In this paper we consider an online scheduling of parallel jobs with preemption on identical machines, where jobs arrive over time. The objective is to minimize the makespan. For the problem that jobs have only two po...In this paper we consider an online scheduling of parallel jobs with preemption on identical machines, where jobs arrive over time. The objective is to minimize the makespan. For the problem that jobs have only two possible widths mj = 1 or m, we present an optimal online algorithm by using ＂temporary schedule＂.展开更多
P k |fix| C max problem is a new scheduling problem based on the multiprocessor parallel job, and it is proved to be NP hard problem when k ≥3. This paper focuses on the case of k =3. Some new observations and new te...P k |fix| C max problem is a new scheduling problem based on the multiprocessor parallel job, and it is proved to be NP hard problem when k ≥3. This paper focuses on the case of k =3. Some new observations and new techniques for P 3 |fix| C max problem are offered. The concept of semi normal schedulings is introduced, and a very simple linear time algorithm Semi normal Algorithm for constructing semi normal schedulings is developed. With the method of the classical Graham List Scheduling, a thorough analysis of the optimal scheduling on a special instance is provided, which shows that the algorithm is an approximation algorithm of ratio of 9/8 for any instance of P 3|fix| C max problem, and improves the previous best ratio of 7/6 by M.X.Goemans.展开更多
Cooperation of multi-domain massively parallel processor systems in computing grid environment provides new opportunities for multisite job scheduling. At the same time, in the area of co-allocation, heterogeneity, ne...Cooperation of multi-domain massively parallel processor systems in computing grid environment provides new opportunities for multisite job scheduling. At the same time, in the area of co-allocation, heterogeneity, network adaptability and scalability raise the challenge for the international design of multisite job scheduling models and algorithms. It presents multisite job scheduling schema through the introduction of multisite job scheduling model and the performance model under the grid environment. It introduces two job multisite and cooperative scheduling models and algorithms with the core of the optimal and greedy-heuristic resource selection strategies. Meanwhile, compared with single and multisite cooperative scheduling models and algorithms introduced by Sabin, Yahyapour and other persons, the validity and advance of the scheduling model and the performance model herein are proved.展开更多
In this paper, we consider scheduling problems with general truncated job-dependent learning effect on unrelated parallel-machine. The objective functions are to minimize total machine load, total completion (waiting)...In this paper, we consider scheduling problems with general truncated job-dependent learning effect on unrelated parallel-machine. The objective functions are to minimize total machine load, total completion (waiting) time, total absolute differences in completion (waiting) times respectively. If the number of machines is fixed, these problems can be solved in time respectively, where m is the number of machines and n is the number of jobs.展开更多
In order to overcome the shortcoming of the classical Hungarian algorithm that it can only solve the problems where the total cost is the sum of that of each job, an improved Hungarian algorithm is proposed and used t...In order to overcome the shortcoming of the classical Hungarian algorithm that it can only solve the problems where the total cost is the sum of that of each job, an improved Hungarian algorithm is proposed and used to solve the assignment problem of serial-parallel systems. First of all, by replacing parallel jobs with virtual jobs, the proposed algorithm converts the serial-parallel system into a pure serial system, where the classical Hungarian algorithm can be used to generate a temporal assignment plan via optimization. Afterwards, the assignment plan is validated by checking whether the virtual jobs can be realized by real jobs through local searching. If the assignment plan is not valid, the converted system will be adapted by adjusting the parameters of virtual jobs, and then be optimized again. Through iterative searching, the valid optimal assignment plan can eventually be obtained.To evaluate the proposed algorithm, the valid optimal assignment plan is applied to labor allocation of a manufacturing system which is a typical serial-parallel system.展开更多
In this paper, a parallel machine scheduling problem was considered , where the processing time of a job is a simple linear function of its starting time. The objective is to minimize makespan. A fully polynomial time...In this paper, a parallel machine scheduling problem was considered , where the processing time of a job is a simple linear function of its starting time. The objective is to minimize makespan. A fully polynomial time approximation scheme for the problem of scheduling n deteriorating jobs on two identical machines was worked out. Furthermore, the result was generalized to the case of a fixed number of machines.展开更多
This paper considers the single machine scheduling problem with uniform parallel machines in which the objective is to minimize the makespan. Four different GA based heuristics are designed by taking different combina...This paper considers the single machine scheduling problem with uniform parallel machines in which the objective is to minimize the makespan. Four different GA based heuristics are designed by taking different combinations of crossover methods, viz. single point crossover method and two point crossover method, and job allocation methods while generating initial population, viz. equal number of jobs allocation to machines and proportionate number of jobs allocation to machines based on machine speeds. A detailed experiment has been conducted by assuming three factors, viz. Problem size, crossover method and job allocation method on 135 problem sizes each with two replications generated randomly. Finally, it is suggested to use the GA based heuristic with single point crossover method, in which the proportionate number of jobs allocated to machines based on machine speeds.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.10971131)the Shanghai Leading AcademicDiscipline Project (Grant No.S30104)the Innovation Foundation of Shanghai University (Grant No.SHUCX091077)
文摘In this paper we consider an online scheduling of parallel jobs with preemption on identical machines, where jobs arrive over time. The objective is to minimize the makespan. For the problem that jobs have only two possible widths mj = 1 or m, we present an optimal online algorithm by using ＂temporary schedule＂.
文摘P k |fix| C max problem is a new scheduling problem based on the multiprocessor parallel job, and it is proved to be NP hard problem when k ≥3. This paper focuses on the case of k =3. Some new observations and new techniques for P 3 |fix| C max problem are offered. The concept of semi normal schedulings is introduced, and a very simple linear time algorithm Semi normal Algorithm for constructing semi normal schedulings is developed. With the method of the classical Graham List Scheduling, a thorough analysis of the optimal scheduling on a special instance is provided, which shows that the algorithm is an approximation algorithm of ratio of 9/8 for any instance of P 3|fix| C max problem, and improves the previous best ratio of 7/6 by M.X.Goemans.
基金This work was supported in part by the National Natural Science Foundation of China （Grant No. 90412001） the National Grand Fundamental Research 973 Program of China （Grant No. G2005CB321806）.
文摘Cooperation of multi-domain massively parallel processor systems in computing grid environment provides new opportunities for multisite job scheduling. At the same time, in the area of co-allocation, heterogeneity, network adaptability and scalability raise the challenge for the international design of multisite job scheduling models and algorithms. It presents multisite job scheduling schema through the introduction of multisite job scheduling model and the performance model under the grid environment. It introduces two job multisite and cooperative scheduling models and algorithms with the core of the optimal and greedy-heuristic resource selection strategies. Meanwhile, compared with single and multisite cooperative scheduling models and algorithms introduced by Sabin, Yahyapour and other persons, the validity and advance of the scheduling model and the performance model herein are proved.
文摘In this paper, we consider scheduling problems with general truncated job-dependent learning effect on unrelated parallel-machine. The objective functions are to minimize total machine load, total completion (waiting) time, total absolute differences in completion (waiting) times respectively. If the number of machines is fixed, these problems can be solved in time respectively, where m is the number of machines and n is the number of jobs.
文摘In order to overcome the shortcoming of the classical Hungarian algorithm that it can only solve the problems where the total cost is the sum of that of each job, an improved Hungarian algorithm is proposed and used to solve the assignment problem of serial-parallel systems. First of all, by replacing parallel jobs with virtual jobs, the proposed algorithm converts the serial-parallel system into a pure serial system, where the classical Hungarian algorithm can be used to generate a temporal assignment plan via optimization. Afterwards, the assignment plan is validated by checking whether the virtual jobs can be realized by real jobs through local searching. If the assignment plan is not valid, the converted system will be adapted by adjusting the parameters of virtual jobs, and then be optimized again. Through iterative searching, the valid optimal assignment plan can eventually be obtained.To evaluate the proposed algorithm, the valid optimal assignment plan is applied to labor allocation of a manufacturing system which is a typical serial-parallel system.
基金supported by the National Natural Science Foundation of China （Grant No.10101010）
文摘In this paper, a parallel machine scheduling problem was considered , where the processing time of a job is a simple linear function of its starting time. The objective is to minimize makespan. A fully polynomial time approximation scheme for the problem of scheduling n deteriorating jobs on two identical machines was worked out. Furthermore, the result was generalized to the case of a fixed number of machines.
文摘This paper considers the single machine scheduling problem with uniform parallel machines in which the objective is to minimize the makespan. Four different GA based heuristics are designed by taking different combinations of crossover methods, viz. single point crossover method and two point crossover method, and job allocation methods while generating initial population, viz. equal number of jobs allocation to machines and proportionate number of jobs allocation to machines based on machine speeds. A detailed experiment has been conducted by assuming three factors, viz. Problem size, crossover method and job allocation method on 135 problem sizes each with two replications generated randomly. Finally, it is suggested to use the GA based heuristic with single point crossover method, in which the proportionate number of jobs allocated to machines based on machine speeds.
