A framework for job shop scheduling with stochastic rework and reprocessing in electronics manufacturing

The demand for electronics products is rapidly increasing and customers are looking forward to multi-featured products. Manufacturing of such products are made possible by complex manufacturing and test processes. Products that fail the tests undergo rework, and in several scenarios, reprocessing (retesting), thus increasing their cycle times. The complex nature of the Printed Circuit Board assembly would further increase the rework time, resulting in longer-than-expected cycle times, missing due dates promised to customers and increasing job tardiness. This research focuses on minimizing the Total Weighted Tardiness (TWT) in such job shops. This research develops Mixed-integer Linear Programming models for the single-machine and multi-machine systems for optimal scheduling. The models consider Total Estimated Processing Time (TEPT), a linear combination of processing, rework and reprocessing times, together with their probabilities. The flexibility to accommodate jobs with different rework rates as well as off-line and in-line rework is also provided in the models. However, since even a single-machine TWT minimization problem is NP-hard, this research will propose algorithms with the objective of providing good quality solutions in reasonably short computation time. An Initial Shortest Total Estimated Processing Time (STEPT) algorithm is proposed that categorizes jobs as (i) new jobs, (ii) jobs that underwent off-line rework (waiting to be reprocessed), and (iii) jobs that are waiting for in-line rework and reprocessing. Different preferences are given when processing these job categories and the TEPT is used to process the new jobs. The algorithm is modified (Modified Shortest Total Estimated Processing Time) to further reduce the TWT, and also extended for the multi-machine system. Experiments using the Initial STEPT algorithm on a high-mix-low-volume system suggest that categorizing the jobs and using TEPT reduces the TWT.;Experiments using the MSTEPT algorithm on single-machine and multi-machine high-volume systems indicate the superior performance of the proposed algorithm compared to an optimal solver and commonly used dispatch rules. Comparison of the proposed algorithm with a modified Genetic Algorithm (GA) suggests that while the modified GA performs better for smaller job shops, the proposed algorithm outperforms the GA for larger job shops in terms of solution quality and computation time.