Parallel Machine Scheduling: Processing Rates Dependent on Number of Jobs in Operation
研究作业加工时间随系统中同时处理作业数量变化的并行机器调度问题，发现对于液压动力源常见的速率函数，完工时间与作业分配无关，且使用一台机器即可最小化流程时间。
We treat the class of n job − m machine scheduling problems with job processing times dependent on the number of jobs being simultaneously processed in the system at any point in time. Such systems occur when jobs are assigned to multiple parallel processors driven by a common power source. In situations typical of hydraulic and pneumatic power sources the level of power delivered to each processor is inversely proportional to the number of processors simultaneously at work. Aside from the variable processing rate assumptions, the remaining assumptions on the structure of the system conform to those of the standard identical parallel processor problem without job preemption. Although the standard n job − m machine problem is NP-hard with respect to a makespan measure, this is not the case when our seemingly complicating variable processing rate function, typical of hydraulic power sources, is included. In this case our main results are exceedingly simple. The makespan is found to be independent of the job-machine assignment, and the flowtime is minimized using one out of m processors. When other job processing rate functions or constant switch-over times are considered, then solving the problem becomes increasingly difficult, and the use of multiple processors is recommended. This paper concludes with a description of a real-world problem (scheduling the refueling of navy boats) which motivated this research.