Single-machine scheduling with deteriorating jobs

In this article, we study a single-machine scheduling problem in which the processing time of a job is a nonlinear function of its basic processing time and starting time. The objectives are to minimise the makespan, the sum of weighted completion times and the sum of the kth powers of completion times. We show that the makespan minimisation problem can be solved in polynomial time. However, the total completion time and the sum of the kth powers of completion times minimisation problems can be solved in polynomial time in some cases. Besides, some useful properties are also provided for the sum of weighted completion times problem under certain conditions.     

One-machine scheduling problems with deteriorating jobs and position-dependent learning effects under group technology considerations

In this paper, we introduce a group scheduling model with general deteriorating jobs and learning effects in which deteriorating jobs and learning effects are both considered simultaneously. This means that the actual processing time of a job depends not only on the processing time of the jobs already processed, but also on its scheduled position. In our model, the group setup times are general linear functions of their starting times and the jobs in the same group have general position-dependent learning effects and time-dependent deterioration. The objective of scheduling problems is to minimise 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 due-date scheduling of jobs with decreasing start-time dependent processing times

We study the problem of scheduling jobs whose processing times are decreasing functions of their starting times. We consider the case of a single machine and a common decreasing rate for the processing times. The problem is to determine an optimal combination of the due date and schedule so as to minimize the sum of due date, earliness and tardiness penalties. We give an O(n log n) time algorithm to solve this problem.     

Three scheduling problems with deteriorating jobs to minimize the total completion time

In this paper, three scheduling problems with deteriorating jobs to minimize the total completion time on a single machine are investigated. By a deteriorating job, we mean that the processing time of the job is a function of its execution start time. The three problems correspond to three different decreasing linear functions, whose increasing counterparts have been studied in the literature. Some basic properties of the three problems are proved. Based on these properties, two of the problems are solved in O(nlogn) time, where n is the number of jobs. A pseudopolynomial time algorithm is constructed to solve the third problem using dynamic programming. Finally, a comparison between the problems with job processing times being decreasing and increasing linear functions of their start times is presented, which shows that the decreasing and increasing linear models of job processing times seem to be closely related to each other.     

Pareto and scalar bicriterion optimization in scheduling deteriorating jobs

In the paper two problems of a single machine bicriterion scheduling of a set of deteriorating jobs are considered. The jobs are independent, nonpreemptable and are ready for processing at time 0$0$. The processing time _pj$p_j$ of each job is a linear function of the starting time _Sj$S_j$ of the job, _pj=1+_αjSj$p_j=1+{\alpha }_j{S}_j$, where _Sj?0$S_j?0$ and _αj>0${\alpha }_j>0$ for j=0,1,...,n$j=0,1,...,n$.     

到达时间依赖于资源分配的单机排序问题*

研究了具有线性退化及学习效应作用下的单机排序问题,对于工件的到达时间是其资源消耗量的正的严格单调递减函数时,考虑了总资源消耗量限定情形下最大完工时间极小化问题,给出了相应的最优算法;也考虑了满足工件最大完工时间限制的条件下极小化资源消耗的总量问题,提出最优资源分配方案。     

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

This paper considers single machine scheduling problems with setup times and deteriorating jobs. The setup times are proportional to the length of the already processed jobs, that is, the setup times are past-sequence-dependent (p-s-d). It is assumed that the job processing times are defined by functions dependent on their starting times. The following objectives are considered: the makespan, the total completion time, and the sum of earliness, tardiness, and due-window starting time and size penalties. We propose polynomial time algorithms to solve these problems.     

Strong NP-hardness of the single machine multi-operation jobs total completion time scheduling problem

We consider the single machine multi-operation jobs total completion time scheduling problem. Each job consists of several operations that belong to different families. In a schedule, each family of job operations may be processed in batches with each batch incurring a set-up time. A job completes when all of its operations have been processed. The objective is to minimize the sum of the job completion times. In the literature, the computational complexity of this problem is posed as open. We show that the problem is strongly NP-hard even when the set-up times are common and the processing time of each operation is 0 or 1.     

Single-machine scheduling problems with deteriorating jobs and learning effects

In this paper, we introduce a new scheduling model in which deteriorating jobs and learning effect are both considered simultaneously. By deterioration and the learning effect, we mean that the actual processing time of a job depends not only on the processing time of the jobs already processed but also on its scheduled position. For the single-machine case, we show that the problems of makespan, total completion time and the sum of the quadratic job completion times remain polynomially solvable, respectively. In addition,we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain conditions.     

A note on scheduling problems with learning effect and deteriorating jobs

In this note, we consider the machine scheduling problems with the effects of deterioration and learning. In this model, job processing times are defined by functions of their starting times and positions in the sequence. The scheduling objectives are makespan (weighted) sum of completion times and maximum lateness. It is shown that even with the introduction of deterioration and learning effect to job processing times, several single machine problems and several flow shop problems remain polynomially solvable, respectively.     

Some scheduling problems with deteriorating jobs and learning effects

Although scheduling with deteriorating jobs and learning effect has been widely investigated, scheduling research has seldom considered the two phenomena simultaneously. However, job deterioration and learning co-exist in many realistic scheduling situations. In this paper, we introduce a new scheduling model in which both job deterioration and learning exist simultaneously. The actual processing time of a job depends not only on the processing times of the jobs already processed but also on its scheduled position. For the single-machine case, we derive polynomial-time optimal solutions for the problems to minimize makespan and total completion time. In addition, we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain agreeable conditions. For the case of an m-machine permutation flowshop, we present polynomial-time optimal solutions for some special cases of the problems to minimize makespan and total completion time.     

An approach for modeling a new single machine scheduling problem with deteriorating and learning effects

This paper presents a new approach to model a mixed-integer mathematical programming for a single machine scheduling problem with deteriorating and learning effects. Neglecting the effect of performing a job on its own processing time is mentioned as a deficiency in the literature of industrial scheduling. At first, self-influential factors are defined and then equations are presented to utilize these new factors. GAMS IDE/CPLEX software is used to validate the represented model by solving small to medium-sized sample problems, in which the associate results are compared with a hybrid meta-heuristic algorithm based on Ant Colony Optimization (ACO), Genetic Algorithm (GA) and Imperialist Competitive Algorithm (ICA). The vitality of considering and modeling the effect of learning and deteriorating made by a job, on its own processing time is tested for several sample problems. Then a significant improvement is observed by comparing the results acquired by neglecting the self-influential factors with the results based on considering them. Finally, the computational results are analyzed and the conclusion is given.     

Single-machine group scheduling problems with deteriorating and learning effect

The concepts of deteriorating jobs and learning effects have been individually studied in many scheduling problems. However, most studies considering the deteriorating and learning effects 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, a new group scheduling model with deteriorating and learning effects is proposed, where learning effect depends not only on job position, but also on the position of the corresponding job group; deteriorating effect depends on its starting time of the job. This paper shows that the makespan and the total completion time problems remain polynomial optimal solvable under the proposed model. In addition, a polynomial optimal solution is also presented to minimise the maximum lateness problem under certain agreeable restriction.     

一类具有资源约束和恶化效应的单机成组排序问题

讨论具有连续资源的单机成组排序问题.这一模型中同一组内的工件不允许分开加工,各工件组的安装时间是所消耗资源的非负减少连续函数.工件的加工时问是开工时问的严格减少函数.针对满足资源消耗总量限制条件下极小化最大完工时问的问题.以及在满足最大完工时间限制条件下极小化资源消耗总量的问题,讨论了最优排序的某些特征,分别给出了求解最优资源分配的方法.最后通过数值例子表明了所提出方法的正确性和有效性.     

A branch and bound algorithm for minimizing makespan on a single machine with unequal release times under learning effect and deteriorating jobs

We present a single-machine problem with the unequal release times under learning effect and deteriorating jobs when the objective is minimizing the makespan. In this study, we introduced a scheduling model with unequal release times in which both job deterioration and learning exist simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. A branch-and-bound algorithm incorporating with several dominance properties and lower bounds is developed to derive the optimal solution. A heuristic algorithm is proposed to obtain a near-optimal solution. The computational experiments show that the branch-and-bound algorithm can solve instances up to 30 jobs, and the average error percentage of the proposed heuristic is less than 0.16%.     

Minimizing the total weighted completion time of deteriorating jobs

The paper deals with a single machine problem of scheduling jobs with start time dependent processing times to minimize the total weighted completion time. The computational complexity of this problem was unknown for ten years. We prove that the problem is NP-hard.     

A note on “Single machine scheduling with time-dependent deterioration and exponential learning effect”

result in a recent paper Huang, Wang, Wang, Gao, and Wang (2010) (Computers & Industrial Engineering 58 (2010) 58–63) is incorrect because job processing times are variable due to both deteriorating jobs and learning effects, which is not taken into account by the authors. In this note, we show by a counter-example that the published result is incorrect.     

A dominant class of schedules for malleable jobs in the problem to minimize the total weighted completion time

This paper is about scheduling parallel jobs, i.e. which can be executed on more than one machine at the same time. Malleable jobs is a special class of parallel jobs. The number of machines a malleable job is executed on may change during its execution.In this work, we consider the NP-hard problem of scheduling malleable jobs to minimize the total weighted completion time (or mean weighted flow time). For this problem, we introduce the class of “ascending” schedules in which, for each job, the number of machines assigned to it cannot decrease over time while this job is being processed.We prove that, under a natural assumption on the processing time functions of jobs, the set of ascending schedules is dominant for the problem. This result can be used to reduce the search space while looking for an optimal solution.     

Single machine scheduling with autonomous learning and induced learning

As an important management tool of winning competitive advantage, induced learning effect has been widely studied in empirical research area. But it is hardly considered in scheduling problems. In this paper, autonomous and induced learning are both taken into consideration. The investment of induced learning is interpreted as specialized time intervals to implement training, knowledge sharing and transferring etc. We present algorithms to determine jointly the optimal job sequence and the optimal position of induced learning intervals, with the objective of minimizing makespan.     

Single machine scheduling problem with interval processing times to minimize mean weighted completion time

The single resource scheduling problem is commonly applicable in practice not only when there is a single resource but also in some multiple-resource production systems where only one of the resources is bottle neck. Thus, the single resource (machine) scheduling problem has been widely addressed in the scheduling literature. In this paper, the single machine scheduling problem with uncertain and interval processing times is addressed. The objective is to minimize mean weighted completion time. The problem has been addressed in the literature and efficient heuristics have been presented. In this paper, some new polynomial time heuristics, utilizing the bounds of processing times, are proposed. The proposed and existing heuristics are compared by extensive computational experiments. The conducted experiments include a generalized simulation environment and several additional representative distributions in addition to the restricted experiments used in the literature. The results indicate that the proposed heuristics perform significantly better than the existing heuristics. Specifically, the best performing proposed heuristic reduces the error of the best existing heuristic in the literature by more than 75% while the computational time of the best performing proposed heuristic is less than that of the best existing heuristic. Moreover, the absolute error of the best performing heuristic is only about 1% of the optimal solution. Having a very small absolute error along with a negligible computational time indicates the superiority of the proposed heuristics.