Single-machine Scheduling With Three Influencing Factors And Resource-dependent Processing Time

Single machine scheduling problems are widely involved in many areas of scientific research,engineering computations and manufacturing, such as steel production、 food manufacturing and so on.Recently researchers pay much attention to single machine prob-lems with different influencing factors.Besides resource-consuming is considered in some manufacturing arcas.it is of great interest to figure out resource assignment problem with other factors.This paper considers the single machine scheduling problems with time-dependent deterioration and exponential learning effect and the starting time, i.e. the actual process-ing time of a job depends not only on the processing time of the jobs already processed but also on its scheduled position and its starting time.Here considers a new model and shows that the single machine scheduling problems to minimize the makespan and the total completion time and the sum of the2th power of job completion times are poly-nomial solvable and they can be solved by the smallest processing time first(SPT) rule respectively. It can be proved that the total weighted completion time minimization prob-lem and the maximum lateness minimization problem are polynomially solvable under certain conditions.In the meantime,we simplify this model to consider resource assign-ment problem with deteriorating jobs.It can be classified to assignment problem and the optimal function require O(n3) time.