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2 Forecasting logistics requirements
2.1 Introduction2.2 Qualitative methods2.3 Quantitative methods2.4 Data preprocessing2.5 Choice of the forecasting method2.6 Advanced forecasting method2.7 Accuracy measure and forecasting monitoring2.8 Interval forecasts2.9 Case study: Forecasting methods at Adriatica Accumulatori
2.10 Case study: Sales forecasting at Orlea2.11 Questions and problems
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Accuracy measures (4/7)
Regens BookWe want to assess the accuracy of the elementary technique, ofthe moving average (with r = 2), of the weighted moving averageand of exponential smoothing (α= 0.1) methods in the RegensBook example, introduced in Section 2.5.4.1. The results of thefour forecasting methods are reported in Table 2. On the basisof the accuracy measures shown in Table 3, we can state that allthe methods provide good-quality forecasts. In particular, themost accurate technique turned out to be the exponentialsmoothing method (with α= 0.1).
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tuning of the forecasting methods (1/5)- Accuracy measures used to tune the forecasting methods
depending on one or more parameters (like exponentialsmoothing and Winters techniques);
- basic idea: assign the parameters the values that wouldhave maximized the accuracy of the forecasts in the past.
Example. By using the mean squared error, the mostsuitable parameter α∗ of the exponential smoothing methodat time period T can be determined as the solution of theoptimization problem:
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tuning of the forecasting methods (1/5)- Accuracy measures used to tune the forecasting methods
depending on one or more parameters (like exponentialsmoothing and Winters techniques);
- basic idea: assign the parameters the values that wouldhave maximized the accuracy of the forecasts in the past.
Example. By using the mean squared error, the mostsuitable parameter α∗ of the exponential smoothing methodat time period T can be determined as the solution of theoptimization problem:
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tuning of the forecasting methods (1/5)- Accuracy measures used to tune the forecasting methods
depending on one or more parameters (like exponentialsmoothing and Winters techniques);
- basic idea: assign the parameters the values that wouldhave maximized the accuracy of the forecasts in the past.
Example. By using the mean squared error, the mostsuitable parameter α∗ of the exponential smoothing methodat time period T can be determined as the solution of theoptimization problem:
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tuning of the forecasting methods (1/5)- Accuracy measures used to tune the forecasting methods
depending on one or more parameters (like exponentialsmoothing and Winters techniques);
- basic idea: assign the parameters the values that wouldhave maximized the accuracy of the forecasts in the past.
Example. By using the mean squared error, the mostsuitable parameter α∗ of the exponential smoothing methodat time period T can be determined as the solution of theoptimization problem:
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tuning of the forecasting methods (1/5)- Accuracy measures used to tune the forecasting methods
depending on one or more parameters (like exponentialsmoothing and Winters techniques);
- basic idea: assign the parameters the values that wouldhave maximized the accuracy of the forecasts in the past.
Example. By using the mean squared error, the mostsuitable parameter α∗ of the exponential smoothing methodat time period T can be determined as the solution of theoptimization problem:
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tuning of the forecasting methods (2/5)
- Number of parameters usually small;- parameters usually bounded in nature;- good approximated solution: through discretization;- δ: parameter to estimate;- A(δ): accuracy measure.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tuning of the forecasting methods (2/5)
- Number of parameters usually small;- parameters usually bounded in nature;- good approximated solution: through discretization;- δ: parameter to estimate;- A(δ): accuracy measure.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tuning of the forecasting methods (2/5)
- Number of parameters usually small;- parameters usually bounded in nature;- good approximated solution: through discretization;- δ: parameter to estimate;- A(δ): accuracy measure.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tuning of the forecasting methods (2/5)
- Number of parameters usually small;- parameters usually bounded in nature;- good approximated solution: through discretization;- δ: parameter to estimate;- A(δ): accuracy measure.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tuning of the forecasting methods (2/5)
- Number of parameters usually small;- parameters usually bounded in nature;- good approximated solution: through discretization;- δ: parameter to estimate;- A(δ): accuracy measure.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tuning of the forecasting methods (4/5)
Regens BookWe want to tune the exponential smoothing method for theRegens Book problem, by utilizing the mean absolute deviationas an accuracy measure.By using αmin = 0, αmax = 1 and ∆= 0.1, we get the deviationsreported in Table 4. On the basis of these results, the mostsuitable value of the forecasting parameter is α= 0.2.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Forecast control
- A forecasting method works correctly if the errors arerandom and not systematic;
- typical systematic errors occur when the variable to bepredicted is constantly underestimated or overestimated, ora seasonal variation is not taken into account;
- forecast control:> aims at identifying systematic errors in periodic
predictions (caused e.g. by a shift in trend) in order toadjust parameters if needed;
> done through a tracking signal or a control chart.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Forecast control
- A forecasting method works correctly if the errors arerandom and not systematic;
- typical systematic errors occur when the variable to bepredicted is constantly underestimated or overestimated, ora seasonal variation is not taken into account;
- forecast control:> aims at identifying systematic errors in periodic
predictions (caused e.g. by a shift in trend) in order toadjust parameters if needed;
> done through a tracking signal or a control chart.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Forecast control
- A forecasting method works correctly if the errors arerandom and not systematic;
- typical systematic errors occur when the variable to bepredicted is constantly underestimated or overestimated, ora seasonal variation is not taken into account;
- forecast control:> aims at identifying systematic errors in periodic
predictions (caused e.g. by a shift in trend) in order toadjust parameters if needed;
> done through a tracking signal or a control chart.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Forecast control
- A forecasting method works correctly if the errors arerandom and not systematic;
- typical systematic errors occur when the variable to bepredicted is constantly underestimated or overestimated, ora seasonal variation is not taken into account;
- forecast control:> aims at identifying systematic errors in periodic
predictions (caused e.g. by a shift in trend) in order toadjust parameters if needed;
> done through a tracking signal or a control chart.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Forecast control
- A forecasting method works correctly if the errors arerandom and not systematic;
- typical systematic errors occur when the variable to bepredicted is constantly underestimated or overestimated, ora seasonal variation is not taken into account;
- forecast control:> aims at identifying systematic errors in periodic
predictions (caused e.g. by a shift in trend) in order toadjust parameters if needed;
> done through a tracking signal or a control chart.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Forecast control
- A forecasting method works correctly if the errors arerandom and not systematic;
- typical systematic errors occur when the variable to bepredicted is constantly underestimated or overestimated, ora seasonal variation is not taken into account;
- forecast control:> aims at identifying systematic errors in periodic
predictions (caused e.g. by a shift in trend) in order toadjust parameters if needed;
> done through a tracking signal or a control chart.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Forecast control
- A forecasting method works correctly if the errors arerandom and not systematic;
- typical systematic errors occur when the variable to bepredicted is constantly underestimated or overestimated, ora seasonal variation is not taken into account;
- forecast control:> aims at identifying systematic errors in periodic
predictions (caused e.g. by a shift in trend) in order toadjust parameters if needed;
> done through a tracking signal or a control chart.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Forecast control
- A forecasting method works correctly if the errors arerandom and not systematic;
- typical systematic errors occur when the variable to bepredicted is constantly underestimated or overestimated, ora seasonal variation is not taken into account;
- forecast control:> aims at identifying systematic errors in periodic
predictions (caused e.g. by a shift in trend) in order toadjust parameters if needed;
> done through a tracking signal or a control chart.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tracking signal (3/7)
PlazaThree months ago, the logistician of the supermarket chainPlaza (in Bolivia) was in charge of devising and monitoringmonthly forecasts for the company’s sportswear items. Thesales of the previous 12 months (in k$) are reported in Table 5.After a preliminary study of the time series, he decided to makeuse of the exponential smoothing method. The optimalsmoothing parameter α was obtained by minimizing MAD12(α).The corresponding solution was α∗ = 0.26 which was associatedwith MAD12(α
∗)= 15.95. The forecasts pt , t = 2, . . . ,12, arereported in the third column of Table 5.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tracking signal (5/7)
PlazaHence, the manager verified that the tracking signal K12 was inthe range [−4,4] (K12 =−1.65). Then, he devised the forecast forthe next month p13 = $ 970.08 k.For the subsequent month (T = 13), the sales turned out to beequal to y13 = $ 1024 k. The associated tracking signal valuewas K13 = 1.44, while the new forecast was p14 = $ 984.22 k.
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Tracking signal (6/7)
PlazaTwo months later (T = 14), the sales were known to bey14 = $ 1035 k; the tracking signal was K14 = 3.63 and theforecast was p15 = $ 997.55 k. Three months later (T = 15), thesales were y15 = $ 1047 k and the relative tracking signal wasK15 = 5.43, out of the feasible range. Thus, the exponentialsmoothing parameter was replaced by α∗ = 0.89, associatedwith MAD15 instead of MAD15(α
∗)= 20.22. The new forecastsare shown in Table 6. The new value of the tracking signal wasK15 = 3.81 and the new forecast was p16 = $ 1045.47 k.
Table 6: Monthly sales of sportsware (in k$) during the first 14 monthsin the Plaza problem and the corresponding exponential smoothingforecasts (with α= 0.89).
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Control charts (5/8)
SoftlineSoftline, a company manufacturing leather sofas, uses themoving average method to forecast (r = 2) the monthly unitproduction cost (assuming sales volume is constant) of its topproduct called Trinity. To assess the forecasting process, thelogistician uses a ‘3-σ’ control chart. Table 7 reports the unitproduction costs as well as the forecasts and the errors madeduring the past two years. The corresponding sample meanerror was
2 Forecasting logistics requirements Accuracy measure and forecasting monitoring
Control charts (7/8)
SoftlineSince this value was a small fraction of a typical monthly unitproduction cost, the forecast was deemed to be unbiased. Thesample standard deviation of the error was computed through(5):
SE =√
MSE24 =e 7.89.
All the errors were in the range of ±3×e 7.89=e 23.67. Hencethe forecasting process was deemed to be under control.Moreover, the visual examination of the chart in Figure 2 did notshow any systematic forecasting error.