具有维护活动及公共工期的加工时间依赖资源的单机排序问题

Single machine scheduling with job-dependent and maintenance activities and processing time dependent on resources with due-date

研究在工件的提前惩罚、延误惩罚等总费用受限的前提下,最小化资源费用的单机排序问题。所有工件具有一个公共工期,工件的加工时间是关于位置与资源的具有退化效应的凸函数。在加工过程中,存在一次维护活动。考虑维护活动对依赖于资源的加工时间的影响,确定最优资源分配、最优公共工期、最优维护位置及维护持续时间,并给出一个求得最小资源费用的多项式时间最优算法。

In this paper,we study the single machine scheduling problem of minimizing resource costs under the conditions that the earliness,tardiness and other penalties are limited. All the jobs have a common duedate,and the actual processing times are defined by a convex function of their normal processing times,positions and the effect index of deteriorating and resources. There is a maintenance activity in the processing.Considering the effect on the processing time of resource from maintenance,we give the optimal resource allocation,the optimal due-date,the optimal place for maintenance and the lasting time of maintenance. An optimal polynomial time algorithm for the minimum resource cost is given.