## 3 Problem Definition and Solution Method
### Current Status of the System  
Our problem addresses an issue frequently encountered by a company operating in the space sector within its production line. Production in the space sector is carried out in \"clean rooms\" with highly sensitive equipment and qualified personnel. Projects in this sector are consistently impacted by schedule congestion, and any malfunction or production flaw leads to substantial delays in the overall timeline. Figure 2 defines the production process, showing the sequential workflow from order initiation to final approval. The process begins when orders are received from designers, followed by scheduling to allocate resources and define timelines. The technicians conduct production activities as per the work sequence. Once production is completed, the output moves to the quality and functionality control phase. If defects are found, the order is rescheduled for rework, ensuring corrections before final approval. If the product meets quality standards, the order is closed, marking the successful completion of the process. Figure 3 represents the information flow within the production system, detailing how various roles exchange data to ensure a well-coordinated manufacturing process. The Production Planner serves as the central node, receiving information from management and designers while coordinating work with technicians and the Quality Manager and Designer. Management provides the Order Strategy (total weighted tardiness--TWT, number of tardy jobs--NTJ) and project schedule to the Production Planner for execution. Once production is underway, the Production Planner reports back to management with estimated completion times and performance metrics, allowing for oversight and performance evaluation. Designers supply the Bill of Materials (BOM), specifying the type and quantity of required components, which is directed to the Production Planner to facilitate resource  
Figure 2: Production process of company. planning. The Production Planner, after processing inputs from management and designers, generates the work sequence for each machine and forwards it to the technicians, who carry out the production activities. Once production tasks are completed, technicians report the completion time of the works to the Production Planner, signaling that the manufacturing phase is finished. The Quality Manager and Designer then take over by conducting quality and functionality controls based on the completed work. They determine whether production is successful or unsuccessful and provide this information to the Production Planner for rescheduling or finalizing the order. Although the production is precise, in practice no work is perfect or error-free. Miss takes are inevitable in every job where people are involved. For this reason, after the production of the produced electronic boards (Printed Circuit Board-PCB) is completed, they are first subjected to quality control and then to a series of functional tests by the designers. When a problem is encountered in both quality control and functional tests, the PCB returns to the production line and the production plan is shifted. While making this change, no optimization or heuristic method is used, and priority is given to the returned card. PCBs are the fundamental components in production. The parameters taken into consideration are the release date and production time. The release date represents the earliest time components can be assorted, depending on supply availability and design readiness. The production time varies based on the type and quantity of the components on the PCB. The release date is considered deterministic. The production time varies depending on the number of components, and the production time/number of components ratio has a  
Figure 3: Information flow of company. distribution function that can be obtained based on historical data. The production time is considered stochastic. No other work can be conducted on the same machine before the production of a card is finished.