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This study addresses cooperative batch scheduling problems based on both serial batch (s-batch) scheduling and parallel batch (p-batch) scheduling. A mixed-integer linear programming model was formulated to describe such problems and a bid construction scheme (BCS) was developed to solve them. In s-batch and p-batch scheduling, the sheet strips function as both bidders and auctioned resources, with different sheet strips forming different batches over multiple rounds of auctioning. Then, a local search operator is applied to optimize the feasible solutions. Numerical experiments were conducted on a series of randomly generated and real-world instances. The results obtained by the proposed BCS were compared with those obtained by four combinations of existing algorithms and analysed by SPSS. The proposed scheme was able to identify feasible solutions quickly and efficiently, proving its the effectiveness, stability, practicality, and suitability for addressing cooperative batch scheduling problems, especially those corresponding to large-scale instances.

Bid construction scheme based on local search to solve serial–parallel cooperative batch scheduling problems