Single machine scheduling with a general exponential learning effect

In this paper we consider the scheduling problem with a general exponential learning effect and past-sequence-dependent (p-s-d) setup times. By the general exponential learning effect, we mean that the processing time of a job is defined by an exponent function of the total weighted normal processing time of the already processed jobs and its position in a sequence, where the weight is a position-dependent weight. The setup times are proportional to the length of the already processed jobs. We consider the following objective functions: the makespan, the total completion time, the sum of the δ ? 0th power of completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the quadratic job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, 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.     

Single machine past-sequence-dependent setup times scheduling with general position-dependent and time-dependent learning effects

In this paper we consider the single machine past-sequence-dependent (p-s-d) setup times scheduling problems with general position-dependent and time-dependent learning effects. By the general position-dependent and time-dependent learning effects, we mean that the actual processing time of a job is not only a function of the total normal processing times of the jobs already processed, but also a function of the job’s scheduled position. The setup times are proportional to the length of the already processed jobs. We consider the following objective functions: the makespan, the total completion time, the sum of the θth (θ ? 0) power of job completion times, the total lateness, the total weighted completion time, the maximum lateness, the maximum tardiness and the number of tardy jobs. We show that the problems of makespan, the total completion time, the sum of the θth (θ ? 0) power of job completion times and the total lateness can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem, maximum tardiness minimization problem and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.     

Single machine scheduling with general time-dependent deterioration, position-dependent learning and past-sequence-dependent setup times

The paper deals with single machine scheduling problems with setup time considerations where the actual processing time of a job is not only a non-decreasing function of the total normal processing times of the jobs already processed, but also a non-increasing function of the job’s position in the sequence. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We consider the following objective functions: the makespan, the total completion time, the sum of the δth (δ ≥ 0) power of job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the δ th (δ ≥ 0) power of job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, 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 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.     

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 past-sequence-dependent delivery times scheduling with general position-dependent and time-dependent learning effects

This paper studies the single machine past-sequence-dependent (p-s-d) delivery times scheduling with general position-dependent and time-dependent learning effects. By the general position-dependent and time-dependent learning effects we mean that the actual processing time of a job is not only a function of the total normal processing times of the jobs already processed, but also a function of the job’s scheduled position. We consider the following objective functions: the makespan, the total completion time, the sum of the θ$\theta$th (θ?0$\theta ?0$) power of job completion times, the total lateness, the total weighted completion time, the maximum lateness, the maximum tardiness and the number of tardy jobs. We show that the problems of minimization of the makespan, the total completion time, the sum of the θ$\theta$th (θ?0$\theta ?0$) power of job completion times and the total lateness can be solved by the smallest (normal) processing time first (SPT) rule, 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, the maximum tardiness minimization problem and the total tardiness minimization problem can be solved in polynomial time under certain conditions.     

Several single-machine scheduling problems with general learning effects

In this paper we consider several single-machine scheduling problems with general learning effects. By general learning effects, we mean that the processing time of a job depends not only on its scheduled position, but also on the total normal processing time of the jobs already processed. We show that the scheduling problems of minimization of the makespan, the total completion time and the sum of the θ  th (θ?0$\theta ?0$) power of job completion times can be solved in polynomial time under the proposed models. We also prove that some special cases of the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time.     

Scheduling problems with past-sequence-dependent setup times and general effects of deterioration and learning

In this paper we consider the single-machine setup times scheduling with general effects of deterioration and learning. By the general effects of deterioration and learning, we mean that the actual job processing time is a general function of the processing times of the jobs already processed and its scheduled position. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We show that the problems to minimize the makespan, the sum of the δ$\delta$th (δ>0$\delta >0$) power of job completion times, the total lateness are polynomially solvable. We also show that the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness (tardiness) minimization problem, the total tardiness minimization problem can be solved in polynomial time under certain conditions.     

同时具有学习效应和退化效应的单机排序问题

本文给出了一种同时具有一般化学习效应和退化效应的单机排序模型。在此模型中,工件的实际加工时间既与工件所在位置又与其开工时间有关,且工件在加工之后具有一个配送时间。其中学习效应是工件所在位置的函数,退化效应是工件开工时间的函数。证明了极小化最大完工时间和极小化总完工时间问题是多项式可解的,在满足一定的条件下,极小化加权总完工时间和极小化最大延误问题也是多项式可解的。推广了一些已有文献中的结论。     

Single machine scheduling with exponential learning functions

In this paper we consider the single machine scheduling problem with exponential learning functions. By the exponential learning functions, we mean that the actual job processing time is a function of the total normal processing times of the jobs already processed. We prove that the shortest processing time (SPT) rule is optimal for the total lateness minimization problem. For the following three objective functions, the total weighted completion time, the discounted total weighted completion time, the maximum lateness, we present heuristic algorithms according to the corresponding problems without exponential learning functions. We also analyse the worst-case bound of our heuristic algorithms. It also shows that the problems of minimizing the total tardiness and discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.     

Some single-machine scheduling with both learning and deterioration effects

In this paper we consider the single-machine scheduling problems with both learning and deterioration effects. By the effects of learning and deterioration, we mean that job processing times are defined by functions of their starting times and positions in the sequence. It is shown that even with the introduction of learning effect and deteriorating jobs to job processing times, single-machine makespan minimization problem and the sum of the θth power of job completion times minimization problem remain polynomially solvable, respectively. But for the following objective functions: the weighted sum of completion times and the maximum lateness, this paper proves that the WSPT rule and the EDD rule can construct the optimal sequence under some special cases, respectively.     

Scheduling jobs with position-dependent processing times

The paper is devoted to some single machine scheduling problems, where job processing times are defined by functions dependent on their positions in the sequence. It is assumed that each job is available for processing at its ready time. We prove some properties of the special cases of the problems for the following optimization criteria: makespan, total completion time and total weighted completion time. We prove strong NP-hardness of the makespan minimization problem for two different models of job processing time. The reductions are done from the well-known 3-Partition Problem. In order to solve the makespan minimization problems, we suggest the Earliest Ready Date algorithms, for which the worst-case ratios are calculated. We also prove that the makespan minimization problem with job ready times is equivalent to the maximum lateness minimization problem.     

Single-machine scheduling with effects of exponential learning and general deterioration

The purpose of this study is to explore the single-machine scheduling with the effects of exponential learning and general deterioration. By the effects of exponential learning and general deterioration, we meant that job processing time is decided by the functions of their starting time and positions in the sequence. Results showed that with the introduction of learning effect and deteriorating jobs to job processing time, single-machine makespan, and sum of completion time (square) minimization problems remained polynomially solvable, respectively. But for the following objective functions: the weighted sum of completion time and the maximum lateness, this paper proved that the weighted smallest basic processing time first (WSPT) rule and the earliest due date first (EDD) rule constructed the optimal sequence under some special cases, respectively.     

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.     

带有退化效应和序列相关运输时间的排序问题

考虑带有退化效应和序列相关运输时间的单机排序问题. 工件的加工时间是其开工时间的简单线性增加函数. 当机器单个加工工件时, 极小化最大完工时间、(加权)总完工时间和总延迟问题被证明是多项式可解的, EDD序对于极小化最大延迟问题不是最优排序, 另外, 就交货期和退化率一致情形给出了一最优算法. 当机器可分批加工工件时, 分别就极小化最大完工时间和加权总完工时间问题提出了多项式时间最优算法.     

Scheduling jobs with truncated exponential learning functions

In this paper we consider the single machine scheduling problem with truncated exponential learning functions. By the truncated exponential learning functions, we mean that the actual job processing time is a function which depends not only on the total normal processing times of the jobs already processed but also on a control parameter. The use of the truncated function is to model the phenomenon that the learning of a human activity is limited. We show that even with the introduction of the proposed model to job processing times, several single machine problems remain polynomially solvable. For the following three objective functions, the total weighted completion time, the discounted total weighted completion time, the maximum lateness, we present heuristic algorithms according to the corresponding problems without truncated exponential learning functions. We also analyse the worst-case bound of our heuristic algorithms.     

Some single-machine scheduling problems with actual time and position dependent learning effects

In this paper we study some single-machine scheduling problems with learning effects where the actual processing time of a job serves as a function of the total actual processing times of the jobs already processed and of its scheduled position. We show by examples that the optimal schedules for the classical version of problems are not optimal under this actual time and position dependent learning effect model for the following objectives: makespan, sum of kth power of the completion times, total weighted completion times, maximum lateness and number of tardy jobs. But under certain conditions, we show that the shortest processing time (SPT) rule, the weighted shortest processing time (WSPT) rule, the earliest due date (EDD) rule and the modified Moore’s Algorithm can also construct an optimal schedule for the problem of minimizing these objective functions, respectively.     

Single-machine scheduling with both deterioration and learning effects

This paper considers a single-machine scheduling problem with both deterioration and learning effects. The objectives are to respectively minimize the makespan, the total completion times, the sum of weighted completion times, the sum of the kth power of the job completion times, the maximum lateness, the total absolute differences in completion times and the sum of earliness, tardiness and common due-date penalties. Several polynomial time algorithms are proposed to optimally solve the problem with the above objectives.     

Single-machine scheduling problems with time and position dependent processing times

We consider single-machine scheduling problems with time and position dependent job processing times. In many industrial settings, the processing time of a job changes due to either job deterioration over time or machine/worker’s learning through experiences. In the models we study, each job has its normal processing time. However, a job’s actual processing time depends on when its processing starts and how many jobs have completed before its start. We prove that the classical SPT (Shortest Processing Time) rule remains optimal when we minimize the makespan or the total completion time. For problems of minimizing the total weighted completion time, the maximum lateness, and the discounted total weighted completion time, we present heuristic sequencing rules and analyze the worst-case bounds for performance ratios. We also show that these heuristic rules can be optimal under some agreeable conditions between the normal processing times and job due dates or weights.