Recent advancements in production scheduling have arisen in response to the need for adaptation in dynamic environments. This paper addresses the challenge of real-time scheduling within the context of sustainable production. We redefine the sustainable distributed permutation flow-shop scheduling problem using an online mixed-integer programming model. The proposed model prioritizes minimizing makespan while simultaneously constraining energy consumption, reducing the number of lost working days and increasing job opportunities within permissible limits. Our approach considers machines operating in different modes, ranging from manual to automatic, and employs two real-time scheduling strategies: predictive-reactive and proactive-reactive scheduling. We evaluate two rescheduling policies: continuous and event-driven. To demonstrate the model's applicability, we present a case study in auto workpiece production. We manage model complexity through various reformulations and heuristics, such as Lagrangian relaxation and Benders decomposition for initial optimization as well as four problem-specific heuristics for real-time considerations. For solving large-scale instances, we employ simulated annealing and tabu search metaheuristic algorithms. Our findings underscore the benefits of the predictive-reactive scheduling strategy and the efficiency of the event-driven rescheduling policy. By addressing dynamic scheduling challenges and integrating sustainability criteria, this study contributes valuable insights into real-time scheduling and sustainable production.

中文翻译：

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考虑可持续性标准和实时调度的分布式排列流程

生产调度的最新进展是为了满足动态环境中适应的需要。本文解决了可持续生产背景下实时调度的挑战。我们使用在线混合整数编程模型重新定义了可持续的分布式排列流水车间调度问题。拟议的模型优先考虑最大限度地缩短完工时间，同时限制能源消耗，减少工作日损失并在允许的范围内增加就业机会。我们的方法考虑了以不同模式运行的机器，从手动到自动，并采用两种实时调度策略：预测-反应和主动-反应调度。我们评估两种重新安排策略：连续的和事件驱动的。为了证明该模型的适用性，我们提出了汽车工件生产的案例研究。我们通过各种重新表述和启发式方法来管理模型复杂性，例如用于初始优化的拉格朗日松弛和 Benders 分解，以及用于实时考虑的四种特定于问题的启发式方法。为了解决大规模实例，我们采用模拟退火和禁忌搜索元启发式算法。我们的研究结果强调了预测反应式调度策略的好处以及事件驱动的重新调度策略的效率。通过解决动态调度挑战并整合可持续性标准，这项研究为实时调度和可持续生产提供了宝贵的见解。