ops mgt 18_Inventory Management_w-o-solutions-1

Uncertain demand to reduce stockouts we add safety

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Uncertain Demand
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To reduce stockouts we add safety stock Receiv e ord er ord er Ti me Ti me Pla ce ord er ord er Lead Time Time Expecte d Lead- time Demand Invento ry Level ROP = Safety Stock + Expecte d LT Demand Order Quantity Q = EOQ Expected LT Demand Safety Stock
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Service level Safety Stock Probability of stock- out Decide what Service Level you want to provide (Service level = probability of NOT stocking out)
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Service level Safety Stock Probability of stock- out Safety stock = (safety factor z)(std deviation in LT demand ) Read z from Normal table for a given service level
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Caution: Std deviation in LT demand Variance over multiple periods = the sum of the variances of each period (assuming independence) Standard deviation over multiple periods is the square root of the sum of the variances, not the sum of the standard deviations!!!
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Average Inventory = (Order Qty)/2 + Safety Stock Receiv e Receiv e ord er ord er Ti me Ti me Pla ce Pla ce ord er ord er Lead Time Lead Time Invento ry Level Order Quanti ty Safety Stock (SS) EOQ /2 Averag e Invento ry
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How to find ROP & Q 1. Order quantity Q = 2. To find ROP, determine the service level (i.e., the probability of NOT stocking out.) Find the safety factor from a z -table or from the graph. Find std deviation in LT demand: square root law. Safety stock is given by: SS = ( safety factor)(std dev in LT demand) Reorder point is: ROP = Expected LT demand + SS 3. Average Inventory is: SS + EOQ/2 2 SD EOQ H = ( ) LT D std dev in LT demand std dev in daily demand days in LT LT = σ = σ
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Example (continued)… Back to the car lot… recall that the lead time is 10 days and the expected yearly demand is 5000. You estimate the standard deviation of daily demand demand to be d = 6. When should you re-order if you want to be 95% sure you don’t run out of cars?
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  • Spring '10
  • CHANG
  • Management, order quantity, Economic Order

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