Single batch machine scheduling with dual setup times for autoclave molding manufacturing

Batch scheduling involves a machine that can process several jobs simultaneously. The existing literature mainly focuses on the batch-size-dependent setup time. However, setup time depends not only on the batch size but also on technological characteristics. This paper investigates a single batch scheduling problem with dual quantitative and technological setup times extracted from autoclave molding production. A mixed-integer linear programming model (MILP) is established, in which the objective function is to minimize the makespan. The quantitative setup time is linear with the batch size, whereas the technological setup time is nonlinear with the occupied area of all jobs (jobs are represented by rectangles) in a batch. Three lower bounds are presented for evaluating the proposed algorithms. Then, a two-stage approximate algorithm is designed to solve the problem. The first stage concerns the normal batch processing time. In the second stage, an iterative local search method focuses on all terms in the objective function and improves the current solution’s quality. Finally, different scales of instances are designed to test the effectiveness and efficiency of the algorithms. Statistical analysis shows that the proposed algorithm in this paper can handle the problem well compared to other algorithms.