Modular scheduling of tightly coupled production lines

Optimising productivity of tightly coupled production lines in, for instance, the production printing or semiconductor industry is difficult due to the diversity of products resulting in different product flows, the variety of constraints, and the precise timing required to coordinate multiple tightly coupled machines. A modular setup provides flexibility and cost reduction through reuse of machinery and schedulers. However, the scheduling of a modular production line is challenging as it leads to a distributed decision process where each module has a limited view of the entire system, while local scheduling decisions have a global impact on schedule feasibility. This work proposes a distributed scheduling method for tightly coupled modular sequential production lines where products cannot overtake each other during production. We develop a multi-agent framework in which a system agent propagates timing constraints of the schedulers of different modules. The system agent aims to reach consensus about the handover times of jobs between modules to converge to a globally feasible schedule. The system agent interacts with local agents that interface with local schedulers, allowing the use of existing local schedulers without modification. We illustrate the approach on production lines with multiple re-entrant flow-shop instances with setup times and due dates, which results in a challenging scheduling problem. The performance of the proposed distributed scheduling method is assessed using a monolithic exact scheduler (implemented as a constraint program, not applicable to modular problems) as a reference. It is found to deliver good quality schedules, having only a 1.15 larger makespan on average than the hypothetical optimum provided by the exact scheduler.