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Measures of Effectiveness 1 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Chapter 7 Demand Forecasting in a Supply Chain Forecasting - 3 Demand Pooling Ardavan Asef-Vaziri Based on Operations management: Stevenson Operations Management: Jacobs, Chase, and Aquilano Supply Chain Management: Chopra and Meindl

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Measures of Effectiveness 2 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Operations Management Session 16: Trend and Seasonality

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Measures of Effectiveness 3 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Previous Lecture The importance of forecasting? Forecast Forecast is not a single number Error measure MAD Moving average Exponential smoothing Tradeoff: stability and responsiveness Static Model for trend and Seasonality

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Measures of Effectiveness 4 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Today’s Lecture An application of the exponential smoothing method Risk-pooling effect again! Trend forecast Seasonal forecast

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Measures of Effectiveness 5 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Forecasts and Probability Distributions: How many to stock? A firm produces Red and Blue T-Shirts

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Measures of Effectiveness 6 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Forecasts and Probability Distributions ( = 0.3) MonthT-Shirt DemandForecast January909.9 February616.7909.9 March1073.3821.94 April1382.9897.348 May1359.51043.014 June1519.91137.96 July344.91252.542 August929.7980.2492 September1328.5965.0844 October6741074.109 November954.0764

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Measures of Effectiveness 7 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Forecasts and Probability Distributions Suppose the company stocks 954 T-shirts, the forecasted number. What is the probability the company will have a stockout, that is, that there will not be enough T-shirts to satisfy demand? The company does not want to have unsatisfied demand, as that would be lost revenue. So the company overstocks. Suppose the company stocks 1,026 units. What is the probability that the actual demand will be larger than 1,026?

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Measures of Effectiveness 8 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 There is a Distribution Around the Forecasted Sale Standard Deviation of Error = 1.25 MAD Error is assumed to NORMALLY DISTRIBUTED with A MEAN (AVERAGE) = 0 STANDARD DEVIATION = 1.25* MAD

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Measures of Effectiveness 9 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Forecasts and Probability Distributions ( = 0.3) MonthT-Shirt DemandForecastAD January909.9 February616.7909.9293.2 March1073.3821.94251.36 April1382.9897.348485.552 May1359.51043.014316.4864 June1519.91137.96381.9405 July344.91252.542907.6417 August929.7980.249250.54916 September1328.5965.0844363.4156 October6741074.109400.1091 November954.0764

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Measures of Effectiveness 10 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 How many to stock Suppose the company desires that the probability of not being able to meet demand is 2.5% Look-up on normal table (show using book)

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Measures of Effectiveness 11 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 How many to stock Note that MAD=383 in this example.

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Measures of Effectiveness 12 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 The Forecast for a Blue Products ( = 0.3)

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Measures of Effectiveness 13 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Blue Product Inventory Level The stocking level, of the blue product, for period 11 is: 1148+1.96*(1.25*237)=1728 Recall that: amt. stocked = forecast + 1.96x1.25xMAD implies the probability of not satisfying demand is P( demand > amt. stocked ) = 0.025.

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Measures of Effectiveness 14 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Total Inventory Level The total inventory for Red and Blue is: 1892 + 1728 = 3620 P( Red demand > # of Red T-shirts stocked ) = 0.025 P( Blue demand > # of Blue T-shirts stocked ) = 0.025

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Measures of Effectiveness 15 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Aggregate Forecasts Can we more accurately forecast the combined demand? Suppose we can make Gray Shirt and then dye the T-shirts either red or blue. What is the Demand for Gray Shirts? We look at the sum of the demands in the past We forecast the demand for the two products combined We compute the MAD for the aggregate forecast

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Measures of Effectiveness 16 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Forecast for the Aggregate Demand Inventory of Gray = 2102 + 1.96*1.25*614 = 3603

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Measures of Effectiveness 17 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Aggregate Demand Forecast Conclusions By stocking 3603 Gray T-shirts, we ensure P( T-shirt demand > # stocked ) = 0.025 Otherwise, we needed to stock 1892 blue T-shirts and 1728 red T-shirts for a combined number of 1892+1728 = 3620 T-shirts to ensure that P( red T-shirt demand > # red shirts stocked) = P( blue T-shirt demand > # blue shirts stocked) = 0.025 3603 < 3620 … we need to stock less T-shirts to ensure a given stockout probability (2.5% in this example) when we have an aggregate forecast.

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