# Multi-Criteria Optimization in Operations Scheduling Applying Selected Priority Rules
## 4 Experimental Study
### Simulation Model  
The discrete-event simulation model in this study represents a hypothetical partially flexible job-shop production system adopted from [46]. It can be categorized as such a class of production systems that produce smaller numbers of different types of products according to several routings in a one-piece flow way, especially following the lean production concept. Regarding to its flexibility, some operations are only achievable on part of the available machines. The model system has been built to maintain the main characteristics of FJS, which are mentioned in the Section 2.1. It meets the typical demands regarding the jobs and machines assumed in the deterministic flexible job shop scheduling problem [5; 20; 27]:All machines and all jobs are available at time t = 0. * The number of jobs and machines are assumed to be finite;
* a job cannot be processed by two machines at the same time;
* each machine is always accessible for production, i.e., no machine breakdowns or order cancelations are supposed;
* the machine can execute only one operation at a time on any job;
* an operation of a job cannot be performed until its preceding operations are completed;
* once started operation must not be interrupted;
* operation is processed by any machine from a given set;
* the model does not include any assembly operations. The studied model system consisted of six partially interchangeable machines with their input and output buffer [46]. A total of seven types of operations (A, B, C, D, E, F, G) were performed in the production system. The system manufactured four types of products, each with the specified determination of the sequence of four operations (that cannot be interchanged) defined in Table 1.  
Transportation of parts between buffers was ensured by conveyors with sensors that allow identifying every coming part. If the appropriate attribute of a part was detected, then the part was accepted for the next processing. The interchangeability of workplaces according to the operations possible to perform at individual machines in the system is shown in Table 2.  
In this study, we implemented consequently selected priority rules FIFO, EDD, and STR to define the order in which the individual operations will be done. This order was determined by the calculated priority with respect to the rule performing. When implementing priority rule EDD into the simulation model, the priority key for the operation associated with a given job was updated with respect to the earliest due date information. In the case of the STR priority rule, Equation (1) was used for the calculation of the priority. Based on the determined priority rule, the machine always selected the operation that had the highest priority of all. If multiple operations had the same priority, these operations were grouped randomly. If the next operation can be done on different machines, the machine with minimal setup costs was selected to process it. The simulation model was designed and built in such a way that it involved the possibility of choice of priority rule at the start of simulation. After selecting the priority rule by the user, the studied system was fully deterministic. Neither breakdowns due to order cancellations nor machine failures were allowed. All internal parameters, such like operation and setup times, and all costs items were keeping as constants during \begin{table}
\begin{tabular}{c c} \hline
**Product Type** & **Operations Order** \\ \hline
1 & A, G, B, F \\
2 & C, B, D, F \\
3 & D, F, G, E \\
4 & G, E, A, C \\ \hline \end{tabular}
\end{table} 
Table 1: Definition of order operations for coming parts. \begin{table}
\begin{tabular}{c c} \hline
**Workplace Number** & **Possible Operation Performance** \\ \hline
1 & A, C, D \\
2 & A, F, G \\
3 & B, C \\
4 & D, E, G \\
5 & B, F, C \\
6 & E, G \\ \hline \end{tabular}
\end{table} 
Table 2: The interchangeability of workplaces. experiments, too. Most of operation times slightly differed due to the type of processing operation and type of product.