Single Machine Scheduling Problem With Processing Time Of A Job Dependent Truncated Control Learning Effect

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 mainly introduce the background,the current situation of scheduling problem and present our works in this paper.In chapter 2,we consider a single machine due-window assignment and scheduling problem with general job-dependent truncated learning effect under convex resource constraints.The actual processing time of a job is a function of the resource amount allocated,general job-dependent truncated learning effect and control parameter.The objective is to determine the due-window location and size,the resource assignment and the job sequence to minimize the total cost of the earliness and tardiness of the jobs,the due-window location and size and the makespan under the condition that the total resource amount is limited.In chapter 3,we study a single machine scheduling problem with truncated job-dependent learning effect and deterioration effects and processing time dependent on resource.The actual processing time of a job is a convex function of the resource amount allocated to it.Each job has a slack due-window.The actual processing time of each job depends on a truncated control parameter,the starting time and the resource amount allocated to it.Two single scheduling problems are studied.The first is to minimize total cost of early and tardy job,the start time,size of each due-window,makespan and total completion time,assume that total resource is limited by a given constant.The second is to minimize the total resource cost under the condition that a total objective value is limited by a given constant.We show that the problem is polynomial solvable by transforming this it into an assignment problem.