| Over the years people have dedicated to the study of the scheduling problems in areas such as management science,computer science,operations research,In traditional scheduling problems,it is assumed that the job processing times are fixed,but in the actual problem,job processing time may be reduced under the action of a machine maintenance,or due to an appropriate resource allocated to the job made the processing time is shorten.This article main content is as follows.In Chapter 1,we focuses on the practical significance of the problem,the progress of the research at present of scheduling problem and present our works in this paper.In Chapter 2,we mainly study the single machine scheduling problem to minimize resource costs under the conditions that the tardiness,earliness and other penalties are limited.All the jobs have a common due-date,and the actual processing time are defined by a convex function of their normal processing times,positions and the effect index of deteriorating and resources.There is only one maintenance activity in the processing.Considering the effect on the processing time of resource from maintenance,we can 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.By solving assignment problem in time O(n~4) we get the optimal solution.In Chapter 3,we mainly study the single machine scheduling problem with past-sequence-dependent(psd)delivery times and processing time depend on the location.Every job has different slack windows.The actual processing time is related to the location but is not fixed function.The objective is to minimize the total cost of total completion time,makespan,windows,tardiness and earliness.An optimal polynomial time algorithm by solving an assignment problem in time O(n~3) is given.Finally,we summarize this paper and provide a few problems needed to study in the future. |
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