In this investigation, the single-machine scheduling problem with deterioration effects and an optional maintenance activity is explored. Deterioration effect means that the actual processing time of the job is a function of its normal processing time and its starting time. As an optional maintenance activity, the machine will perform a maintenance activity. After the maintenance activity is completed, the machine will return to the initial state, and the job deterioration will start again. The goal is to determine an optimal sequence and the location of the maintenance activity that minimizes some objective functions. We prove that the problem of minimizing the makespan, total completion time, and total absolute differences in completion (waiting) times can be solved in polynomial time \(O(n^4)\), where n is the number of jobs. For the total weighted completion time minimization, if the weights are positional-dependent weights, we prove that the problem can be solved in polynomial time; if the weights are job-dependent weights, this problem is NP-hard. To solve the problem with job-dependent weights, we present the heuristic, tabu search, and branch-and-bound algorithms.

在本次调查中，研究了具有劣化效应和可选维护活动的单机调度问题。劣化效应是指作业的实际处理时间是其正常处理时间和开始时间的函数。作为可选的维护活动，机器将执行维护活动。维护活动完成后，机器将恢复到初始状态，工作恶化将重新开始。目标是确定一个最佳序列和维护活动的位置，以最小化一些目标函数。我们证明了最小化制造时间、总完成时间和完成（等待）时间的总绝对差异的问题可以在多项式时间\(O(n^4)\)中解决，其中n是工作的数量。对于总加权完成时间最小化，如果权重是位置相关的权重，我们证明问题可以在多项式时间内解决；如果权重是与工作相关的权重，则此问题是 NP-hard。为了解决与工作相关的权重问题，我们提出了启发式、禁忌搜索和分支定界算法。