## 6 Case Study  
A bay of a steel reinforcing installation that refers to one of the pilots of FACTLOG project is considered as a case study. The processes performed involve cutting and shaping various diameters of steel reinforcing bar, using various manual or automatic operations. Three types (or families) of final products can be produced: coils, bars and bent bars of different diameters and with different numbers of bents. Coils and bars are produced after a one-stage process, while bent bars need a two-stage process (first cutting and then bending--there is no flexibility between the two stages). For the previously described processes, four machines are available (in parallel) for coil cutting (\(M_{1}\)-\(M_{4}\)), two for bar cutting (\(M_{5}\)-\(M_{6}\)) and three machines (\(M_{7}\)-\(M_{9}\)) for bar bending. Machines performing a type of process are not all identical per stage, as they have different constraints (e.g., maximum size of raw materials that they can process) and production characteristics (e.g., process and speeds). Each machine performs strictly processes of one stage, and setup is necessary before changing the operation type performed in it. Moving equipment (cranes) is used for transportation loading and unloading of parts and products between machines and buffers, but the respective delays are considered negligible. The possible flows of the described process are presented in Figure 3 as a three-stage process, where stages 1 and 2 are completely independent, while the parts receiving the bending process (stage 3) must be already cut to the given dimensions (stage 2). Different types of raw materials are initially available and with respect to the specifications of product characteristics concerning, size, geometry, weight, type of raw material used, etc., can be produced. It is obvious that the production system considered refers to parallel machines and for this case, schedule per machine is necessary in order to construct the \(PN\) model. The main entities considered are the machines of the three production stages according to the specifications provided. In order to build the respective Petri net models of the machines, the jobs under process must be considered. The orders consist of jobs that refer to batches of products with similar characteristics. The main assumptions regarding process modelling and simulation concern the orders that have to be scheduled, as well as the characteristics (batch sizes, processing times in the alternative machines per stage, setup times, etc.) of all jobs. When a job is scheduled, no preemption-interruption is allowed, and no job can be processed by more than one machine at the same time (i.e., job splitting is not allowed). In addition, machines cannot process multiple jobs at the same time, and if a product is flagged as finished, then it cannot be processed again. Finally, raw material availability in all cases is considered infinite. The fundamental structural element of the Petri net model of a machine is the model of a process shown in Figure 4. According to this, the model consists of three places and two transitions between them. The initial place (\(p_{1}\)) refers to the available unprocessed parts (resources), (\(p_{2}\)) describes the available parts that are ready for the process after machine setup has finished, while the final one (\(p_{3}\)) refers to products after the performance of the process. First transition refers to the machine setup and the second one to the performance of the batch process. According to the modelling procedure described, a timed Petri net model for each machine is implemented. In order to do this, the number as well as the sequence of jobs  
Figure 4: Timed PN model of a process with machine setup. Figure 3: Flowchart of the installation. performed in this machine according to the schedule received must be fed from the optimisation algorithm or scheduling rule used. For each job, the structure of Figure 4 is iterated.