Chapter 03 Forecasting Operation Management KUET IEM 3-1
- 1. 1-1 Presented By Md. Golam Kibria Assistant Professor Dept. of IEM, KUET
- 3. FORECAST: A statement about the future Used to help managers Plan the system Plan the use of the system 1-3
- 4. Forecast Uses Plan the system Generally involves long-range plans related to: Types of products and services to offer Facility and equipment levels Facility location Plan the use of the system Generally involves short- and medium-range plans related to: Inventory management Workforce levels Purchasing Budgeting 1-4
- 5. Assumes causal system past ==> future Forecasts rarely perfect because of randomness Forecasts more accurate for groups vs. individuals Forecast accuracy decreases as time horizon increases I see that you will get an A this quarter. Common Features 1-5
- 6. Elements of a Good Forecast Timely Accurate Reliable Written 1-6
- 7. Steps in the Forecasting Process Step 1 Determine purpose of forecast Step 2 Establish a time horizon Step 3 Select a forecasting technique Step 4 Gather and analyze data Step 5 Make the forecast Step 6 Monitor the forecast “The forecast” 1-7
- 8. Types of Forecasts Judgmental - uses subjective inputs (qualitative) Time series - uses historical data assuming the future will be like the past (quantitative) Associative models - uses explanatory variables to predict the future 1-8
- 9. Judgmental Forecasts (Qualitative) Consumer surveys Delphi method Executive opinions Opinions of managers and staff Sales force. 1-9
- 10. Time Series Forecasts (Quantitative) Trend - long-term movement in data Seasonality - short-term regular variations in data Irregular variations - caused by unusual circumstances Random variations - caused by chance CYCLE- wave like variations lasting more than one year 1-10
- 11. Forecast Variations Trend Irregular variation Cycles Seasonal variations 90 89 88 Figure 3-1 cycle 1-11
- 12. The Forecast of Forecasts Naïve Simple Moving Average Weighted Moving Average Exponential Smoothing ES with Trend and Seasonality 1-12
- 13. Naïve Forecast Simple to use Virtually no cost Data analysis is nonexistent Easily understandable Cannot provide high accuracy 1-13
- 14. NAÏVE METHOD No smoothing of data Period 1 2 3 4 5 6 7 8 Average Demand 74 86 88 Forecast 98 90 change 12 2 1-14
- 15. Techniques for Averaging Moving average Weighted moving average Exponential smoothing 1-15
- 16. Simple Moving Average Smoothes out randomness by averaging positive and negative random elements over several periods n - number of periods (this example uses 4) Period 1 2 3 4 5 6 7 Demand 74 90 100 60 80 90 Forecast 81 82.5 82.5 1-16
- 17. Points to Know on Moving Averages Pro: Easy to compute and understand Con: All data points were created equal…. …. Weighted Moving Average 1-17
- 18. Weighted Moving Average Similar to a moving average methods except that it assigns more weight to the most recent values in a time series. n -- number of periods ai – weight applied to period t-i+1 1 2 3 Alpha Period 1 2 3 4 5 6 7 8 Average Demand 46 48 47 23 40 Forecast 32.70 35.60 a t 1 n t i i 1 i t 1 t A F 0.6 0.3 0.1 1-18
- 19. Exponential Smoothing Simpler equation, equivalent to WMA a – exponential smoothing parameter (0< a<1) ) ( 1 1 1 t t t t F A F F a a 0.1 Period 1 2 3 4 5 6 7 8 Average Demand 74 90 100 60 Forecast 72 72.2 73.98 1-19
- 20. F2 = 37 + (0.30)(37-37) = 37 F3 =37+ (0.30)(40-37) = 37.9 Exponential Smoothing (α=0.30) PERIOD MONTH DEMAND 1 Jan 37 2 Feb 40 3 Mar 41 4 Apr 37 5 May 45 6 Jun 50 7 Jul 43 8 Aug 47 9 Sep 56 10 Oct 52 11 Nov 55 12 Dec 54 ) ( 1 1 1 t t t t F A F F a 1-20
- 21. FORECAST, Ft + 1 PERIOD MONTH DEMAND (a = 0.3) (a = 0.5) 1 Jan 37 – – 2 Feb 40 37.00 37.00 3 Mar 41 37.90 38.50 4 Apr 37 38.83 39.75 5 May 45 38.28 38.37 6 Jun 50 40.29 41.68 7 Jul 43 43.20 45.84 8 Aug 47 43.14 44.42 9 Sep 56 44.30 45.71 10 Oct 52 47.81 50.85 11 Nov 55 49.06 51.42 12 Dec 54 50.84 53.21 13 Jan – 51.79 53.61 Exponential Smoothing (cont.) 1-21
- 22. AFt +1 = Ft +1 + Tt +1 where T = an exponentially smoothed trend factor Tt +1 = (Ft +1 - Ft) + (1 - ) Tt where Tt = the last period trend factor = a smoothing constant for trend Adjusted Exponential Smoothing 1-22
- 23. Adjusted Exponential Smoothing (β=0.30) PERIOD MONTH DEMAND 1 Jan 37 2 Feb 40 3 Mar 41 4 Apr 37 5 May 45 6 Jun 50 7 Jul 43 8 Aug 47 9 Sep 56 10 Oct 52 11 Nov 55 12 Dec 54 T3 = (F3 - F2) + (1 - ) T2 = (0.30)(38.5 - 37.0) + (0.70)(0) = 0.45 AF3 = F3 + T3 = 38.5 + 0.45 = 38.95 T13 = (F13 - F12) + (1 - ) T12 = (0.30)(53.61 - 53.21) + (0.70)(1.77) = 1.36 AF13 = F13 + T13 = 53.61 + 1.36 = 54.96 1-23
- 24. Adjusted Exponential Smoothing: Example FORECAST TREND ADJUSTED PERIOD MONTH DEMAND Ft +1 Tt +1 FORECAST AFt +1 1 Jan 37 37.00 – – 2 Feb 40 37.00 0.00 37.00 3 Mar 41 38.50 0.45 38.95 4 Apr 37 39.75 0.69 40.44 5 May 45 38.37 0.07 38.44 6 Jun 50 38.37 0.07 38.44 7 Jul 43 45.84 1.97 47.82 8 Aug 47 44.42 0.95 45.37 9 Sep 56 45.71 1.05 46.76 10 Oct 52 50.85 2.28 58.13 11 Nov 55 51.42 1.76 53.19 12 Dec 54 53.21 1.77 54.98 13 Jan – 53.61 1.36 54.96 1-24
- 25. Linear Trend Equation b is the line slope. Yt = a + bt 0 1 2 3 4 5 t Y a 1-25
- 26. Calculating a and b b = n (ty) - t y n t2 - ( t)2 a = y - b t n Yes… Linear Regression!! 1-26
- 27. Linear Trend Equation Example t y Week t2 Sales ty 1 1 150 150 2 4 157 314 3 9 162 486 4 16 166 664 5 25 177 885 t = 15 t2 = 55 y = 812 ty = 2499 (t)2 = 225 1-27
- 28. Linear Trend Calculation y = 143.5 + 6.3t a = 812 - 6.3(15) 5 = b = 5 (2499) - 15(812) 5(55) - 225 = 12495-12180 275-225 = 6.3 143.5 Look on page 85 1-28
- 29. Disadvantage of simple linear regression 1-apply only to linear relationship with an independent variable. 2-one needs a considerable amount of data to establish the relationship ( at least 20). 3-all observations are weighted equally 1-29
- 30. Forecast Accuracy Forecast error difference between forecast and actual demand MAD mean absolute deviation MAPD mean absolute percent deviation Cumulative error Average error or bias 1-30
- 31. Mean Absolute Deviation (MAD) where t = period number At = demand in period t Ft = forecast for period t n = total number of periods = absolute value At - Ft n MAD = 1-31
- 32. MAD Example 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 3.15 557 49.31 53.39 PERIOD DEMAND, At Ft (a =0.3) (At - Ft) |At - Ft| At - Ft n MAD = = = 4.85 53.39 11 1-32
- 33. Other Accuracy Measures Mean absolute percent deviation (MAPD) MAPD = |At - Ft| At Cumulative error E = et Average error (E )= et n 1-33
- 34. Comparison of Forecasts FORECAST MAD MAPD E (E) Exponential smoothing (a= 0.30) 4.85 9.6% 49.31 4.48 Exponential smoothing (a= 0.50) 4.04 8.5% 33.21 3.02 Adjusted exponential smoothing 3.81 7.5% 21.14 1.92 (a= 0.50, = 0.30) 1-34
- 35. Forecast Control Tracking signal monitors the forecast to see if it is biased high or low Tracking signal = = (At - Ft) MAD E MAD 1-35
- 36. Tracking Signal Values 1 37 37.00 – – – 2 40 37.00 3.00 3.00 3.00 3 41 37.90 3.10 6.10 3.05 4 37 38.83 -1.83 4.27 2.64 5 45 38.28 6.72 10.99 3.66 6 50 40.29 9.69 20.68 4.87 7 43 43.20 -0.20 20.48 4.09 8 47 43.14 3.86 24.34 4.06 9 56 44.30 11.70 36.04 5.01 10 52 47.81 4.19 40.23 4.92 11 55 49.06 5.94 46.17 5.02 12 54 50.84 3.15 49.32 4.85 DEMAND FORECAST, ERROR E = PERIOD At Ft At - Ft (At - Ft) MAD TS3 = = 2.00 6.10 3.05 Tracking signal for period 3 – 1.00 2.00 1.62 3.00 4.25 5.01 6.00 7.19 8.18 9.20 10.17 TRACKING SIGNAL 1-36
- 37. Sources of forecast errors The model may be inadequate. Irregular variation may be occur. The forecasting technique may be used incorrectly or the results misinterpreted. There are always random variation in the data. 1-37
- 38. End Notes The two most important factors in choosing a forecasting technique: Cost Accuracy Keep it SIMPLE! =FORECAST(70,{23,34,12},{67,76,56}) (if you can…let the computer do it) 1-38