BA 301 Operations Management Spring 2003 Inventory Management Chapter 12 Continued

Calculating Order Size When material is ordered from a supplier outside the firm, use the EOQ model and extend this with “quantity discount” information when appropriate. When sub-assemblies are fabricate within the firm, use the Production Order Quantity (POQ) model

Order Quantity Annual Cost Holding Cost Curve Total Cost Curve Order (Setup) Cost Curve Optimal Order Quantity (Q*) EOQ Model How Much to Order?

EOQ Model When To Order Reorder Point (ROP) Time Inventory Level Average Inventory (Q*/2) Lead Time Optimal Order Quantity (Q*)

Production Order Quantity Part A-60 is a “sub-assembly”. It is a platform for the computer “motherboard”. The company requires 3000 of these per year. This part is fabricated in the production facility. The machine that fabricates the platform (A-60) can make 30 per day. Two hours of labor time are required to do the set-up for the fabricating machine. Labor time costs $100 per hour

POQ Model Inventory Levels Inventory Leve l Time Supply Begins Supply Ends Production portion of cycle Demand portion of cycle with no supply

POQ continued The item cost of the platform (A-60) is $20. The holding cost is 25% of the item cost. What is the “Order Quantity”?

Inventory Costs for Production Order Quantity Holding costs Holding costs - associated with holding or “carrying” inventory over time Setup costs Setup costs - cost to prepare a machine or process for manufacturing an order

Setup Costs Clean-up costs Re-tooling costs Adjustment costs These costs are primarily determined by the labor time necessary to perform the tasks.

POQ continued We need to derive a formula that minimizes the Total Cost (Annual Holding Cost + Annual Set- up Cost). Differences between POQ situation for the A- 60 platform and the EOQ situation for the A-61 microprocessor: We fabricate the item rather than purchase it from a supplier. We use the item while it is being made. This results in a difference in the maximum inventory.

POQ continued In the EOQ model, maximum inventory was equal to the Order Size. In the POQ model, maximum inventory is less than the Order Size. Why? Because we make the item and use it while it is being made. Assume that the Order Size is 300. –How long would it take to make this order? –What would the inventory level be at the end of the first day? –What would the inventory level be when we had finished the order? –How can we use this information to derive a general formula for Production Order Quantity?

EOQ Model When To Order Reorder Point (ROP) Time Inventory Level Average Inventory (Q*/2) Lead Time Optimal Order Quantity (Q*)

POQ Model Inventory Levels Time Inventory Level Production Portion of Cycle Max. Inventory Q·(1- d/p) Q* Supply Begins Supply Ends Inventory level with no demand Demand portion of cycle with no supply

POQ continued Maximum Inventory = (p-d)(# days production) This is the inventory build-up rate (p-d) times the number of days the fabrication machine makes the part. Let “# days production” = t (for “time”) Maximum Inventory = (p-d)t = pt-dt Order Size = Q = pt; t = Q/p Max Inv Level = (p-d)(Q/p) = p(Q/p) – d(Q/p) = Q – Q(d/p) = Q(1 - d/p) Ave Inv Level = Q(1 – d/p)/2

POQ continued The Production Order Quantity formula: Q* = POQ = sq.rt.(2DS/(H(1-d/p)) See formula 12.7 on page 491 For part A-60: POQ = sq.rt.(2x3000x200/(5(1-10/30)) POQ = 600 (rounded) Calculate AHC, ASC, & Total Annual Cost