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FORECAST ACCURACY By: Agung Utama INTRODUCTION A forecast is never completely accurate, there will be always deviation from the actual demand. This difference between the foracast and the actual is the forecast error. Although forecast eror is inevitable, the objective of forecasting is that it be as slight as possible. There are different measures of forecast error, including: Mean Absolute Deviation (MAD), Mean Absolute Percent Deviation (MAPD), Cummulative Error (CE), and Error Bias (E). MEAN ABSOLUTE DEVIATION (MAD) MAD is an average of the difference between the forecast and actual demand, as computed by the following formula: MAD= Σ І Dt-Ft I n Where: t =The period number Dt= Demand in period t Ft = The forecast for period t n = The total number of periods I I = Absolute value The smaller the value of MAD, the more accurate the forecast, although viewed alone, MAD is difficult to assess. COMPUTATIONAL VALUES FOR MAD period Demand (Dt) Forecast Ft (α = 0.30) Error (et) (Dt-Ft) 1 37 37.00 - 2 40 37.00 3.00 3.00 3 41 37.90 3.10 3.10 4 37 38.83 -1.83 1.83 5 45 38.28 6.72 6.72 6 50 40.29 9.69 9.69 7 43 43.20 -0.20 0.20 8 47 43.14 3.86 3.86 9 56 44.30 11.70 11.70 10 52 47.81 4.19 4.19 11 55 49.06 5.94 5.94 12 54 50.84 3.15 3.15 49.32 53.38 557 I dt-Ft I Using the data in the table, MAD is computed: MAD=ΣI Dt-Ft I n = 53l39 11 = 4.85 THE MEAN ABSOLUTE PERCENT DEVIATION Measures the absolute error as a percentage of demand rather than per period. As a result, it eliminates the problem of interpreting the measure of accuracy relative to the magnitude of the demand and forecast values, as MAD does. A lower percent deviation implies a more accurate forecast. MAPD = ΣI Dt-Ft I Σ Dt = 53.39 520 = 0.10 or 10% CUMULATIVE ERROR Cumulative error is computed simply by summing the forecast errors, as shown in the formula: E=Σ et A large positive value indicates that the forecast is probably consistently lower than the actual demand, or is biased low. The comulative eror based on the previuos data is simply computed as: E=Σ et = 49.31 AVERAGE ERROR (BIAS) It is computed by averaging the comulative error over the number of time periods The comulative error is interpreted similarly to the comulative error. A positive value indicates low bias, and a negative value indicates high bias. A value close to zero implies a lack of bias. The formula is: Ḗ=Σ et n = 49.32 11 = 4.48 DISCUSSION QUESTIONS a) b) Registration number for a marketing seminar over the past 10 weeks are shown below: Week 1 2 3 4 5 6 7 8 9 10 Registrations 22 21 25 27 35 29 33 37 41 37 Starting with week 2 and ending with week 11, forecast registrations using the naïve forecasting method. Starting with week 3 and ending with week 11, forecast registrations using a two-week moving average. Demand for heart transplant surgery at RSCM has increased steadily in the past few years: Year 1 2 3 4 5 6 Heart Transplant 45 50 52 56 58 ? The director of medical services predicted 6 years ago that demand in year 1 would be 41 surgeries. a) Use exponential smoothing, first with a smoothing constant of 0.6 and then with 1.9, to develop forecasts for years 2 through 6. b) Use MAD criterion, which of the two forecasting methods is best? Given the following data, use least squares regression to derive a trend equation. What is your estimate of the demand in period 7? In period 12? Period 1 2 3 4 5 6 Number 7 9 5 11 10 15