This paper considers the combination of the general sum-of-processing-time effect and position-dependent effect on a single machine. The actual processing time of a job is defined by functions of the sum of the normal processing times of the jobs processed and its position and control parameter in the sequence. We consider two monotonic effect functions: the nondecreasing function and the nonincreasing function. Our focus is the following objective functions, including the makespan, the sum of the completion time, the sum of the weighted completion time, and the maximum lateness. For the nonincreasing effect function, polynomial algorithm is presented for the makespan problem and the sum of completion time problem, respectively. The latter two objective functions can also be solved in polynomial time if the weight or due date and the normal processing time satisfy some agreeable relations. For the nondecreasing effect function, assume that the given parameter is zero. We also show that the makespan problem can remain polynomially solvable. For the sum of the total completion time problem and is the deteriorating rate of the jobs, there exists an optimal solution for ; a V-shaped property with respect to the normal processing times is obtained for . Finally, we show that the sum of the weighted completion problem and the maximum lateness problem have polynomial-time solutions for under some agreeable conditions, respectively.

中文翻译：

---

具有一般处理时间总和和位置相关效应函数的单机调度问题

本文考虑了在单个机器上的一般处理时间总和效应和位置相关效应的组合。一个作业的实际加工时间由所加工作业的正常加工时间与其在序列中的位置和控制参数之和的函数定义。我们考虑两个单调效应函数：非递减函数和非递增函数。我们的重点是以下目标函数，包括makespan、完成时间的总和、加权完成时间的总和和最大延迟。对于非增效应函数，分别针对完工时间问题和完工时间总和问题提出多项式算法。后两个目标函数如果权重或到期日与正常处理时间满足一些合适的关系，也可以在多项式时间内求解。对于非递减效应函数，假设给定参数为零。我们还表明，makespan 问题可以保持多项式可解。对于总完成时间问题和 是工作的恶化率，存在一个最优解 ; 获得了相对于正常处理时间的 V 形属性. 最后，我们表明加权完成问题和最大延迟问题的总和具有多项式时间解 在一些合适的条件下，分别。