可控准备时间和加工时间的系列分批排序

Single machine serial-batching scheduling with controllable setup time and job processing times

在许多实际生产环境中,工件的加工时间不是固定不变的,由于工人或机器的工作时间较长,其加工工件的效率降低,使得实际的加工时间加长,也就产生了所谓的退化效应。为考察退化效应对工件排序的影响,讨论在退化效应的条件下,研究工件带有可控准备时间和可控加工时间的单机系列批排序问题。在退化效应的条件下,工件的加工时间为它的开始时间的递增函数;所有的工件从一开始就被划分为连续的批次,并在单机上分批进行加工;在每批工件加工前,都有一个依赖于开始时间的准备时间。目标是确定工件的排序,并将其划分成批,从而最小化最大完工时间和最大延误,并且给出最优算法来求解最小化最大完工时间和最大延误问题。

In the actual production environment,we often encounter the situation that the job processing times vary with time.Because operator and machine work for a long time,the machine efficiency is lower,so the actual processing time becomes longer,which produces deterioration effects.In this paper,we study the single machine serial-batching scheduling problem,where both setup and job processing times are controllable by deteriorating effect.With the assumption of deteriorating jobs,the job processing times are described by an increasing function of their starting times.All the jobs are first partitioned into serial batches and then processed on a single serialbatching machine.Before each batch is processed,deteriorating setup time is required.The objective is to determine the optimal sequence of jobs,and partition the jobs in batches to minimize the makespan and the maximum lateness.We present an optimal algorithm to solve the problem of minimizing the makespan and the maximum lateness.