# Switch-Off Policies in Job Shop Controlled by Workload Control Concept
## 3 Research Context  
The proposed switch-off policies in a job shop controlled by workload mechanism were evaluated using the same model introduced in previous studies [25,26] and investigated in many works afterward. The main characteristics of the production system are briefly described below. The job shop consists of six work centers, and each work center includes one machine. The jobs enter the system following a random routing sequence without any preferred routing; then, a statistical processing time for each machine (as described in the simulation experiments section) and a due date are assigned to each job. According to previous works [27,28], all jobs are accepted, and raw materials are always available. Moreover, the main assumptions of the manufacturing system are the following: operations cannot be pre-empted; each machine can process only one task at once; the queues are managed by the Earliest Due Date (EDD) policy to improve the lateness performance; the machining time includes the material handling time; and the handling resources are always available. The notation used is described in the following:  
\begin{tabular}{c c c} \hline \hline  & **Notation** & **Definition** \\ \hline Indices & \(M\) & The number of work centers/machines that compose the manufacturing system \\  & \(m\) & The index of the machines \(m=1,\,\ldots\,\,,M\) \\  & \(i\) & The index of the jobs \\ \hline Parameters & \(PT_{im}\) & The processing time of the job \(i\) in the machine \(m\) \\  & \(\text{a}_{\text{im}}\) & A binary value equal to \(1\) if the job \(i\) must visit the machine \\  & \(m\); 0 otherwise \\  & DD\({}_{1}\) & The due date assigned to the job \(i\) \\  & Seq\({}_{\text{im}}\) & The ordered sequence of the machine \(m\) for the job \(i\) \\  & WLnorm & The norm of the workload control mechanism \\ \hline Computation & WLm & Workload of the machine \(m\) \\ \hline \hline \end{tabular}  
The workload control mechanism applied is a classical approach proposed in the literature [27] following a continuous order release and fixed workload norm according to the following steps. The jobs enter the pre-shop queue of the manufacturing system that is managed according to the Earliest Due Date rule. Then, starting from the first job in the pre-shop queue, the potential workload of each machine added by the job is computed. The potential workload is computed using the corrected aggregate load method [26], as shown in Expression (1):  
\[WL_{m}=WL_{m}+\sum_{m=1}^{M}\frac{PT_{im}*a_{im}}{Seq_{im}} \tag{1}\]  
The corrected workload (Expression (1)) converts the load contribution considering that the processing time of an operation is divided by the position of the corresponding machine in the routing of the job. The potential workload computed supports the decision on the release of the job in the manufacturing system. The job can enter the manufacturing system if the workload of each machine is lower than the workload norm WLnorm. If the job is released, the workload computed as shown in Expression (1) is updated for each work center.  
When job \(i\) leaves a machine, the workload of the machine is updated, as shown in Expression (2):  
\[WL_{m}=WL_{m}-\frac{PT_{im}}{Seq_{im}} \tag{2}\]  
The workload is updated considering the position of the machine in the routing of the job to keep correct the input/output of the workload computation.