Normal Processing Time Of Jobs Research Articles

Single-machine scheduling with sum-of-logarithm-processing-times-based learning considerations

Scheduling with learning effects has attracted growing attention of the scheduling research community. A recent survey classifies the learning models in scheduling into two types, namely position-based learning and sum-of-processing-times-based learning. However, the actual processing time of a given job drops to zero precipitously as the number of jobs increases in the first model and when the normal job processing times are large in the second model. Motivated by this observation, we propose a new learning model where the actual job processing time is a function of the sum of the logarithm of the processing times of the jobs already processed. The use of the logarithm function is to model the phenomenon that learning as a human activity is subject to the law of diminishing return. Under the proposed learning model, we show that the scheduling problems to minimize the makespan and total completion time can be solved in polynomial time. We further show that the problems to minimize the maximum lateness, maximum tardiness, weighted sum of completion times and total tardiness have polynomial-time solutions under some agreeable conditions on the problem parameters.

Single machine scheduling with a time-dependent learning effect and deteriorating jobs

The paper deals with the single machine scheduling problems with a time-dependent learning effect and deteriorating jobs. By the effects of time-dependent learning and deterioration, we mean that the processing time of a job is defined by function of its starting time and total normal processing time of jobs in front of it in the sequence. It is shown that even with the introduction of a time-dependent learning effect and deteriorating jobs to job processing times, the single machine makespan minimization problem remain polynomially solvable. But for the total completion time minimization problem, the classical shortest processing time first rule or largest processing time first rule cannot give an optimal solution.

Single-machine scheduling with a sum-of-processing-time based learning effect and deteriorating jobs

The paper deals with the single-machine scheduling problem with a sum-of-processing-time- based learning effect and deteriorating jobs. By the effects of sum-of-processing-time-based learning and deterioration, we mean that the processing time of a job is defined by function of its starting time and total normal processing time of jobs in front of it in the sequence. It is shown that, even with the introduction of the effects of sum-of-processing-time-based learning and deterioration to job processing times, the single-machine makespan minimization problem remains polynomially solvable.

Single-Machine Scheduling Problems with a Sum-of-Processing-Time-Based Learning Function

Recently, learning scheduling problems have received increasing attention. However, the majority of the research assume that the actual job processing time is a function of its position. This paper deals with the single-machine scheduling problem with a sum-of-processing-time-based learning effect. By the effect of sum-of-processing-time-based learning, we mean that the processing time of a job is defined by total normal processing time of jobs in front of it in the sequence. We show that the single-machine makespan problem remains polynomially solvable under the proposed model. We show that the total completion time minimization problem for a≥1 remains polynomially solvable under the proposed model. For the case of 0<a<1, we show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to normal job processing times.

A note on single-machine total completion time problem with general deteriorating function

In this paper, we consider the single-machine scheduling problem with a deteriorating function. By the deteriorating function, we mean that the actual job processing time is a function of jobs already processed. We show that the total completion time minimization problem for a ≥ 1 remains polynomially solvable under the proposed model, where a denotes the deterioration rate. For the case of 0 < a < 1, we show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to normal job processing times. We use the classical smallest processing time first rule as a heuristic algorithm for the case of 0 < a < 1 and analyze its worst-case bound.

Single-machine scheduling with a time-dependent deterioration

The paper deals with the single-machine scheduling problems with a time-dependent deterioration. By time-dependent deterioration, we mean that the processing time of a job is defined by an increasing function of total normal processing time of jobs in front of it in the sequence. We show that, even with the introduction of time-dependent deterioration to job processing times, the single-machine makespan minimization problem remains polynomially solvable. We also show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to normal job processing times.