The trend towards decentralized production increases the complexity of operational processes. To address the complexity of scheduling in production networks, this paper investigates a centralized solution approach for a distributed permutation flow shop problem. The fundamental model is extended by integrating factory eligibility constraints and options to qualify factories via tool or personnel relocation. Further, costs for emitting carbon emissions due to production, tool transfer, and job delivery are considered. The study focuses on a bi-objective optimization problem, aiming to minimize total weighted tardiness and total cost. Factory-dependent due dates, limited transport capacity and processing time deviation enhance practical relevance. A computational study examines the impact of increased carbon emission prices and limited transfer options. Key findings indicate that scheduling decisions strongly depend on factory and customer locations, factory eligibility, and tool/product weight, emphasizing the importance of considering transportation as a decisive factor in distributed scheduling.