## 4 Computational Experiments and Results
### Tuning of Production Systems' Parameters  
In this section, the buffer size for each product model is optimized using the Taguchi method [37]. Different buffer sizes are allocated for each product model in each experiment  
Figure 4: The scheduling results of the product models for each customer based on NEH, CDS, and heuristic based on the DBR method. Figure 5: Order releasing and multi-item scheduling in the rolling three day planning horizon. Figure 6: NP results for each category of problem in different scenarios. to test if the considered buffer sizes can complete customer orders on time. These buffer sizes for each product model are the parameters of the production systems which are required to be optimized. For each product model, different levels are considered here which show the buffer size. These levels are made to test various sets of experiments by combining different levels of these parameters. Product models A, B, C, D, and E have buffer sizes of {30, 45, 60}, {30, 40, 50}, {40, 55, 70}, {40, 45, 55}, and {35, 50, 65} for levels 1, 2, and 3, respectively. The Taguchi method is used in the current study for tuning the system parameters to determine the optimal level of the buffer sizes of each product model. The Taguchi design set of experiment defines levels of the parameters. Buffer size of each product is considered as one experimental parameter for each product model. Therefore, five parameters are taken in the design of the experiment and, for each parameter, three different levels are considered. It contains a total of 27 experiments with different combinations of parameter levels. Signal-to-noise S/N ratio is used to determine the value of the objective function and its variance ratio, which can be used to determine the optimal levels of parameters. In the current experiment design, each problem is tested according to different levels of parameters and the corresponding value of the objective function is computed for each experiment. Once the problem is tested according to the parameters given by the 27 experiments, the mean value of the objective for each parameter is computed for all problems. For example, the mean value of objectives for the parameter 'buffer size for product model A' at level 1 is obtained from the first nine experiments. Similarly, mean value for parameter 'buffer size for product model A' at level 2 is calculated by taking the average of objective values obtained from the next nine experiments. A similar procedure is employed to obtain the mean value of the objective against each parameter for each level. After that, the mean of means for each level of problems is computed. Furthermore, the measured values that are obtained through experiments are transformed into a signal-to-noise (S/N) ratio. This ratio indicates the amount of variation in the response variable. Based on the current scheduling problem features, the current research applies nominal-is-best. The considered S/N value is calculated using Equation (15):  
\[{(S/N)}_{nominal}=10 log\bigg{(}\frac{mean^{2}}{Variance^{2}}\bigg{)} \tag{15}\]  
where \((mean)^{2}\) and \((variance)^{2}\) indicate the mean and the variance value of the optimizing objective. \(S/N\) values for the considered objective are calculated according to the experiments designed based on the Taguchi method. Then, the mean values of \(S/N\) of each objective for all levels of parameters are computed. In the current case, the level of parameter that gives a higher value of the optimizing objective is preferred because of the maximization objective function. Moreover, the level of parameter at which the maximum value of \(S/N\) is obtained is preferred. In the current study, a total of six problem categories based on the demand and due dates are considered and investigated to tune buffer sizes for each product model. Each problem category is tested on ten different customer demand scenarios. Each scenario is tested against 27 experiments as designed in an OA array.