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Unformatted text preview: 11 Operations Management Class 1: Introduction to OM and Process Analysis Class 2: Process Design Class 3: Process Analysis Class 4 & 5: Process Analysis Class 6: Process Analysis » Shouldice Class 7: Project Management Class 8 & 9: Variability in processes Class 10: Forecasting Class 11: Midterm review Class 12: Midterm exam Class 13: Quality Management and JustInTime/Lean Operations Class 14: Inventory Management: EOQ Class 15: Inventory Management: Lead time and demand uncertainty Class 16: Inventory Management: Risk pooling and Newsvendor 22 Risk Pooling 33 Risk Pooling  Example 1 ◆ Your firm operates in four markets, and you have a warehouse stocking finished goods for each market. Each warehouse experiences daily demand N ( μ , σ ) with mean = 100 & std = 50 ◆ Assuming Service level of 90% (i.e., z=1.28) and a lead time of one, what is the safety stock at each warehouse? ◆ What is total inventory at the four warehouses combined? 44 Risk Pooling  Example 1 ◆ You decide to serve all four markets from a central warehouse. What is the distribution of demand experienced by the warehouse? ◆ What is the total safety stock? 55 Risk Pooling or Demand Aggregation ◆ Independent demand streams impose greater variability when compared to a “pooled” demand stream ◆ Approach: Adding independent random variables ◆ Example Applications: – Component commonality in product design – Portfolio effects in finance – Safety stock 66 The square root rule ◆ Key statistical property: you can add variances but not standard deviations ◆ Use it (for example): – If you are given standard deviation of daily demand and want to calculate standard deviation of weekly demand – If you are given the standard deviation of demand at one location, and want to calculate combined standard deviation over several locations 77 What happens if you sum uncertainty from two locations or products? O bj1 0 O bj1 0 1 Distribution of one random variable Distribution of sum of two identical random variables N (10, 2) N (20, x ) σ σ σ σ Suppose daily demand at one warehouse is normally distributed with mean = 10 and standard deviation = 2 Suppose you combine two identical warehouses into one. What is the mean and standard deviation of demand at the combined warehouse? 88 Risk Pooling  Example 2 ◆ Computer product 1 has hard drive A with daily demand mean = 100 & std = 30 ◆ Computer product 2 has hard drive B with daily demand mean = 300 & std = 40 ◆ Assume order lead time of 1 day ◆ If you want a 98% critical fractile, how much inventory should you keep? (Use z = 2 for 98% service) – For product 1: Inventory = … – For product 2: Inventory = … – Total inventory = … 99 Risk Pooling  Example 2...
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 Spring '09
 Krishnan
 Standard Deviation, ........., Sport Obermeyer

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