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.

在本文中，我们研究了广义的单批处理机（SBPM）调度问题。给定一组在大小，处理时间和到期日期方面不同的作业，广义的SBPM问题旨在将这些作业分为多个批次，并在一台功能强大的批次处理机器上一次处理每个批次，以使总提前期和尽量减少工作的拖延，这是即时目标。我们调查问题的最佳解决方案的内在属性，在此基础上发展有效的跨度限制树搜索（SLTS）启发式算法，以找到具有指定处理顺序的受限SBPM问题的近似最优解。通过改变序列，我们将SLTS方法嵌入到自适应遗传算法中，以进一步探索原始问题的解空间。提出了一种混合的跨度有限树搜索和遗传算法。在具有共同的到期日和不相同的到期日的各种随机实例上进行的大量数值实验的结果表明，所提出的方法在获得高质量的接近最优解中是有效的。