An improved NSGA-Ⅱ for multi-objective job shop scheduling problems with overtime work consideration

In make-to-order (MTO) manufacturing systems, the workshop capacity is limited due to the production time horizon constraint of the order contract. If the total work load exceeds the shop capacity, a delay incurs, followed by a penalty, costs increasing and loss of customer loyalty. Overtime work is the most common resource to expand shop capacity. However, overtime work is often not used reasonably in the real manufacturing environment. In order to use overtime work optimally, a multi-objective job shop scheduling problem with overtime work consideration (MOJSSP/O) is studied in this paper. An improved NSGA-Ⅱ (INSGA-Ⅱ) algorithm with a two-stage decoding scheme, an adaptive mechanism and a local search procedure is designed to address the problem. The problem-specific two-stage decoding scheme equips the algorithm with the ability to further explore the solution space. The adaptive mechanism can extend the search space and accelerate the convergence speed. Furthermore, the local search procedure is applied to enhance the local exploitation capacity. The objective function of this study is to minimize total tardiness and overtime costs. The proposed algorithm is evaluated on 14 modified benchmarks, and compared with three state-of-the-art multi-objective algorithms. Computational results show that the proposed INSGA-Ⅱ outperforms the other three comparison algorithms on all test instances for balancing the costs of tardiness and overtime.