost Order (Setup) Cost EOQ Model

Order Quantity Annual Cost Holding Cost Total Cost Curve Order (Setup) Cost Optimal Order Quantity (Q*) EOQ Model

EOQ Formula Derivation D = Annual Demand (units) C = Unit Cost ($) Q = Quantity per Order (units) S = Cost per Order ($) I = Inventory Carrying Rate (%) H = Carrying Cost ($) = I x C Number of Orders = D / Q Ordering Cost = S x (D / Q) Average Inventory Units = Q / 2 $ = (Q / 2) x C Average Inventory Carrying Cost = (Q / 2) x I x C = (Q /2) x H Total Cost = (Q/2) x I x C + S x (D/Q) carrying cost + ordering cost Take the 1st derivative: d(TC)/d(Q) = (I x C) / 2 - (D x S) / Q² To Optimise: set d(TC)/d(Q) = 0 DS/ Q² = IC / 2 Q²/DS = 2 / IC Q²= (DS x 2 )/ IC Q = sqrt (2DS / IC)

Efficient Order Quantity EOQ = [(2*S*D)/(I*C)] 1/2 EOQ = Economic Order S = Cost to place one order ($/order) D = Annual Demand (units/yr) I = Inventory Carrying Rate (%/yr) C = Unit Cost ($/unit)

EOQ: Equations of the Model Optimum Quantity Number of Orders N* Time Between Orders /       Q DS H D Q T N d D ROPdL * * 2 D = Annual Demand S = Setup Cost (order) H = Inv. Carrying Cost d = Demand per Day L = Lead Time (days) Working Days Year / Working Days Year

EOQ Example You are the buyer of SaveMart Stores. SaveMart needs 1000 coffee makers per year. The cost of each coffee maker is $78. The cost to place one order is $100. Inventory carrying rate is 40%. The Lead Time is 5 days. SaveMart opnes 365 days/yr. What is the Economic Order Quantity (EOQ) and the Reorder Point (ROP)?

× Solution EOQ* ()()() ()() ()() Q DS H d D ROPdL *.... = ×× == === === unidades /day unidades / Dias LaboralesAñoAño

Cost to Place one Purchase Order Stationery Deliver the PO Communications Authority Entering the PO Processing the PO Inspecting the PO Tracking the PO Staff Procurement Dept. Office Space Materials

Supply Costs

Automatic Calculation of EOQ

Ordering Cost Reduction Blanket Orders (Fixed Quantity Order) Joint Replenishment Cycles Procurement Cards Vendor Managed Inventory (VMI) Delivery Programs Anticipated Supply Notice (ASN) JIT II Supplier puts the order from the Customer’s Warehouse Orders via Internet

Set-Up Cost Reduction Parallel Process (Indy Cars) Just in Time (Toyota) Internal Separation / Interruption for External Requirements Minimise Internal Interruption Requirements Sequential work to reduce change cycles Set-Up cost elimitation with Dedicated Lines Dedicated Factories Practice and Experience Minimise Equipment Brands vs the Lower Bid Cost

Adjusting the EOQ Space Available in Warehouse Number of Orders that Can be Processed Budget Constraints Quantity Discounts

EOQ with Quantity Discounts Example You are the Buyer of SaveMart Stores. You typically buy a Soft drink in cases of 24 bottles. Demand is 10 cases per week. The supplier charges $60/case but offers a discount of 1% for orders greater than 100 cases and an additional discount of 1% for orders greater than 150 cases ($60/case in orders smaller than 100 cases, $58.81 in orders greater than 150 cases and $59.40 in orders between 100 y 150 cases). The cost to place one order is $100. The inventory carrying rate is 40%. What is the Optimal Order Quantity?

Total Cost Order Quantity EOQ with Quantity Discounts

Order Quantity Total Cost Disc. Qty. 1 Base Price Disc. Price 1 EOQ with Quantity Discounts

Order Quantity Total Cost Base Price Disc. Price 1 Disc Price 2 Disc. Qty. 1 Disc. Qty. 2 EOQ with Quantity Discounts

Order Quantity Total Cost Base Price Disc. Price 1 Disc Price 2 Total Base Price Disc. Qty. 1 Disc. Qty. 2 EOQ with Quantity Discounts

Order Quantity Total Cost Base Price Disc. Price 1 Disc Price 2 Total Base Price EOQ Disc. Qty. 1 Disc. Qty. 2 EOQ with Quantity Discounts

Order Quantity Total Cost Base Price Disc. Price 1 Disc Price 2 Total Base Price EOQ Outside of Price Bracket Disc. Qty. 1 Disc. Qty. 2 EOQ with Quantity Discounts

Order Quantity Total Cost Base Price Disc. Price 1 Disc Price 2 Disc. Qty. 2 Total Disc Price EOQ Disc. Qty. 1 EOQ with Quantity Discounts

Order Quantity Total Cost Base Price Disc. Price 1 Disc Price 2 Disc. Qty. 2 Total Disc Price EOQ Disc. Qty. 1 Outside of Price Bracket Outside of Price Bracket EOQ with Quantity Discounts

Order Quantity Total Cost Base Price Disc. Price 1 Disc Price 2 Disc. Qty. 2 Total Disc Price EOQ Disc. Qty. 1 Outside of Price Bracket Outside of Price Bracket EOQ with Quantity Discounts

Order Quantity Total Cost Base Price Disc. Price 1 Disc Price 2 Disc. Qty. 2 Total Disc Price 2 EOQ Disc. Qty. 1 EOQ with Quantity Discounts

Order Quantity Total Cost Base Price Disc. Price 1 Disc Price 2 Disc. Qty. 2 Total Disc Price 2 EOQ Disc. Qty. 1 Outside of Price Bracket EOQ with Quantity Discounts

Order Quantity Total Cost Base Price Disc. Price 1 Disc Price 2 Disc. Qty. 2 Total Disc Price 2 EOQ Disc. Qty. 1 Outside of Price Bracket EOQ with Quantity Discounts

Order Quantity Total Cost Base Price Disc. Price 1 Disc Price 2 Disc. Qty. 2 Disc. Qty. 1 Lowest Cost EOQ with Quantity Discounts

EOQ = [(2 x S x D) / (I x (1-d ) x C)] d = discount rate

Calculate EOQ for Each Discount Level If the Result is not within the offered range? –If not, buy the quantity at the lower discount limit Calculate the Total Cost (order & hold) for each EOQ or the minimum quantity within the discount range Select the minimum quantity with the minium Total Cost EOQ with Quantity Discounts

Periodic Order Quantity (POQ) Periodic Order Quantity derives from the Economic Order Quantity and the Annual Cost POQ denotes the optimal time between orders POQ = EOQ/AD = Optimal Time Between Orders

Economic Time of Supply (ETS) ETS = [(2*S)/(D*C*I)] 1/2 Denotes the Optimal time between orders to Suppliers Is a Direct function of the Cost to Place a Purchase Order Indirect Function of Annual Demand, Inventory cost and its carrying rate

Economic Logistics Quantity (ELQ) ELQ = EOQ +/- –Considerations of Warehousing Capacity –Transportation Capacity –Quantity and Capacity of Pallets –Agreed Quantities –Packing Quantities –etc.

Coordinated and Consolidated Deliveries Savings in Purchasing Costs Savings in Transportation Costs Savings in Ordering Costs Easy to Schedule

Optimising EOQ by SKU