Production systems are subject to machine deterioration and resource consumption constraints. The deterioration increases the processing time which leads to an increase in resource consumption. In this study, we investigate and model the behavior of a parallel machine scheduling problem with respect to the processing time. The machine is subject to deterioration and includes two resource consumption constraints. The first resource R₁ controls the processing time so that additional amounts of R₁ decrease the processing time. The second R₂ is controlled by the actual processing time so that R₂ consumption is a linear function of the actual processing time. The increment of R₁ consumption leads to processing time and so R₂ decrement. Solving this problem consists in finding the optimal schedule that will minimize both makespan and resources cost. This paper provides a mathematical programming model. In fact, due to the deterioration effect and the two resource consumptions, solving such a problem may be very difficult and requires a large computational time. In this paper, we introduce a multi objective simulated annealing (MOSA) in order to solve the combinatorial optimization problem related to finding the best combination (machine, job, position, R₁). Literally the best jobs assignment and resources allocation so that makespan and resources cost are minimized. In order to improve the quality of the results we also developed a 2-steps algorithm by decomposing the original problem into two sub problems: an assignment problem and a resources allocation problem. Some simulations were performed to analyze the performances of the two algorithms. The results show that the 2-steps algorithm is very efficient and outperforms MOSA.

中文翻译：

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多目标模拟退火解决具有退化效应和资源消耗约束的相同并行机调度问题

生产系统容易受到机器性能下降和资源消耗的限制。劣化增加了处理时间，这导致资源消耗的增加。在这项研究中，我们针对处理时间调查并建模了并行机器调度问题的行为。机器容易老化，并且包括两个资源消耗约束。第一资源R ₁控制处理时间，使得R _1的附加量减少处理时间。第二R ₂由实际处理时间控制，使得R ₂消耗是实际处理时间的线性函数。R ₁的增量消耗量导致处理时间，因此R ₂减少。解决此问题的方法是找到可以将制造时间和资源成本降至最低的最佳计划。本文提供了一个数学编程模型。实际上，由于恶化效果和两个资源消耗，解决这样的问题可能非常困难并且需要大量的计算时间。在本文中，我们引入了多目标模拟退火（MOSA），以解决与找到最佳组合（机器，作业，位置，R _1）相关的组合优化问题。）。从字面上看，最佳的工作分配和资源分配是为了使制造时间和资源成本最小化。为了提高结果的质量，我们还通过将原始问题分解为两个子问题（分配问题和资源分配问题）开发了一种两步算法。进行了一些仿真，以分析这两种算法的性能。结果表明，两步算法非常有效，优于MOSA。