Framework

The framework is applied to data on hand and the problem of predicting the learning curves of suppliers. An analysis is performed for each sustainability topic and learning behavior. That means for each sustainability field and learning behavior, learning curve parameters which are determined after fitting learning curve models to the historical evolution of suppliers through-out the assessments are used as dependent variables for the prediction models. Figure 15 illustrates how scores of a sustainability topic can be used for estimating the learning curve parameters.

Figure 15: The applied framework to construct prediction models

As can be seen from Figure 15, there are several variables(parameter 1,...,n) that are needed for constructing the learning curves. The number of parameters that are needed to construct the learning curves depends on the selected learning curve model. Those parameters can be estimated by using non-linear least squares method as the learning curve models are mostly

4.2 Applied Model: Company Case non-linear. In addition to that, since the learning curve parameters are considered as depen-dent variables for the prediction model, there should be a separate prediction model for each learning curve parameters, each learning behavior and each sustainability topic. Supplier char-acteristics of suppliers(xi) are used as independent variables.

For the data-set, as it is explained in the § 3.2.4, there are 124 suppliers (Sequence 3 and Se-quence 4 suppliers) whose learning behavior for each sustainability topic is determined. There-fore, the same supplier set is used for constructing the prediction model for learning curve parameters. As those suppliers are also considered as suppliers who already realized their improvement potentials, their historical sustainability scores can be used while estimating the learning curve parameters. The data-set that is used to construct learning curve parameters and prediction models can be seen in Table 18.

Table 18: Analysis of data used for RQ2

As the indifferent suppliers do not show any significant improvement amounts, a learning curve model cannot be applied to those suppliers. That is why they are excluded from the anal-ysis. After estimating the learning curve parameters which are dependent variables, prediction models are constructed by using the supplier characteristics. Table 3 represents candidate in-dependent variables that can be used to predict the learning curve parameters of the suppliers.

Lean adoption and press freedom cannot be used due to lack of information. In addition to variables that are explained in Table 3, there are also extra independent variables are included in the analysis as Philips keep additional information which can be considered as supplier characteristics. The list of supplier characteristics that are used as independent variables can be seen in Appendix E. Those variables are also used in explaining the learning behavior of suppliers in RQ1. However, since the aim and the dependent variables are different, the same variables can be used to predict other information.

4.2.2 Model

The final prediction models are constructed for parameters that are explained in appendix I.1 for time constant learning curve model. The reasons why those models are constructed and selected can be found in appendix I. Dependent variables or the learning curve parameters such as initial sustainability score, learning rate and maximum improvement potential are es-timated by using non-linear least square method which is explained in Appendix J. Each model is constructed for each sustainability topic and overall sustainability score, and each parameter.

Supplier characteristics are used as independent variables in the models. For each model, root mean squared error(RMSE) value is calculated and compared with each other as performance measure.

4.2 Applied Model: Company Case 4.2.3 Application and Results

When applying the models, hyper-parameter optimization must be conducted to determine optimal parameters for the models. In Appendix K and L, the search space for the model parameters of different models can be found. To prevent over-fitting while determining the model parameters, 10-fold cross-validation is also performed. While constructing the models, the combination of subset 2 and 3 is used as they have enough historical data to construct their learning curves and learning behaviors which are the output of RQ1. Dependent variables on the other hand are estimated from the curve fitting technique. Table 19 represents dependent variables for different learning behaviors.

Table 19: Dependent variables for each learning behavior

As can be seen from the Table 19, there are 2 common dependent variables for each learning behavior except indifferent suppliers: Learning rate and improvement potential. It should be noted that there is an additional dependent variable for lagged fast learner suppliers. It is because the learning curves for lagged fast learner suppliers refer to the evolution process after sequence 2 as they start learning after sequence 2. An illustration of the learning curve of a lagged fast learner supplier can be seen in Figure 16.

Figure 16: Illustration of learning curves of lagged fast learner suppliers

In the Figure 16, part (1) represents the adaptation time of lagged fast learner suppliers for the learning process to be started. Part (2) represents the learning curve where the learning occurs. Therefore, the initial score or sequence 2 score is the additional parameter that needs to be predicted for constructing the learning curve for lagged fast learner suppliers. As the only difference between learning process of lagged fast learner suppliers and fast learner suppliers

4.2 Applied Model: Company Case is that learning process starts from sequence 1 for fast learner suppliers, the learning process starts from sequence 2 for lagged fast learner suppliers, the learning process of fast learner suppliers and lagged fast learner suppliers can be considered same. However, slow learner suppliers have smaller learning rates than lagged fast learners and fast learners. That is why 2 different models can be used for different learning behaviors. One is for lagged fast learner and fast learner suppliers, the other one is for slow learner suppliers.

The list of independent variables that are used for predicting the learning curve parameters can be seen in Table 6. They are the same variables that are used in RQ1 as the supplier character-istics do not change. As the pre-processing methods were already applied to the independent variables in RQ1 and explained in Appendix D, it is not necessary to apply them again.

The performances of the models for each sustainability topic and overall sustainability score can be seen in table for ˆy_f (the maximum improvement potential for suppliers). It should be noted that for each topic, separate models for slow learner suppliers are constructed as lagged fast learner suppliers and fast learner suppliers have the same pattern for their learning curves.

Table 20: Performance of models for predicting improvement potential parameter

From Table 20, it can be stated that random forest regressor outperforms XGBoost regressor.

RMSE values change from 0.15 to 0.38 which can be considered as decent performance for prediction of the maximum improvement potential. The highest RMSE value is for business ethics topic and slow learner suppliers. The reason is that the sample size for that model is small. Consequently, the training data can be increased to enhance the performance of the model

The performance of the models when the dependent variable is τ (the rate of learning) can be found in Table 21 for XGBoost regressor and random forest regressor.

By looking at RMSE values for different topics and different learning classes, random forest regressor outperforms in overall sustainability score, environment, health and safety and hu-man capital topic. However, XGBoost regressor slightly outperforms random forest regressor in business ethics topic but the difference can be considered as negligible. The worst perfor-mance obtained for slow learners in business ethics topic. As the data size is relatively small for that data-set, the performance can be increased by including more suppliers for that model.

Due to the time constraint, it was not possible to collect more data for the models. Except the

4.2 Applied Model: Company Case Table 21: Performance of models for predicting learning rate parameter

model for slow learner suppliers in business ethics topic, the performances can be considered as satisfactory for predicting the learning rate.

As mentioned in this section, there is also an additional dependent variable for lagged fast learner suppliers as their learning curve starts at sequence 2. That is why the sequence 2 score must be also predicted to construct the learning curves. The performance of models for each topic when the dependent variable is ˆyc(the initial level of performance) can be found in Table 22.

Table 22: Performance of models for predicting initial score parameter

RMSE values for different topics show that there is also a small difference between the perfor-mance of random forest regressor and XGBoost regressor.

For implementation purposes, random forest regressor is chosen for each topic, each class and each dependent variable as random forest regressor outperforms XGBoost most of the time.

In addition to that, the performance difference is small when XGBoost outperforms random forest regressor.

4.2.4 Conclusions and Recommendation to Philips: Prediction of Suppliers’ Learning Curve