A matheuristic for lot-streaming scheduling in a flexible job shop with variable sublots and intermingling settings

A multi-variety and variable-batch production mode enhances manufacturing systems’ flexibility and efficiency, satisfying personalised demands while adapting to ever-shortening product life cycles. Within this context, the lot-streaming flexible job shop scheduling problem (LSFJSP) has become very popular. Existing studies mainly focus on variable sublots, while the intermingling setting for sublot processing–allowing sublots of one operation to be interrupted by those of another–has received scant attention, despite its notable effectiveness in achieving more flexible scheduling schemes. This paper incorporates variable sublots with an intermingling setting into LSFJSP and formulates the resulting problem (LSFJSP-VI) with a mixed-integer programming model. In response to the high complexity of LSFJSP-VI, a matheuristic method based on a memetic algorithm with variable-length individuals is proposed, enhanced by both problem-level and algorithm-level decompositions. The problem-level decomposition involves four designed MILP-based strategies, with each resolving a specific sub-problem of LSFJSP-VI. Further, at the algorithm level, each operation is applied only to the selected promising part of the solution for its designated sub-problem, i.e. relaxed sublots, with the remaining part (non-relaxed sublots) left unchanged. Extensive experiments based on the well-known Fdata and Brandimarte benchmarks confirm the method's effectiveness and efficiency, and a real-world industrial case further demonstrates its applicability and superiority.