Single-machine scheduling simultaneous with position-based and sum-of-processing-times-based learning considerations under group technology assumption

This paper considers the problems of scheduling with the effect of learning on a single-machine under group technology assumption. We propose a new learning model where the job actual processing time is linear combinations of the scheduled position of the job and the sum of the normal processing time of jobs already processed. We show that the makespan minimization problem is polynomially solvable. We also prove that the total completion time minimization problem with the group availability assumption remains polynomially solvable under agreeable conditions.     

Single-machine scheduling problems with actual time-dependent and job-dependent learning effect

In this study, we introduce an actual time-dependent and job-dependent learning effect into single-machine scheduling problems. We show that the complexity results of the makespan minimization problem and the sum of weighted completion time minimization problem are all NP-hard. The complexity result of the maximum lateness minimization problem is NP-hard in the strong sense. We also provide three special cases which can be solved by polynomial time algorithms.     

Single-machine and two-machine flowshop scheduling problems with truncated position-based learning functions

Scheduling with learning effects has received growing attention nowadays. A well-known learning model is called ‘position-based learning’ in which the actual processing time of a job is a non-increasing function of its position to be processed. However, the actual processing time of a given job drops to zero precipitously as the number of jobs increases. Motivated by this observation, we propose two truncated learning models in single-machine scheduling problems and two-machine flowshop scheduling problems with ordered job processing times, respectively, where the actual processing time of a job is a function of its position and a control parameter. Under the proposed learning models, we show that some scheduling problems can be solved in polynomial time. In addition, we further analyse the worst-case error bounds for the problems to minimize the total weighted completion time, discounted total weighted completion time and maximum lateness.     

Single-machine group scheduling problems with deteriorated and learning effect

In many realistic situation, a job processed later consumes more time than the same job when it is processed earlier, this phenomenon is known as deteriorated effect. The skills of workers continuously improve when repeating the same or similar tasks, this phenomenon is as the “learning effect” in the literature. However, most studies considering the deteriorated and learning effect ignore the fact that production efficiency can be increased by grouping various parts and products with similar designs and/or production processes. This phenomenon is known “group technology” in the literature. In this paper, we propose a new group scheduling with deteriorated and learning model where the learning effect not only depends on job position, but also depends on the group position; the deteriorated effect depends on its starting time of the job. We then show that the single-machine makespan and the total completion time problems remain polynomial optimal solvable under the proposed model. In addition, we show the maximum lateness have a polynomial optimal solution under certain agreeable restriction.     

Single-machine total completion time scheduling with a time-dependent deterioration

In this paper, we consider the single-machine scheduling problems with a time-dependent deterioration. By the 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. The objective is to minimize the total completion time. We develop a mixed integer programming formulation for the problem. The complexity status of this problem remains open. Hence, we use the smallest normal processing time (SPT) first rule as a heuristic algorithm for the general cases and analyze its worst-case error bound. Two heuristic algorithms utilize the V-shaped property are also proposed to solve the problem. Computational results are presented to evaluate the performance of the proposed algorithms.     

A note on single-machine group scheduling problems with position-based learning effect

In many situations, the skills of workers continuously improve when repeating the same or similar tasks. This phenomenon is known as the “learning effect” in the literature. However, most studies considering the learning effect ignore the fact that production efficiency can be increased by grouping various parts and products with similar designs and/or production processes. This phenomenon is known as “group technology” in the literature. In this paper, we propose a new group scheduling learning model where the learning effect not only depends on the job position, but also depends on the group position. We then show that the makespan and the total completion time problems remain polynomially solvable under the proposed model.     

基于加工时间之和学习效应下的单机成组排序问题

研究具有加工时间之和学习效应下的一个新型成组排序问题,工件的学习效应是之前工件加工时间之和的函数,组学习效应是成组加工所在的位置的函数. 考虑最大完工时间和总完工时间两个问题,证明了这两个问题都是多项式时间可解的,并提出了相应的多项式时间算法.     

Single-machine group scheduling with general deterioration and learning effects

In this paper we consider single-machine group scheduling problems with effects of learning and deterioration at the same time. By effects of learning and deterioration, we mean that the group setup times are general linear functions of their starting times and the jobs in the same group have general position-dependent and time-dependent learning effects. The objective of scheduling problems is to minimize the makespan and the sum of completion times, respectively. We show that the problems remain solvable in polynomial time under the proposed model.     

Single-machine scheduling problems with a learning effect

In many situations, the skills of workers continuously improve when repeating the same or similar tasks. This phenomenon is known as the “learning effect” in the literature. In most studies, the learning phenomenon is implemented by assuming the actual job processing time is a function of its scheduled position [D. Biskup, Single-machine scheduling with learning considerations, Eur. J. Oper. Res. 115 (1999) 173–178]. Recently, a new model is proposed where the actual job processing time depends on the sum of the processing times of jobs already processed [C. Koulamas, G.J. Kyparisis, Single-machine and two-machine flowshop scheduling with general learning functions, Eur. J. Oper. Res. 178 (2007) 402–407]. In this paper, we extend their models in which the actual job processing time not only depends on its scheduled position, but also depends on the sum of the processing times of jobs already processed. We then show that the single-machine makespan and the total completion time problems remain polynomially solvable under the proposed model. In addition, we show that the total weighted completion time has a polynomial optimal solution under certain agreeable solutions.     

Single-machine scheduling with a sum-of-actual-processing-time-based learning effect

In this paper we consider the single-machine scheduling problems with a sum-of-actual-processing-time-based learning effect. By the sum-of-actual-processing-time-based learning effect, we mean that the processing time of a job is defined by a function of the sum of the actual processing time of the already processed jobs. We show that even with the introduction of the sum-of-actual-processing-time-based learning effect to job processing times, the makespan minimization problem, the total completion time minimization problem, the total completion time square minimization problem, and some special cases of the total weighted completion time minimization problem and the maximum lateness minimization problem remain polynomially solvable, respectively.     

Serial-batching scheduling with time-dependent setup time and effects of deterioration and learning on a single-machine

This paper deals with serial-batching scheduling problems with the effects of deterioration and learning, where time-dependent setup time is also considered. In the proposed scheduling models, all jobs are first partitioned into serial batches, and then all batches are processed on a single serial-batching machine. The actual job processing time is a function of its starting time and position. In addition, a setup time is required when a new batch is processed, and the setup time of the batches is time-dependent, i.e., it is a linear function of its starting time. Structural properties are derived for the problems of minimizing the makespan, the number of tardy jobs, and the maximum earliness. Then, three optimization algorithms are developed to solve them, respectively.     

Single-machine scheduling with past-sequence-dependent setup times and general effects of deterioration and learning

Scheduling with learning effect and deteriorating jobs has become more popular. However, most of the research assume that the setup time is negligible or a part of the job processing time. In this paper, we propose a model where the deteriorating jobs, the learning effect, and the setup times are present simultaneously. Under the proposed model, the setup time is past-sequence-dependent and the actual job processing time is a general function of the processing times of the jobs already processed and its scheduled position. We provide the optimal schedules for some single-machine problems.     

Single-machine scheduling problems with past-sequence-dependent setup times

This paper studies single-machine scheduling problems with setup times which are proportionate to the length of the already scheduled jobs, that is, with past-sequence-dependent or p-s-d setup times. The following objective functions are considered: the maximum completion time (makespan), the total completion time, the total absolute differences in completion times and a bicriteria combination of the last two objective functions. It is shown that the standard single-machine scheduling problem with p-s-d setup times and any of the above objective functions can be solved in O(nlog n) time (where n is the number of jobs) by a sorting procedure. It is also shown that all of our results extend to a “learning” environment in which the p-s-d setup times are no longer linear functions of the already elapsed processing time due to learning effects.     

Single-machine scheduling with learning considerations

The focus of this work is to analyze learning in single-machine scheduling problems. It is surprising that the well-known learning effect has never been considered in connection with scheduling problems. It is shown in this paper that even with the introduction of learning to job processing times two important types of single-machine problems remain polynomially solvable.     

Single-machine scheduling with learning functions

In this study we consider the single-machine scheduling problems with a sum of-processing-times-based learning effect. The sum of-processing-times-based learning effect of a job is assumed to be a function of the sum of the normal processing time of the already processed jobs. The objective is to minimize one of two regular objective functions, namely the weighted sum of completion times and the maximum lateness. We use the weighted shortest processing time (WSPT) rule and the earliest due date (EDD) rule as heuristics for the general cases and analyze their worst-case error bounds. We also provide computational results to evaluate the performance of the heuristics.     

Single-machine scheduling with deteriorating jobs and past-sequence-dependent setup times

In many realistic scheduling settings a job processed later consumes more time than the same job processed earlier – this is known as scheduling with deteriorating jobs. Most research on scheduling with deteriorating jobs assumes that the actual processing time of a job is an increasing function of its starting time. Thus a job processed late may incur an excessively long processing time. On the other hand, setup times occur in manufacturing situations where jobs are processed in batches whereby each batch incurs a setup time. This paper considers scheduling with deteriorating jobs in which the actual processing time of a job is a function of the logarithm of the total processing time of the jobs processed before it (to avoid the unrealistic situation where the jobs scheduled late will incur excessively long processing times) and the setup times are proportional to the actual processing times of the already scheduled jobs. Under the proposed model, we provide optimal solutions for some single-machine problems.     

Single-machine scheduling with a general sum-of-actual-processing-times-based and job-position-based learning effect

In this paper, we bring into the scheduling field a general learning effect model where the actual processing time of a job is not only a general function of the total actual processing times of the jobs already processed, but also a general function of the job’s scheduled position. We show that the makespan minimization problem and the sum of the kth power of completion times minimization problem can be solved in polynomial time, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.     

Single-machine scheduling problems with an actual time-dependent deterioration

In this paper, we consider the single machine scheduling problems with an actual time-dependent deterioration effect. By the actual time-dependent deterioration effect, we mean that the processing time of a job is defined by increasing function of total actual processing time of jobs in front of it in the sequence. We show that even with the introduction of an actual time-dependent deterioration to job processing times, makespan minimization problem, total completion time minimization problem, the total lateness, and the sum of the quadratic job completion times minimization problem remain polynomially solvable, respectively. We also show that the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, and the total tardiness minimization problem can be solved in polynomial time under certain conditions.