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BA 301 Operations Management Spring 2003 Inventory Management Chapter 12

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Determining the Order Size for the A-61 Microprocessor We have 3 suppliers for the A-61 Microprocessor: Intel, Micron, and Minnesota Data Products. All three suppliers have quoted a price of $20 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.

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Types of Inventory Raw material: The A-61 microprocessors and the A-60 motherboard. Work-in-progress: The A-62 motherboard assembly. This is microprocessors (A-61) attached to a mother board (A-60) Maintenance/repair/operating supplies (tools needed to calibrate machinery, toilet paper, etc…) Finished goods (laptop computers)

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The Functions of Inventory To decouple or separate various parts of the production process To provide a stock of goods that will provide a selection for customers To take advantage of quantity discounts To hedge against inflation and upward price changes

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Higher costs –Item cost (if purchased) –Ordering (or setup) cost Costs of forms, clerks wages etc. –Holding (or carrying) cost Building lease, insurance, taxes etc. Difficult to control Hides production problems Disadvantages of Inventory

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Independent versus Dependent Demand Independent demand Independent demand - demand for item is independent of demand for any other item Dependent demand Dependent demand - demand for item is dependent upon the demand for some other item

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Inventory Costs Holding costs Holding costs - associated with holding or carrying inventory over time Ordering costs Ordering costs - associated with costs of placing order and receiving goods Setup costs Setup costs - cost to prepare a machine or process for manufacturing an order

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Holding Costs Obsolescence Insurance Extra staffing Interest Pilferage Damage Warehousing Etc.

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Table 12.1 – Determining Inventory Holding Costs Category Housing costs Material handling costs Labor cost from extra handling Interest costs Pilferage, scrap, and obsolesence Average Holding Cost = 26% Cost as a % of Inventory Value 6% (3 - 10% 3% (1 - 3.5%) 3% (3 - 5%) 11% (6 - 24%) 3% (2 - 5%)

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Ordering Costs Supplies Forms Order processing Clerical support Etc.

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Setup Costs Clean-up costs Re-tooling costs Adjustment costs Etc.

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The Two Basic Questions of Inventory Management How much to order? (Lot Size) –When we place an order for raw materials or component parts from a supplier, what amount should we order? When should we place the order? (Reorder Point) –If we have already determined How much to order, when should the order be placed to insure that we dont stock out?

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Fixed order-quantity models –Economic order quantity –Production order quantity –Quantity discount Probabilistic models Fixed order-period models Help answer the inventory planning questions! © 1984-1994 T/Maker Co. Inventory Models

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Known and constant demand Known and constant lead time Instantaneous receipt of material No quantity discounts Only order (setup) cost and holding cost No stockouts EOQ Assumptions

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Deriving an EOQ Develop an expression for setup or ordering costs Develop an expression for holding cost Set setup cost equal to holding cost Solve the resulting equation for the best order quantity

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More units must be stored if more are ordered. A larger $ value of inventory must be financed and this creates a higher interest charge. Purchase Order DescriptionQty. Microwave Order quantity Purchase Order DescriptionQty. Microwave1000 Order quantity Why Do Holding Costs Increase as Order Size Increases? 1

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Costs are repeated for each order. Example: You need 1000 microwave ovens Purchase Order DescriptionQty. Microwave1 Purchase Order DescriptionQty. Microwave1 Purchase Order DescriptionQty. Microwave1 Purchase Order Description Qty. Microwave 1 1 Order (Postage $ 0.33) 1 Order (Postage $ 0.33) 1000 Orders (Postage $330) Order quantity Purchase Order Description Qty. Microwave1000 Why Order Costs Decrease as Order Size Increase?

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Mathematical Expressions for Holding Costs and Ordering Costs Annual Holding Costs = Average Inventory * Holding Cost per Unit AHC = (Order Size)/2 (Holding Cost/Unit) = Q/2 *H Annual Ordering Cost = Number of time and order is place * Cost per Order AOC = Demand/Order Size * Order Cost = D/Q * S

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

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Back to the A-61 Microprocessors We forecast a demand for 2000 of A-61 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.

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Calculating the Order Size using EOQ EOQ = square root (2D*S/H) EOQ = sq rt (2*2000*200/0.25*20) EOQ = 400 To minimize the annual inventory costs for the A-61 Microprocessors, we would buy in order quantities of 400.

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Calculating the Total Annual Inventory Cost TAIC = Annual Holding Cost + Annual Ordering Cost TAIC = (Q/2)H + (D/Q)S TAIC = (400/2)*5 + (2000/400)*200 TAIC = $1000 + $1000 = $2000 Notice that the AHC and AOC are almost the same.

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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

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Determining the Reorder Point We want to place an order (aka reorder) with a supplier in enough time so that we dont run out of the item before we receive the order. Our lead time with the suppliers of the A-61 Microprocessor is 5 days. How much inventory do we need to have when we reorder so that we wont run out while the order is in process?

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

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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

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Calculating Order Size with Quantity Discounts Minnesota Data Products has sent us the following price information for the A-61 Microprocessor Order Quantity Price each 1 – 400 $20.00 401 – 1600 19.00 1601 & over 18.50 How does this change our Order Size?

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