## 3 Modeling of the Station-Sequence Feeding Policy  
In order to analyze how the performance of a mixed model assembly system, working under the station-sequence parts feeding policy, is affected by dynamic time perturbations and variations of the model mix, an assembly line is modeled with the aid of simulation software. The chosen software was Plant Simulation  
The simulation model includes five assembly stations where three different models (M1, M2, and M3) can be assembled. The assembly system, represented in Figure 2, was modeled according to the following set of assumptions:  
* The modeled system is a mixed-model assembly line that includes a buffer between the parts feeding system and each assembly station. This buffer stores the sequences of parts that constitute the \"station sequence\". * There is a buffer along the assembly line between each pair of assembly stations. * The station sequence follows the predicted models mix of the assembly line. * The sequence for each station considers one part for each model at a time. * The time distribution of both the assembly line cycle time and the parts feeding period are considered stochastic with uniform distribution (this assumption will be clarified below once the input parameters of the simulation model are introduced). Reference [10] suggested that the variations of the model mix alongside the perturbations of the timing of the materials supply to the stations can have a significant impact on the performance of the assembly system when the parts feeding policy is the station sequence. Therefore, in order to examine this link in depth, the following parameters were considered as variables in our simulation model:  
* The assembly line cycle time. * The parts feeding period. * The sequences of the model mix. These variables were formalized with the five following inputs of the simulation model (the complete set of notations adopted in the simulation are reported in Table 1):  
* \(ALCT_{i}\), average assembly line cycle time. Figure 2: Representation of the modeled assembly system. \begin{table}
\begin{tabular}{c c c} \hline \hline _Symbol_ & **Description** \\ \hline _id_ = 1,... \(I\) & Simulation scenario ID Index \\ \(n\) = 1,..., \(N\) & Assembly station index \\ _ALCT\({}_{i}\)_ & Assembly Line average Cycle Time of scenario \(i\) [s/piece] \\ _ALCTV\({}_{i}\)_ & Assembly line cycle time variation compared to the average cycle time of scenario \(i\) [\(\pm\)s/piece] \\ _FP\({}_{i}\)_ & Average parts feeding period of scenario \(i\) [s/sequence] \\ _PECTV\({}_{i}\)_ & Parts feeding period variation compared to the average parts feeding period of scenario \(i\) [\(\pm\)s/sequence] \\ _PEQ\({}_{i}\)_ & Parts fed for each feeding period [parts/feeding period] \\ _SEQ\({}_{i}\)_ & Models sequence of scenario \(i\) \\ _PPSEQ\({}_{i}\)_ & Parts feeding sequence of scenario \(i\) \\ _BS\({}_{n,i}\)_ & Maximum parts quantity within the parts buffer for station \(n\) of scenario \(i\) [pieces] \\ _BS\({}_{i}\)_ & Total Maximum parts quantity within the parts buffers of scenario \(i\) [pieces] \\ _W\({}_{n,i}\)_ & Working time for station n of scenario \(i\) [\%] \\ _THR\({}_{i}\)_ & Total throughput during the simulation period of scenario \(i\) [pieces] \\ _MinBS_ & Minimum value of the total buffer content [pieces] \\ _Max_ & Maximum value of the total throughput [pieces] \\ _W\({}_{i}\)_ & Average stations working time of scenario \(i\) [\%-100] \\ _T\({}_{i}\)_ & Relative total throughput [\%-100] \\ _B\({}_{i}\)_ & Relative total Buffer Content [\%-100] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Adopted notations.