In this paper, a single-machine scheduling model with a given common due date and simple linear processing times was considered. The objective is the total weighted tardiness penalty and earliness award. Some polynomi...In this paper, a single-machine scheduling model with a given common due date and simple linear processing times was considered. The objective is the total weighted tardiness penalty and earliness award. Some polynomial time solvable cases for this problem are given. A dynamic programming algorithm was provided and a branch and bound algorithm for general case of the problem was provided based on a rapid method for estimating the lower bound.展开更多
In this paper, a single-machine scheduling model with a given common due date is considered. Job processing time is a linear decreasing function of its starting time. The objective function is to minimize the total we...In this paper, a single-machine scheduling model with a given common due date is considered. Job processing time is a linear decreasing function of its starting time. The objective function is to minimize the total weighted earliness award and tardiness penalty. Our aim is to find an optimal schedule so as to minimize the objective function. As the problem is NP-hard, some properties and polynomial time solvable cases of this problem are given. A dynamic programming algorithm for the general case of the problem is provided.展开更多
The strong non-deterministic polynomial-hard( NP-hard)character of job shop scheduling problem( JSSP) has been acknowledged widely and it becomes stronger when attaches the nowait constraint,which widely exists in man...The strong non-deterministic polynomial-hard( NP-hard)character of job shop scheduling problem( JSSP) has been acknowledged widely and it becomes stronger when attaches the nowait constraint,which widely exists in many production processes,such as chemistry process, metallurgical process. However,compared with the massive research on traditional job shop problem,little attention has been paid on the no-wait constraint.Therefore,in this paper, we have dealt with this problem by decomposing it into two sub-problems, the timetabling and sequencing problems,in traditional frame work. A new efficient combined non-order timetabling method,coordinated with objective of total tardiness,is proposed for the timetabling problems. As for the sequencing one,we have presented a modified complete local search with memory combined by crossover operator and distance counting. The entire algorithm was tested on well-known benchmark problems and compared with several existing algorithms.Computational experiments showed that our proposed algorithm performed both effectively and efficiently.展开更多
The single machine scheduling problem which involves uncertain job due dates is one of the most important issues in the real make-to-order environment. To deal with the uncertainty, this paper establishes a robust opt...The single machine scheduling problem which involves uncertain job due dates is one of the most important issues in the real make-to-order environment. To deal with the uncertainty, this paper establishes a robust optimization model by minimizing the maximum tardiness in the worst case scenario over all jobs. Unlike the traditional stochastic programming model which requires exact distributions, our model only needs the information of due date intervals. The worst case scenario for a given sequence that belongs to a set containing only n scenarios is proved, where n is the number of jobs. Then, the model is simplified and reformulated as an equivalent mixed 0-1 integer linear programming(MILP) problem. To solve the MILP problems efficiently, a heuristic approach is proposed based on a robust dominance rule. The experimental results show that the proposed method has the advantages of robustness and high calculating efficiency, and it is feasible for large-scale problems.展开更多
Considering the imprecise nature of the data in real-world problems, the earliness/tardiness (E/T) fiowshop scheduling problem with uncertain processing time and distinct due windows is concerned in this paper. A fu...Considering the imprecise nature of the data in real-world problems, the earliness/tardiness (E/T) fiowshop scheduling problem with uncertain processing time and distinct due windows is concerned in this paper. A fuzzy scheduling model is established and then transformed into a deterministic one by employing the method of maximizing the membership function of middle value. Moreover, an effective scatter search based particle swarm optimization (SSPSO) algorithm is proposed to minimize the sum of total earliness and tardiness penalties. The proposed SSPSO algorithm incorporates the scatter search (SS) algorithm into the frame of particle swarm optimization (PSO) algorithm and gives full play to their characteristics of fast convergence and high diversity. Besides, a differential evolution (DE) scheme is used to generate solutions in the SS. In addition, the dynamic update strategy and critical conditions are adopted to improve the performance of SSPSO. The simulation results indicate the superiority of SSPSO in terms of effectiveness and efficiency.展开更多
The m-machine no-wait flowshop scheduling problem is addressed where setup times are treated as separate from processing times. The objective is to minimize total tardiness. Different dispatching rules have been inves...The m-machine no-wait flowshop scheduling problem is addressed where setup times are treated as separate from processing times. The objective is to minimize total tardiness. Different dispatching rules have been investigated and three were found to be superior. Two heuristics, a simulated annealing (SA) and a genetic algorithm (GA), have been proposed by using the best performing dispatching rule as the initial solution for SA, and the three superior dispatching rules as part of the initial population for GA. Moreover, improved versions of SA and GA are proposed using an insertion algorithm. Extensive computational experiments reveal that the improved versions of SA and GA perform about 95% better than SA and GA. The improved version of GA outperforms the improved version of SA by about 3.5%.展开更多
The intense competition in the current marketplace ha s forced firms to reexamine their methods of doing business, using superior manu facturing practices in the form of just-in-time (JIT), production with JIT pra cti...The intense competition in the current marketplace ha s forced firms to reexamine their methods of doing business, using superior manu facturing practices in the form of just-in-time (JIT), production with JIT pra ctices pursue completion on time and zero inventory, which is often instruct ed according to the custom’s demand or the sale contract. Earliness and tardine ss are undesirable because both of them will bring the extra cost, cost will als o be increased by some factors such as operation condition, intermediate storage , clean method, etc, to minimize the total cost is often the main scheduling objective, but sometime it is most important for factories to eliminate the tar diness cost in order to maintain the commercial credit and to avoid penalty, the refore, minimum of tardiness cost becomes the first objective. It is more import ant to select a reasonable objective by the actual condition during scheduli ng. In this paper scheduling problem of chemical batch process with due date is studied, two different intermediate storage policies and two different productio n modes are also discussed, production scheduling with different intermediate st orage policy and different production mode is proposed and the result is compare d. In order to complete all products within the due date, not only earliness and tardiness but also holding problem is considered, the objective is to selec t a proper intermediate storage policy and production mode and to minimize the c ost resulted by the earliness and tardiness, even the cost result by the interme diate storage. Scheduling with multiple stage and multiple machine is known as a NP-hard problem, mathematical program (MP) method, such as branch-and-bound (BAB), mixed integer linear program (MILP), etc, is often used to solve the sche duling problem. But as is well known, MP method is not good for combination opti mization, especially for large scale and complex optimal problem, whereas geneti c algorithm (GA) can overcome the MP method’s shortcoming and is fit for solvin g such scheduling problem. In this paper a modified genetic algorithm with speci al crossover operator and mutation operator is presented to solve this schedulin g problem. The results show such problem can be solved effectively with the pres ented method.展开更多
In this paper, we give a mathematical model for earliness-tardiness job scheduling problem with a common due window on parallel and non-identical machines. Because the job scheduling problem discussed in the paper con...In this paper, we give a mathematical model for earliness-tardiness job scheduling problem with a common due window on parallel and non-identical machines. Because the job scheduling problem discussed in the paper contains a problem of minimizing make-span, which is NP-complete on parallel and uniform machines, a heuristic algorithm is presented to find an approximate solution for the scheduling problem after proving an important theorem. Two numerical examples illustrate that the heuristic algorithm is very useful and effective in obtaining the near-optimal solution.展开更多
The optimality of a fuzzy logic alternative to the usual treatment of uncertainties in a scheduling system using fuzzy numbers is examined formally. Processing times and due dates are fuzzified and presented by fuzzy ...The optimality of a fuzzy logic alternative to the usual treatment of uncertainties in a scheduling system using fuzzy numbers is examined formally. Processing times and due dates are fuzzified and presented by fuzzy numbers. With introducing the necessity measure, we compare fuzzy completion times of jobs with fuzzy due dates to decide whether jobs are tardy. The object is to minimize the numbers of tardy jobs. The efficient solution method for this problem is proposed. And deterministic counterpart of this single machine scheduling problem is a special case of fuzzy version.展开更多
In this paper,attention is paid to study an algorithm for the common due datetotal weighted tardiness problem of single machine scheduling. Anapproximation alsorithm is given. It performs well in the sense of worst-ca...In this paper,attention is paid to study an algorithm for the common due datetotal weighted tardiness problem of single machine scheduling. Anapproximation alsorithm is given. It performs well in the sense of worst-casebehaviour and its worst-case performance ratio is 2.展开更多
To describe the earliness/tardiness production planning problems in the JIT environment, a nonlinear semi\|infinite programming model was proposed in \. Due to a nonconvex objective function and many infinite constrai...To describe the earliness/tardiness production planning problems in the JIT environment, a nonlinear semi\|infinite programming model was proposed in \. Due to a nonconvex objective function and many infinite constraints, the model is difficult to be solved by traditional methods. In this paper, simulated annealing method combined with a heuristic is developed. Numerical results shows that the present approach is very efficient. Theoretically, the developed method is an attempt to solve a continuous domain problem by using simulated annealing.展开更多
This paper considers scheduling n jobs on a single machine where the job processing times anddue dates are independent random variables with arbitrary distribution functions.We consider the casethat the weighted job t...This paper considers scheduling n jobs on a single machine where the job processing times anddue dates are independent random variables with arbitrary distribution functions.We consider the casethat the weighted job tardiness in expectation is minimized.It is assumed that job's due dates arecompatible with processing times and weights.We show that the jobs should be sequenced indecreasing stochastic order of their due dates.展开更多
边缘计算广泛应用于物联网、车联网和在线游戏等新兴领域,通过网络边缘部署计算资源为终端设备提供低延迟计算服务.针对如何进行任务卸载以权衡任务执行时间与传输时间、如何调度多个不同截止期任务以最小化总延迟时间等挑战性问题,提出...边缘计算广泛应用于物联网、车联网和在线游戏等新兴领域,通过网络边缘部署计算资源为终端设备提供低延迟计算服务.针对如何进行任务卸载以权衡任务执行时间与传输时间、如何调度多个不同截止期任务以最小化总延迟时间等挑战性问题,提出1种异构边缘协同的任务卸载和调度框架,包括边缘网络拓扑节点排序、边缘节点内任务排序、任务卸载策略、任务调度和结果调优等算法组件;设计多种任务卸载策略和任务调度策略;借助多因素方差分析(multi-factor analysis of variance,ANOVA)技术在大规模随机实例上校正算法算子和参数,得到统计意义上的最佳调度算法.基于EdgeCloudSim仿真平台,将所提出调度算法与其3个变种算法从边缘节点数量、任务数量、任务分布、截止期取值区间等角度进行性能比较.实验结果表明,所提出调度算法在各种情形下性能都优于对比算法.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.19771057)
文摘In this paper, a single-machine scheduling model with a given common due date and simple linear processing times was considered. The objective is the total weighted tardiness penalty and earliness award. Some polynomial time solvable cases for this problem are given. A dynamic programming algorithm was provided and a branch and bound algorithm for general case of the problem was provided based on a rapid method for estimating the lower bound.
文摘In this paper, a single-machine scheduling model with a given common due date is considered. Job processing time is a linear decreasing function of its starting time. The objective function is to minimize the total weighted earliness award and tardiness penalty. Our aim is to find an optimal schedule so as to minimize the objective function. As the problem is NP-hard, some properties and polynomial time solvable cases of this problem are given. A dynamic programming algorithm for the general case of the problem is provided.
基金National Natural Science Foundations of China(Nos.61174040,61104178)Shanghai Commission of Science and Technology,China(No.12JC1403400)the Fundamental Research Funds for the Central Universities,China
文摘The strong non-deterministic polynomial-hard( NP-hard)character of job shop scheduling problem( JSSP) has been acknowledged widely and it becomes stronger when attaches the nowait constraint,which widely exists in many production processes,such as chemistry process, metallurgical process. However,compared with the massive research on traditional job shop problem,little attention has been paid on the no-wait constraint.Therefore,in this paper, we have dealt with this problem by decomposing it into two sub-problems, the timetabling and sequencing problems,in traditional frame work. A new efficient combined non-order timetabling method,coordinated with objective of total tardiness,is proposed for the timetabling problems. As for the sequencing one,we have presented a modified complete local search with memory combined by crossover operator and distance counting. The entire algorithm was tested on well-known benchmark problems and compared with several existing algorithms.Computational experiments showed that our proposed algorithm performed both effectively and efficiently.
基金supported by the National Natural Science Foundation of China(61503211,U1660202)。
文摘The single machine scheduling problem which involves uncertain job due dates is one of the most important issues in the real make-to-order environment. To deal with the uncertainty, this paper establishes a robust optimization model by minimizing the maximum tardiness in the worst case scenario over all jobs. Unlike the traditional stochastic programming model which requires exact distributions, our model only needs the information of due date intervals. The worst case scenario for a given sequence that belongs to a set containing only n scenarios is proved, where n is the number of jobs. Then, the model is simplified and reformulated as an equivalent mixed 0-1 integer linear programming(MILP) problem. To solve the MILP problems efficiently, a heuristic approach is proposed based on a robust dominance rule. The experimental results show that the proposed method has the advantages of robustness and high calculating efficiency, and it is feasible for large-scale problems.
基金supported by National Natural Science Foundation of China(Nos.61174040 and 61104178)Shanghai Commission of Science and Technology(No.12JC1403400)the Fundamental Research Funds for the Central Universities
文摘Considering the imprecise nature of the data in real-world problems, the earliness/tardiness (E/T) fiowshop scheduling problem with uncertain processing time and distinct due windows is concerned in this paper. A fuzzy scheduling model is established and then transformed into a deterministic one by employing the method of maximizing the membership function of middle value. Moreover, an effective scatter search based particle swarm optimization (SSPSO) algorithm is proposed to minimize the sum of total earliness and tardiness penalties. The proposed SSPSO algorithm incorporates the scatter search (SS) algorithm into the frame of particle swarm optimization (PSO) algorithm and gives full play to their characteristics of fast convergence and high diversity. Besides, a differential evolution (DE) scheme is used to generate solutions in the SS. In addition, the dynamic update strategy and critical conditions are adopted to improve the performance of SSPSO. The simulation results indicate the superiority of SSPSO in terms of effectiveness and efficiency.
文摘The m-machine no-wait flowshop scheduling problem is addressed where setup times are treated as separate from processing times. The objective is to minimize total tardiness. Different dispatching rules have been investigated and three were found to be superior. Two heuristics, a simulated annealing (SA) and a genetic algorithm (GA), have been proposed by using the best performing dispatching rule as the initial solution for SA, and the three superior dispatching rules as part of the initial population for GA. Moreover, improved versions of SA and GA are proposed using an insertion algorithm. Extensive computational experiments reveal that the improved versions of SA and GA perform about 95% better than SA and GA. The improved version of GA outperforms the improved version of SA by about 3.5%.
文摘The intense competition in the current marketplace ha s forced firms to reexamine their methods of doing business, using superior manu facturing practices in the form of just-in-time (JIT), production with JIT pra ctices pursue completion on time and zero inventory, which is often instruct ed according to the custom’s demand or the sale contract. Earliness and tardine ss are undesirable because both of them will bring the extra cost, cost will als o be increased by some factors such as operation condition, intermediate storage , clean method, etc, to minimize the total cost is often the main scheduling objective, but sometime it is most important for factories to eliminate the tar diness cost in order to maintain the commercial credit and to avoid penalty, the refore, minimum of tardiness cost becomes the first objective. It is more import ant to select a reasonable objective by the actual condition during scheduli ng. In this paper scheduling problem of chemical batch process with due date is studied, two different intermediate storage policies and two different productio n modes are also discussed, production scheduling with different intermediate st orage policy and different production mode is proposed and the result is compare d. In order to complete all products within the due date, not only earliness and tardiness but also holding problem is considered, the objective is to selec t a proper intermediate storage policy and production mode and to minimize the c ost resulted by the earliness and tardiness, even the cost result by the interme diate storage. Scheduling with multiple stage and multiple machine is known as a NP-hard problem, mathematical program (MP) method, such as branch-and-bound (BAB), mixed integer linear program (MILP), etc, is often used to solve the sche duling problem. But as is well known, MP method is not good for combination opti mization, especially for large scale and complex optimal problem, whereas geneti c algorithm (GA) can overcome the MP method’s shortcoming and is fit for solvin g such scheduling problem. In this paper a modified genetic algorithm with speci al crossover operator and mutation operator is presented to solve this schedulin g problem. The results show such problem can be solved effectively with the pres ented method.
基金Zhejiang Provincial Natural Science Foundation (No. 698069) and High-Tech. Research andDevelopment Program (No. 863-511-945-002)
文摘In this paper, we give a mathematical model for earliness-tardiness job scheduling problem with a common due window on parallel and non-identical machines. Because the job scheduling problem discussed in the paper contains a problem of minimizing make-span, which is NP-complete on parallel and uniform machines, a heuristic algorithm is presented to find an approximate solution for the scheduling problem after proving an important theorem. Two numerical examples illustrate that the heuristic algorithm is very useful and effective in obtaining the near-optimal solution.
文摘The optimality of a fuzzy logic alternative to the usual treatment of uncertainties in a scheduling system using fuzzy numbers is examined formally. Processing times and due dates are fuzzified and presented by fuzzy numbers. With introducing the necessity measure, we compare fuzzy completion times of jobs with fuzzy due dates to decide whether jobs are tardy. The object is to minimize the numbers of tardy jobs. The efficient solution method for this problem is proposed. And deterministic counterpart of this single machine scheduling problem is a special case of fuzzy version.
文摘In this paper,attention is paid to study an algorithm for the common due datetotal weighted tardiness problem of single machine scheduling. Anapproximation alsorithm is given. It performs well in the sense of worst-casebehaviour and its worst-case performance ratio is 2.
文摘To describe the earliness/tardiness production planning problems in the JIT environment, a nonlinear semi\|infinite programming model was proposed in \. Due to a nonconvex objective function and many infinite constraints, the model is difficult to be solved by traditional methods. In this paper, simulated annealing method combined with a heuristic is developed. Numerical results shows that the present approach is very efficient. Theoretically, the developed method is an attempt to solve a continuous domain problem by using simulated annealing.
文摘This paper considers scheduling n jobs on a single machine where the job processing times anddue dates are independent random variables with arbitrary distribution functions.We consider the casethat the weighted job tardiness in expectation is minimized.It is assumed that job's due dates arecompatible with processing times and weights.We show that the jobs should be sequenced indecreasing stochastic order of their due dates.
文摘边缘计算广泛应用于物联网、车联网和在线游戏等新兴领域,通过网络边缘部署计算资源为终端设备提供低延迟计算服务.针对如何进行任务卸载以权衡任务执行时间与传输时间、如何调度多个不同截止期任务以最小化总延迟时间等挑战性问题,提出1种异构边缘协同的任务卸载和调度框架,包括边缘网络拓扑节点排序、边缘节点内任务排序、任务卸载策略、任务调度和结果调优等算法组件;设计多种任务卸载策略和任务调度策略;借助多因素方差分析(multi-factor analysis of variance,ANOVA)技术在大规模随机实例上校正算法算子和参数,得到统计意义上的最佳调度算法.基于EdgeCloudSim仿真平台,将所提出调度算法与其3个变种算法从边缘节点数量、任务数量、任务分布、截止期取值区间等角度进行性能比较.实验结果表明,所提出调度算法在各种情形下性能都优于对比算法.