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BA 301 Operations Management Spring 2003 Inventory Management Chapter 12 Continued

BA 301 Operations Management Spring 2003 Inventory Management Chapter 12 Continued

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## BA 301 Operations Management Spring 2003 Inventory Management Chapter 12 Continued

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**BA 301Operations Management**Spring 2003Inventory ManagementChapter 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**EOQ ModelHow Much to Order?**Annual Cost Total Cost Curve Holding Cost Curve Order (Setup) Cost Curve Order Quantity Optimal Order Quantity (Q*)**Inventory Level**AverageInventory (Q*/2) Optimal Order Quantity(Q*) Reorder Point (ROP) Time Lead Time EOQ ModelWhen To Order**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**Inventory Level**Production portion of cycle Demand portion of cycle with no supply Time Supply Begins Supply Ends POQ Model Inventory Levels**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 - associated with holding or “carrying” inventory over time • 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?**Inventory Level**AverageInventory (Q*/2) Optimal Order Quantity(Q*) Reorder Point (ROP) Time Lead Time EOQ ModelWhen To Order**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