Homework 1 - solutions

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Feb 20, 2024

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Problem 1 a) strategic b) operational c) strategic d) tactical e) tactical f) strategic g) tactical h) tactical i) operational j) operational k) tactical Problem 2 Qualitative are appropriate when lacking historical data and have expert input. Useful for new products. Goo Quantitative methos are used when historical data is available and this data is proved to have trends/pattern The main difference is that qualitative methods rely on subjective information (can not be measured) from e

od as a supplement for quantitative methods. ns that can explain the demand experts, while quantitative methods rely on objective numerical data (can be measured)

Forecast from Method 1 Forecast from Method 2 Error (method 1) 223 210 256 33 289 320 340 51 430 390 375 -55 134 112 110 -24 190 150 225 35 550 490 525 -25 Realized values of series (D) Compare the effectiveness of these methods by computing the MSE, the MAD, and the MAPE. Do accuracy indicate that the same forecasting technique is best? If not, why?

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Error (method 2) Error^2 (method 1) Error^2 (method 2) |Error| (method 1) |Error| (method 2) 46 1089 2116 33 46 20 2601 400 51 20 -15 3025 225 55 15 -2 576 4 24 2 75 1225 5625 35 75 35 625 1225 25 35 1523.50 1599.17 37.17 32.17 MSE (method 1) MSE (method 2) MAD (method 1) MAD (method 2) o each of the measures of forecasting

0.12890625 0.1796875 0.15 0.05882352941176 0.14666666666667 0.04 0.21818181818182 0.01818181818182 0.15555555555556 0.33333333333333 0.04761904761905 0.06666666666667 14.12% 11.61% MAPE (method 1) MAPE (method 2) |Error/D|*100 (method 1) |Error/D|*100 (method 2)

Month Demand (a) (b) |Error (a)| |Error (b)| January 89 February 57 March 144 April 221 May 177 June 280 July 223 205.5 149.75 17.5 73.25 August 286 225.25 205.5 60.75 80.5 212 241.5 225.25 29.5 13.25 October 275 250.25 241.5 24.75 33.5 188 249 250.25 61 62.25 December 312 240.25 249 71.75 63 44.21 54.29 The one step ahead forecasts gav (c) MAD (a) MAD (b) (a) Using a four-month moving average, determine the one-step-ahead forecasts for July through December. (b) Using a four-month moving average, determine the two-step-ahead forecast for July through December. (H (c) Compute the MAD for the forecasts obtained in problems (a) and (b). Which method gave better results? B Septembe r Novembe r

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ve better results (and should have according to the theory). Hint: The two-step-ahead forecast for July is based on the observed demands in February through May.) Based on forecasting theory, which method should have given better results?

α = 0.15 0.4 (a) (b) Error^2 (a) Error^2 (b) January 23.3 25 25 February 72.3 24.75 24.32 2261.48 2302.08 March 30.3 31.88 43.51 2.49 174.56 April 15.5 31.64 38.23 260.55 516.53 May 29.22 29.14 841.51 997.72 MSE (a) MSE (b) α = 0.15 gave better forecast (a) If the forecast for January was 25, determine the one-step-ahead forecasts for February through May using expo (b) Repeat the calculation in part (a) for a value of α = .40. What difference in the forecasts do you observe? (c) Compute the MSEs for the forecasts you obtained in parts (a) and (b) for February through April. Which value o

onential smoothing with a smoothing constant of α = .15. of α gave more accurate forecasts, based on the MSE?

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(a) (b) (c) Month S G 2196 500.54 January 133 February 183 March 285 April 640 May 1,876 June 2,550 July 2,150 2614.56 492.34 August 2,660 3039.87 485.64 3525.50 one-step October 4011.14 two-step December 5076.27 α 0.15 β 0.1 Number of Patrons Septembe r Novembe r Use as the initial values of slope (trend) 500.54 and intercept (level) as 2,196 in Holt’s method. Assume that α = .15, β = .10 for all calculations. (a) Suppose that the actual number of visitors using the park in July was 2,150 and the number in August was 2,660. Use Holt’s method to update the estimates of the slope and intercept based on these observations. (b) What are the one-step-ahead and two-step-ahead forecasts that Holt’s method gives for the number of park visitors in September and October? (c) What is the forecast made at the end of July for the number of park attendees in December?

Step 4: Computing deseasonalized f Quarter Demand S G 48.34375 0.5625 Year 1 Q1 12 Q2 25 Q3 76 Q4 52 Year 2 Q1 16 Q2 32 Q3 71 Q4 62 Year 3 Q1 14 Q2 45 Q3 84 Q4 47 Year 4 Q1 18 55.65 50.255 0.765 Q2 Q3 Q4 V1 45.25 V2 47.5 α 0.2 β 0.15 γ 0.1 Step 2: Computing deseasonalized demand (a) Using the data from years 2 and 3, determine initial values of the intercept, slope, and seasonal facto (b) Assume that the observed demand for the first quarter of year 4 was 18. Using α =. 2, β = .15, and γ = (c) What are the forecasts made at the end of the first quarter of year 4 for the remaining three quarters

forecast SF Average for Q1 15.00 Average for Q2 38.50 Average for Q3 77.50 Average for Q4 54.50 Overall average 46.38 0.327 42.3561 86.5403 61.7562 Step 5: Computing the actual forecast ors for Winters’s method. = .10, update the estimates of the series, the slope, and the seasonal factors. s of year 4?

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Step 1: Seasonal Factor SF for Q1 0.3235 SF for Q2 0.8302 SF for Q3 1.6712 SF for Q4 1.1752

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