This paper presents models and solution algorithms for a two-machine scheduling problem with position-dependent job processing times subject to both aging and maintenance effects. Aiming to minimize the overall makespan for two identical parallel machines, two cases are analyzed. In the first case, no maintenance is scheduled. In the second case, maintenance is scheduled within the job processing sequence, restoring the machine to as-new condition. Assuming the number and the positions of maintenance stops to be variable, machine maintenance and job processing are scheduled simultaneously. Integer linear programming (ILP) models are formulated to determine the optimal maintenance and job processing sequence on each machine. To solve large-size problems, six heuristic solution methods are developed and compared. The maximum delay penalty (MDP) heuristic is best for the no-maintenance case, while the variable neighborhood search (VNS) metaheuristic is best for the with-maintenance case. Both methods quickly produce near-optimal solutions for large-size problems.

本文介绍了双机调度问题的模型和求解算法，该问题具有受老化和维护影响的位置相关作业处理时间。为了最小化两台相同的并联机器的总完工时间，分析了两种情况。在第一种情况下，不安排维护。在第二种情况下，在作业处理序列中安排维护，将机器恢复到新状态。假设维修站的数量和位置是可变的，机器维修和作业处理是同时安排的。整数线性规划 (ILP) 模型用于确定每台机器上的最佳维护和作业处理顺序。为了解决大型问题，开发并比较了六种启发式求解方法。最大延迟惩罚 (MDP) 启发式最适合无维护情况，而可变邻域搜索 (VNS) 元启发式最适合有维护情况。这两种方法都可以快速为大型问题生成近乎最优的解决方案。