Hybrid approach for a single-batch-processing machine scheduling problem with a just-in-time objective and consideration of non-identical due dates of jobs

In this paper, we study a generalized single-batch-processing machine (SBPM) scheduling problem. Given a set of jobs that differ in terms of size, processing time and due date, the generalized SBPM problem aims to cluster the jobs into batches and process each batch one at a time on a capacitated batch-processing machine such that the total earliness and tardiness of jobs, a just-in-time objective, is minimized. We investigate the intrinsic properties of the optimal solutions of the problem, based on which an effective span-limited tree search (SLTS) heuristic is developed to find the near-optimal solutions to a restricted SBPM problem with a specified processing sequence of jobs. Varying the sequence, we embed the SLTS approach into a self-adapted genetic algorithm to further explore the solution space of the original problem. A hybrid span-limited tree search and genetic algorithm approach is proposed. The results of extensive numerical experiments on various random instances with a common due date and non-identical due dates of jobs demonstrate the effectiveness and efficiency of the proposed approaches in obtaining high-quality near-optimal solutions.