### Forecasting the Unit Cost of a Product with Some Linear Fuzzy Collaborative Forecasting Models

Toly Chen
2012 Algorithms
Forecasting the unit cost of every product type in a factory is an important task. However, it is not easy to deal with the uncertainty of the unit cost. Fuzzy collaborative forecasting is a very effective treatment of the uncertainty in the distributed environment. This paper presents some linear fuzzy collaborative forecasting models to predict the unit cost of a product. In these models, the experts' forecasts differ and therefore need to be aggregated through collaboration. According to the
more » ... experimental results, the effectiveness of forecasting the unit cost was considerably improved through collaboration. Keywords: fuzzy collaborative forecasting; unit cost Prec AR (WT(0.3)) = 0.56 Prec AR (WT(0.6)) = 1.14 Prec AR (FCF(WT(0.3), WT(0.6))) = 0.53 Therefore, the quality of collaboration with respect to the forecasting precision can be evaluated as QoCp MPI,AR (FCF(WT(0.3), WT(0.6))) = max((1.14 − 0.53)/1.14, (0.56 − 0.53)/0.56) = 54%. QoCp API,AR (FCF(WT(0.3), WT(0.6))) = ((1.14 − 0.53)/1.14 + (0.56 − 0.53)/0.56)/2 = 29%. In order to evaluate the forecasting accuracy, the forecasts by the two objects are defuzzified using the center of gravity (COG) method, and then are compared with the actual values: Accu RMSE (WT(0.6)) = 0.31 while in the fuzzy collaborative forecasting method, the forecasts by the two objects are aggregated using the fuzzy intersection and back propagation network approach to generate a single crisp value: Accu MAE (FCF(WT(0.3), WT(0.6))) = 0.06 Accu MAPE (FCF(WT(0.3), WT(0.6))) = 4% Accu RMSE (FCF(WT(0.3), WT(0.6))) = 0.10 Therefore, the quality of collaboration with respect tothe forecasting accuracy can be evaluated as QoCa MPI,MAE (FCF(WT(0.3), WT(0.6))) = max((0.16 − 0.07)/0.16, (0.24 − 0.07)/0.24) = 71%. QoCa API,MAE (FCF(WT(0.3), WT(0.6))) = ((0.16 − 0.07)/0.16 + (0.24 − 0.07)/0.24)/2 = 64%. QoCa MPI,MAPE (FCF(WT(0.3), WT(0.6))) = max((10% − 5%)/10%, (15% − 5%)/15%) = 67%. QoCa API,MAPE (FCF(WT(0.3), WT(0.6))) = ((10% − 5%)/10% + (15% − 5%)/15%)/2 = 58%. QoCa MPI,RMSE (FCF(WT(0.3), WT(0.6))) = max((0.19 − 0.15)/0.19, (0.31 − 0.15)/0.31) = 52%. QoCa API,RMSE (FCF(WT(0.3), WT(0.6))) = ((0.19 − 0.15)/0.19 + (0.31 − 0.15)/0.31)/2 = 36%. Model 2. FCF(Peters(d 1 ), Peters(d 2 )) In this model, both objects use Peters(d), but with different d values to predict the unit cost. In Peters(d), the most precise forecast is associated with the minimum value of d that satisfies the constraints. In addition, the results when d is large often contain the results when d is relatively small. As a result, the benefits of collaboration are not obvious. In the previous example, assuming the d values specified by the objects are 0.3 and 0.5, respectively. The forecasting performances of the two objects are evaluated as Algorithms 2012, 5 460 Prec AR (Peters(0.3)) = 0.48 Prec AR (Peters(0.5)) = 0.68 Accu MAE (Peters(0.3)) = 0.16 Accu MAE (Peters(0.5)) = 0.20 Accu MAPE (Peters(0.3)) = 10% Accu MAPE (Peters(0.5)) = 12% Accu RMSE (Peters(0.3)) = 0.19 Accu RMSE (Peters(0.5)) = 0.25 After collaboration, the forecasting precision and accuracy are both improved: Prec AR (FCF(Peters(0.3), Peters(0.5))) = 0.48 Accu MAE (FCF(Peters(0.3), Peters(0.5))) = 0.07 Accu MAPE (FCF(Peters(0.3), Peters(0.5))) = 6% Accu RMSE (FCF(Peters(0.3), Peters(0.5))) = 0.13 The quality of collaboration in the two aspects can be evaluated as QoCp MPI,AR (FCF(Peters(0.3), Peters(0.5))) = 29%. QoCp API,AR (FCF(Peters(0.3), Peters(0.5))) = 15%. and QoCa MPI,MAE (FCF(Peters(0.3), Peters(0.5))) = 65%. QoCa API,MAE (FCF(Peters(0.3), Peters(0.5))) = 61%. QoCa MPI,MAPE (FCF(Peters(0.3), Peters(0.5))) = 50%. QoCa API,MAPE (FCF(Peters(0.3), Peters(0.5))) = 45%. QoCa MPI,RMSE (FCF(Peters(0.3), Peters(0.5))) = 48%. QoCa API,RMSE (FCF(Peters(0.3), Peters(0.5))) = 40%. respectively. Model 3. FCF(Donoso(k 11 , k 21 , s 1 ), Donoso(k 12 , k 22 , s 2 )) In this model, both objects use Donoso(k 1 , k 2 , s), but with different parameter values to predict the unit cost. This method has more parameters that can be adjusted, so there is a greater degree of freedom, which provides a space for coordination. Assuming in the previous example, the parameter values specified by the two objects are (k 11 , k 21 , s 1 ) = (0.2, 0.8, 0.2) (k 12 , k 22 , s 2 ) = (0.7, 0.3, 0.3) Then their forecasting performances are Prec AR (Donoso(0.2, 0.8, 0.2)) = 0.48 Prec AR (Donoso(0.7, 0.3, 0.3)) = 0.57 Accu MAE (Donoso(0.2, 0.8, 0.2)) = 0.15 Accu MAE (Donoso(0.7, 0.3, 0.3)) = 0.14 Accu MAPE (Donoso(0.2, 0.8, 0.2)) = 9% Accu MAPE (Donoso(0.7, 0.3, 0.3)) = 9% Accu RMSE (Donoso(0.2, 0.8, 0.2)) = 0.17 Accu RMSE (Donoso(0.7, 0.3, 0.3)) = 0.18 Comparatively, the forecasting performance of the fuzzy collaborative forecasting method is