## 4 Computational Experiments and Results
### Performance of the Proposed Heuristic Method
#### 4.1.1 Data Generation for Problem Instances  
The specifications of required data for all the considered problems are as follows:  
* Processing times of product models on each machine are made from DU [5; 35]. Figure 3: Order release mechanism based on DBR. Defining proper due dates can positively affect the performance [35; 36]. Two different factors are introduced to define due dates: tardiness factor (T) and due date range factor (R). The tardiness factor (T) is used to create loose or tight due dates, and \(T\) is defined as \(T=1-\overline{d}/C_{max}\), where \(\overline{d}\) is the average due date and \(C_{max}\) is the maximum completion time of all jobs. \(C_{max}\) is considered as the sum of processing time of the demand of product models that are received and that are to be processed from the previous planning horizon in the current planning horizon. The due date range factor (R) decides the variability of due dates. The range factor (R) is equal to \((d_{max}-d_{min})/C_{max}\), where \(d_{min}\) is the minimum due date among all customer orders of the product models, and \(d_{max}\) is the maximum one in a planning horizon \(\tau\). Different combinations of \(T\) and R can provide different characteristics for randomly generated due dates. In current research, the values of \(T\) are considered as 0.85, 0.75, and 0.7 for tight due dates for TS, TM, and TL problems, respectively. Moreover, the values of \(T\) are considered as 0.6, 0.5, and 0.4 for loose due dates for LS, LM, and LL problems, respectively. Furthermore, the value of R is set to 0.6 which can provide due date variances. Then, the due dates are uniformly distributed over the interval \(\left[\overline{d}-R\overline{d},\ \overline{d}\right]\) with probability \(T\) and over the interval \(\left[\overline{d},\ \overline{d}+\left(C_{max}-\overline{d}\right)R\right]\) with probability \((1-T)\). In the current research, there are five serially connected machines in the production shop. NEH and CDS methods which are made to schedule jobs on flow shops are used here to make the schedule of the product models. In the current problem, the customer orders received for one product model is considered as one job with the specific due date. The demand of the customer order that is received in three consecutive days is collectively considered to schedule on five machine flow shops using the NEH and CDS schedule, whereas the customer orders with the respective demand of each product model and due date are scheduled on a daily basis using the proposed heuristic based on the DBR method. NEH, CDS, and proposed heuristic based on the DBR method are coded in Matlab, and all the experiments are performed on the same system. The products demand and due date of customer orders vary in six different ranges in each experiment. Different types of problems are considered based here on the demand of product models and due date of orders. The due date of customer orders can be tight with small demand (TS), tight due dates with medium demand (TM), and tight due dates with large demand (TL). Moreover, there are three more possibilities of due dates and customer demands, which includes loose due dates with small product demands (LS), loose due dates with medium demand (LM), and loose due dates with larger demands (LL). This combination of demand and due dates makes six different problems. For each problem, in different situations of the demand and due dates, the buffer size of products is required to be optimized. Therefore, in the current study, the experimental parameters for these aforementioned problems are given in Table 1.  
The example data for one demand scenario of product models in three consecutive days from different customers received for a TS problem is given in Table 2.