Better Heuristics for a Two-Stage Multi-Machine Assembly Scheduling Problem to Minimize Total Completion Time

 We address the two-stage multi-machine assembly scheduling problem to minimize total completion times of all jobs. The first stage consists of m independently working machines where each machine produces its own component. The second stage consists of two independent and identical assembly machines. The processing of a job at the second stage cannot start until its m components, produced by the m machines at the first stage, are complete. This problem has been recently addressed in the literature for which an efficient heuristic, called SAK, was developed for the case when m=2. In this paper, we address the problem for the case m≥2. We propose a hybrid tabu search (HTS) heuristic and show that the overall average error of SAK is more than twice that of HTS while the average CPU time of SAK is five times that of HTS. This clearly indicates that the heuristic HTS is much better than the only existing heuristic available for the problem, i.e., SAK. We also propose two more heuristics, called SDE and NSDE, and show that the overall average error of SDE is about half of that of HTS. Furthermore, we show that the overall average error of NSDE is about one third that of SDE.