Problem Description: At a manufacturing facility, there are four distinct types of electrical circuits procured, labeled as Parts A, B, C, and D. Their initial step in the production process is the Soldermask process, ensuring they meet specific foundational standards. After successfully undergoing the Soldermask phase, they transition to the second phase: surface finishing. This phase involves specialized machinery tailored to the unique requirements of the parts. For Parts A and B, they are allocated between Finishing Machine One and Finishing Machine Two. The choice between these two machines is based on the current workload; the machine with the lesser number of parts in its queue gets the next batch. Both these machines are identical in function and capabilities. Conversely, Parts C and D are processed on either Finishing Machine Three or Four, once again depending on the lesser queue. Just like the first two, Machines Three and Four are identical to each other, ensuring consistent quality across the board. Upon completion of the surface finishing, the parts are prepared for transport to the next building, designated for packaging. The outputs of Finishing Machines One and Two require 2 minutes for transportation, while the parts from Finishing Machines Three and Four take 1.5 minutes. When it comes to resource availability, Finishing Machine One operates with one resource for the initial 3 hours of the shift, after which a second resource is added for enhanced efficiency. In contrast, Finishing Machine Three runs with a single resource for the first 5 hours and then scales up to two resources for the remainder of the shift, ensuring smooth and uninterrupted operation. Once in the packaging facility, the components are introduced to the final phase before distribution. Two identical packaging machines are on standby. For Packaging Machine One, however, there's an important operational note: it tends to fail after approximately 300 hours of operation. This failure rate comes with a standard deviation of 0.05. When such a failure occurs, the machine's downtime is about 30 minutes, after which it resumes its operation. The choice between the two packaging machines is driven by efficiency: the machine with the lesser number of parts in its queue is selected for the next batch. Quality control remains a top priority in the manufacturing process. After packaging, each batch undergoes rigorous inspection. Approximately 1% of the parts are sent to rework, with the rework process lasting precisely 11 seconds. About 0.05% of the parts are directly disposed of, while the remaining 98.95% are cleared for final distribution or sale, showcasing the facility's commitment to excellence.