An approximate mathematical framework for resource-constrained multistage batch scheduling

A rigorous representation of the multistage batch scheduling problem is often useless to even provide a good feasible schedule for many real-world industrial facilities. In order to derive a much simpler scheduling methodology, some usual features of multistage batch plants should be exploited. A common observation in industry is that multistage processing structures usually present a bottleneck stage (BS) controlling the plant output level. Therefore, the quality of the production schedule heavily depends on the proper allocation and sequencing of the tasks performed at the stage BS. Every other part of the processing sequence should be properly aligned with the selected timetable for the bottleneck tasks. A closely related concept with an empirical basis is the usual existence of a common batch sequencing pattern along the entire processing structure that leads to define the constant-batch-ordering rule (CBOR). According to this rule, a single sequencing variable is sufficient to establish the relative ordering of two batches at every processing stage in which both have been allocated to the same resource item. This work introduces a CBOR-based global precedence formulation for the scheduling of order-driven multistage batch facilities. The proposed MILP approximate problem representation is able to handle sequence-dependent changeovers, delivery due dates and limited manufacturing resources other than equipment units. Optimal or near-optimal solutions to several large-scale examples were found at very competitive CPU times.