Forecasting - 4 Forecasting - 3 Demand Pooling Ardavan Asef-Vaziri Based on Operations management: Stevenson Chapter 7 Operations Management: Jacobs, Chase, and Aquilano Demand Forecasting Supply Chain Management: Chopra.
Download ReportTranscript Forecasting - 4 Forecasting - 3 Demand Pooling Ardavan Asef-Vaziri Based on Operations management: Stevenson Chapter 7 Operations Management: Jacobs, Chase, and Aquilano Demand Forecasting Supply Chain Management: Chopra.
Forecasting - 4 Forecasting - 3 Demand Pooling Ardavan Asef-Vaziri Based on Operations management: Stevenson Chapter 7 Operations Management: Jacobs, Chase, and Aquilano Demand Forecasting Supply Chain Management: Chopra and Meindl in a Supply Chain Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 1 Forecasting - 4 Operations Management Session 16: Trend and Seasonality Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 2 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 Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 3 Forecasting - 4 Today’s Lecture An application of the exponential smoothing method Risk-pooling effect again! Trend forecast Seasonal forecast Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 4 Forecasting - 4 Forecasts and Probability Distributions: How many to stock? A firm produces Red and Blue T-Shirts Month/demand January February March April May June July August September October Ardavan Asef-Vaziri 6/4/2009 Red Shirts 909.9 616.7 1073.3 1382.9 1359.5 1519.9 344.9 Blue Shirts 1185.0 546.2 1229.5 1248.7 1337.9 1539.6 1300.8 Measures of Effectiveness 5 Forecasting - 4 Forecasts and Probability Distributions ( = 0.3) Month T-Shirt Demand Forecast January 909.9 February 616.7 909.9 March 1073.3 821.94 April 1382.9 897.348 May 1359.5 1043.014 June 1519.9 1137.96 July 344.9 1252.542 August 929.7 980.2492 September 1328.5 965.0844 674 1074.109 October November Ardavan Asef-Vaziri 6/4/2009 954.0764 Measures of Effectiveness 6 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? Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 7 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 Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 8 Forecasting - 4 Forecasts and Probability Distributions ( = 0.3) Month T-Shirt Demand Forecast AD January 909.9 February 616.7 909.9 293.2 March 1073.3 821.94 251.36 April 1382.9 897.348 485.552 May 1359.5 1043.014 316.4864 June 1519.9 1137.96 381.9405 July 344.9 1252.542 907.6417 August 929.7 980.2492 50.54916 September 1328.5 965.0844 363.4156 674 1074.109 400.1091 October November Ardavan Asef-Vaziri 954.0764 6/4/2009 Measures of Effectiveness 9 Forecasting - 4 How many to stock Suppose the company desires that the probability of not being able to meet demand is 2.5% P( Nov.demand amt.stocked) P( N(954,1.25 MAD) amt.stocked) amt.stocked- 954 P N(0,1) 1.25 MAD Look-up on normal table 0.025 (show using book) amt.stocked- 954 when 1.96 1.25 MAD Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 10 Forecasting - 4 How many to stock Amt.stocked 954 1.96 1.25 MAD implies Amt.stocked 1.961.25 MAD 954 1892 Note that MAD=383 in this example. Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 11 Forecasting - 4 The Forecast for a Blue Products ( = 0.3) January February March April May June July August September October Ardavan Asef-Vaziri 6/4/2009 1185.0 546.2 1229.5 1248.7 1337.9 1539.6 1300.8 1084.4 1211.8 965.6 1185.0 993.3 1064.2 1119.5 1185.1 1291.4 1294.2 1231.3 1225.4 1147.5 638.7429 236.1592 184.5132 218.4141 354.516 9.349969 209.8464 19.48862 259.8598 236.7656 Measures of Effectiveness 12 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. Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 13 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 Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 14 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 Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 15 Forecasting - 4 Forecast for the Aggregate Demand Month/demand January February March April May June July August September October November Red Shirts Blue Shirts Gray Shirts 909.9 1185.0 2094.9 616.7 546.2 1162.9 1073.3 1229.5 2302.8 1382.9 1248.7 2631.6 1359.5 1337.9 2697.5 1519.9 1539.6 3059.5 344.9 1300.8 1645.7 929.7 1084.4 2014.1 1328.5 1211.8 2540.3 674.0 965.6 1639.5 Forecast AD 2094.9 1815.292 1961.535 2162.565 2323.031 2543.976 2274.489 2196.378 2299.549 2101.549 931.9782 487.4767 670.1002 534.888 736.4826 898.2896 260.3722 343.9045 660.0016 613.722 Inventory of Gray = 2102 + 1.96*1.25*614 = 3603 Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 16 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. Ardavan Asef-Vaziri 6/4/2009 Measures of Effectiveness 17