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Short Questions and Multiple Choices 1. Given an actual demand of 60 for a period when forecast of 70 was anticipated, and an alpha of 0.3, what would the forecast for the next period be using simple exponential smoothing? F = (1-0.3)(70)+0.3(60) = 67 2. Suppose you have been asked to generate a demand forecast for a product for year 2012 using an exponential smoothing method. The forecast demand in 2011 was 910. The actual demand in 2011 was 850. Using this data and a smoothing constant of 0.3, which of the following is the demand forecast for year 2012? A) 850 B) 885 C) 892 D) 925 E) 930 F = (1-0.3)(910)+0.3(850) = 892 Short Questions and Multiple Choices 3. The president of State University wants to forecast student enrollments for this academic year based on the following historical data: 5 years ago ; 15,000, 4 years ago ; 16,000, 3 years ago; 18,000, 2 years ago; 20,000, Last year; 21,000. What is the forecast for this year using exponential smoothing with α = 0.4, if the forecast for two years ago was 16,000? t 1 2 3 4 5 At 15000 16000 18000 20000 21000 Ft 16000 Forecast for last year F5 = (1-α)F4+ α(A4) F5 = 0.6(16000)+0.4(20000)=17600 Forecast for this year F6 = (1-α)F5+ α(A5) F6 = 0.6(17600)+0.4(21000)=18960 17600 Short Questions and Multiple Choices 4. Use exponential smoothing to forecast this period’s demand if = 0.2, previous actual demand was 30, and previous forecast was 35. A) 29 B) 31 C) 34 D) 36 E) 37 F = (1-0.2)(35)+0.2(30) = 34 5. Exponential smoothing is being used to forecast demand. The previous forecast of 66 turned out to be 5 units larger than actual demand. The next forecast is 65. Compute ? F(t+1) = Ft + (At-Ft) 65 66 65 = 66 + (-5) +5 -5 5=1 = 0.2 Short Questions and Multiple Choices 6. A forecast based on the previous forecast plus a percentage of the forecast error is: A) a naive forecast B) a simple moving average forecast F = (1-α)Ft+ α(At) C) a centered moving average forecast t+1 D) an exponentially smoothed forecast Ft+1 = Ft+ α(At-Ft ) E) an associative forecast 7. In exponential smoothing forecasting, using large values of the smoothing coefficient generates forecasts that are more: A) accurate B) responsive C) random Ft+1 = (1-α)Ft+ α(At) D) stable E) level Short Questions and Multiple Choices 8. For what value of α, exponential smoothing becomes naїve method? Ft+1 = (1-α)Ft+ α(At) A) α =0 B) α =0.25 Ft+1 = (At) C) α =0.5 Ft+1 = (1-1)Ft+ 1(At) D) α =0.75 E) α =1 9. For what value of α, exponential smoothing becomes a straight line? Ft+1 = (1-α)Ft+ α(At) A) α =0 B) α =0.25 Ft+1 = Ft C) α =0.5 Ft+1 = (1-0)Ft+ 0(At) D) α =0.75 E) α =1 Problem 1 Given the following demand data Month Feb Mar Apr May Jun Demand 19 18 15 20 18 Jul 22 Aug 20 a) Draw the data. b) Forecast for September using Five period moving average. c) Forecast for September using Exponential smoothing. Alpha is 0.2 and forecast for march was 19. d) Forecast for September using Naïve method e) Compute MAD for Naïve Method and Exponential Smoothing. Which one is preferred? Naïve Method and Exponential Smoothing? f) Forecast for September using Linear Regression (a) Plot the Data Sales (1000) 19 18 15 20 18 22 20 Monthly Sales 25 Sale (1000) 1 2 3 4 5 6 7 Month Feb Mar Apr May Jun Jul Aug 20 15 Monthly Sales 10 5 0 0 2 4 Month 6 8 ( b) Forecast for Sep Using 5 Period Moving Average t 1 2 3 4 5 6 7 At 19 18 15 20 18 22 20 F8 =MA7= (A7+A6+A5+A4+A3)/5 = (20+22+18+20+15)/5 F8 =MA7= 19 (b) Forecast Using 5 Period Moving Average for All Periods t 1 2 3 4 5 6 7 At 19 18 15 20 18 22 20 Moving Average MAt Ft 18 18.6 19 18 18.6 19 (c)Forecast for Sep Using Exponential Smoothing α =0.2 and F(Mar) = 19 t 1 2 3 4 5 6 7 At 19 18 15 20 18 22 20 F3 = (1-α)F2 + α A2 F3 = (0.8)19+ 0.2(18) F3 = 18.8 March is period 2 (c) Forecast for Sep Using α =.2 and F(Mar) = 19 Using the same formula, we compute F4, F5, F6, F7, and finally F8 which is the demand for Sep. 1 2 3 4 5 6 7 At 19 18 15 20 18 22 20 Ft 19 18.80 18.04 18.43 18.35 19.08 19.26 (d) Forecast for Sep Using Naïve Method F8 =A7 F(t +1) =At F8 = 20 Forecast for all periods using Naïve Method t 1 2 3 4 5 6 7 At 19 18 15 20 18 22 20 Ft 19 18 15 20 18 22 20 (e) Which Technique ? When comparing several methods, we need to use the same time horizon for all methods. We need to have actual as well as forecasts for all methods for all periods of MAD computations Here we have Actual for periods 1 to 7; that is 7 periods. Regression can provide us with forecast for periods 1 to ∞ Five period moving average can only provide forecast for periods 6 and 7; that is 2 periods Therefore, to compare all these methods, we can compute MAD only over 2 periods. But two period is not enough. Naïve Method or Exponential Smoothing ? Naïve method forecasts for periods 2 to 7; That is 6 periods Exponential Smoothing for periods 2 to 7; That is 6 periods We can compare NM and ES over 6 periods. (e) Naïve Method or Exponential Smoothing ? Period Actual Naïve Method Expo. Smoothing 2 18 19 19.00 3 15 18 18.80 4 20 15 18.04 5 18 20 18.43 6 22 18 18.35 7 20 22 19.08 NM 1 3 5 2 4 2 ES 1.00 3.80 1.96 0.43 3.65 0.92 2.83 1.96 Better However, we need to keep all methods, because we need more actual data. A MAD computed just 6 periods is not a reliable measure. It is better to have all methods for say 10-20 more periods, and then identify the best method Short Questions and Multiple Choices For what value of alpha the forecast for the next period is equal to 90% of the actual of this period. A) 0.9 B) 0.1 C) 0.5 D) all of the above E) we do not know The larger the α, the larger the number of periods in the moving average. True or false? Why? False Age of data = 1/α α = 0.5 age of data is 2 periods. α = 0.2 age of data is 5 periods. α = 0.1 age of data is 10 periods. Short Questions and Multiple Choices Given the following demand Suppose the forecast for period 2 is equal to the actual for period 1. What is your forecast for period 4 using exponential smoothing Period Demand and α=0.5? 1 300 A) 300 B) 400 C) 500 D) 550 E) none of the above Ft+1 = (1-α)Ft+ α(At) Ft+1 = (1-0.5)Ft+ 0.5(At) Ft+1 = (1/2) Ft+ (1/2) (At) Ft+1 = (Ft+At)/2 F3 = (F2+A2)/2 F3 = (300+500)/2= 400 F4 = (F3+A3)/2 = (400+600)/2 = 500 2 3 500 600 Short Questions and Multiple Choices Given a forecast using a 6 period moving average. What is the average age of data? The last piece (newest piece) of data is only 1 period old. The first piece (oldest piece) of data in a 6 period moving average is 6 periods old. The average age of data is (1+6)/2 = 3.5 If the age of data in exponential smoothing is 1/ α, for what value of α, exponential smoothing performs close to a six period moving average? The age of data in a 6 period moving average is 3.5. The age of data in exponential smoothing is 1/ α. 1/ α = 3.5 α = 1/3.5 α = 0.29