1. BA 301 Operations Management Spring 2003 Inventory Management Chapter 12 Quantity Discounts

2. Determining the Order Size for Part A-63 (40-Gig Hard Drive) We have 3 suppliers for the 40-Gig hard drive: Intel, Micron, and Minnesota Data Products. All three suppliers have quoted a price of $70 per hard drive. All three quote a 5-day delivery time. We want to determine the amount to order each time we place an order. We also want to determine when to place an order, aka the “reorder point”.

3. Types of Inventory Raw material Work-in-progress (WIP) Maintenance/repair/operating supply Finished goods

4. Order Quantity for the 40 Gig Hard Drive We forecast a demand for 2003 of the 40-Gig hard drives (Part A-63) during the coming year. (D = 2000) Our ordering cost each time we place and order is $200. (S = 200) Our inventory holding cost/year is 25% of the item cost. (H = 0.25 P) All of the assumptions for the EOQ model hold.

5. Calculating the Order Quantity using EOQ EOQ = square root (2D*S/H) EOQ = sq rt (2*2000*200/0.25*70) EOQ = 214 (rounded) To minimize the annual inventory costs for the A-63 (40-Gig hard drive), we would buy in order quantities of 214.

6. Calculating the Total Annual Inventory Cost TAIC = Annual Holding Cost + Annual Ordering Cost TAIC = (Q/2)H + (D/Q)S TAIC = (214/2)*17.50 + (2000/214)*200 TAIC = 1872.50 + 1869.16 = $3741.66 Notice that the AHC and AOC are almost the same.

7. Order Quantity Annual Cost Holding Cost Curve Total Cost Curve Order (Setup) Cost Curve Optimal Order Quantity (Q*) At the Optimal Order Quantity, Annual Holding Costs=Annual Order Costs

8. Determining the Reorder Point We want to “reorder” raw material items so that we don’t run out of the item before we receive the order. Our “lead time” with the suppliers of part A-63 (40-Gig hard drive) is 5 days. At what inventory level do we need to reorder so that we won’t run out while the order is in process?

9. EOQ Model “Reorder Point” Reorder Point (ROP) Time Inventory Level Average Inventory (Q*/2) Lead Time Optimal Order Quantity (Q*)

10. Determining the Reorder Point To calculate the Reorder Point, we have to calculate the demand during lead time (DDLT), i.e. the amount we will use during the five days that the shipment will take to receive after we have placed the order. DDLT = Demand per Day * Lead Time D = 2000, WDPY = 250, Demand per Day = 8 DDLT = 8 * 5 = 40 = Reorder Point

11. Calculating Order Size with Quantity Discounts Minnesota Data Products has sent us the following price information for part A-63, the 40 Gig Hard Drive Order Quantity Price each 1 – 299 $70.00 300 – 999 67.50 1000 & over 66.50 How does this change our Order Size?

12. Since we have Quantity Discounts, the EOQ becomes the starting point for determining order size First, calculate the EOQ for each “Price”. Next, we determine which EOQ is feasible. Order Oty. Price H EOQ Feasible? 1 – 299 $70.00 $17.50 300 – 999 67.50 16.875 1000 & + 66.50 16.62

13. Finding the order quantity that minimizes TAC Order Oty. Price H EOQ Feasible? 1 – 299 $70.00 $17.50 214Yes 300 – 999 67.50 16.875 218No 1000 & + 66.50 16.625 219No Now, calculate the Total Annual Costs for the “feasible” EOQ: TAC = AHC + AOC + Product Cost = (214/2)17.5 + (2000/214)200 + 2000(70) = $1,872.50 + $1,869.16 + $140,000 = $143,741.66

14. Finding the order quantity that minimizes TAC Determine if there are any lower price options than the “feasible” EOQ. If so, calculate the TAC for the lower price option, using the minimum order size necessary to obtain that price. Price = $67.50 Order Qty = 300TAC = ? Price = $66.50Order Qty = 1000TAC = ? Chose the order quantity that minimizes TAC!

15. Finding the order quantity that minimizes TAC Price = $67.50 Order Qty = 300 TAC = (300/2)16.875 + (2000/300)200 + (2000)67.50 = 2,531.25 + 1,333.33 +135,000 = $138,864.58 Price = $66.50Order Qty = 1000 TAC = (1000/2)16.625 + (2000/1000)200 + (2000)66.50 = 8,312.5 + 400 + 132,000 = $141,712.50 What order size would you choose? Other Options?