Bicriteria scheduling problems involving job rejection, controllable processing times and rate-modifying activity
研究单机上同时考虑工作拒绝、可控加工时间和速率修改活动的双目标调度问题，目标是在总完工时间与资源消耗成本之和、总拒绝成本之间寻找权衡，并给出了不同模型的计算复杂性和求解方法。
This paper addresses the bicriteria scheduling problems with simultaneous consideration of job rejection, controllable processing times and rate-modifying activity on a single machine. A job is either rejected, in which case a rejection penalty will be incurred, or accepted and processed on the machine. The rate-modifying activity is an activity on the machine that changes the processing times of the jobs scheduled after the activity. The processing time of a job scheduled after the rate-modifying activity decreases with a job-dependent factor. The processing time of each job can also be controlled by allocating extra resource which is either a linear or a convex function of the amount of a common continuously divisible resource allocated to the job. The objective is to determine the rejected job set, the accepted job sequence, the time (location) of the rate-modifying activity and the resource allocation that jointly find the trade-off between two criteria, where the first criterion is measured as the sum of total completion time and resource consumption cost while the second criterion is the total rejection cost. We consider four different models for treating the two criteria. The computational complexity status and solution procedures are provided for the problems under consideration.