ABSTRACT

This article considers single-machine problems in which the actual processing time of a job is a function of its position in a sequence (i.e. position-dependent deterioration effects). In this model, a job is either accepted or rejected. If the job is accepted, it is processed on a single machine, but if the job is rejected, a penalty (cost) is imposed. The goal is to minimize the sum of the given scheduling objectives, including the makespan, the total completion time, the total absolute differences in completion times and the total absolute differences in waiting times of the accepted jobs and total rejection penalty of the rejected jobs. It is illustrated that these problems remain polynomially solvable under the proposed models. Finally, computational results demonstrate that the proposed algorithms can solve instances of various size problems in attractive times. An extension to the problems is offered by assuming time-dependent deterioration effects.

摘要

本文考虑单机问题，其中作业的实际处理时间是其在序列中的位置的函数（即位置相关的劣化效应）。在此模型中，作业要么被接受，要么被拒绝。如果作业被接受，它将在单台机器上处理，但如果作业被拒绝，则会施加惩罚（成本）。目标是最小化给定调度目标的总和，包括制造时间、总完成时间、完成时间的总绝对差和已接受作业的等待时间总绝对差以及被拒绝作业的总拒绝惩罚。说明这些问题在所提出的模型下仍然是多项式可解决的。最后，计算结果表明，所提出的算法可以在有吸引力的时间内解决各种规模问题的实例。通过假设时间相关的劣化效应提供了对问题的扩展。