The combination of online or semi-online with deterioration jobs has never been researched in scheduling problems. In this paper, two semi-online parallel machine scheduling problems with linear deterioration processi...The combination of online or semi-online with deterioration jobs has never been researched in scheduling problems. In this paper, two semi-online parallel machine scheduling problems with linear deterioration processing time are considered. In the first problem, it is assumed that the deterioration rates of jobs are known in an interval, that is, bj ∈[0, α], where 0 〈α≤ 1 and bj denotes the linear deterioration rate. In the second problem, it is assumed that the largest deterioration rate of jobs is known in advance, that is, b = max1≤j≤n {bj }. For each of the two problems, a heuristic MBLS algorithm is worked out and its worst-case ratio is analyzed. At the same time, the worst-case ratio of the list （LS） algorithm is investigated and it is proved that all the ratios are tight.展开更多
We consider several uniform parallel-machine scheduling problems in which the processing time of a job is a linear increasing function of its starting time.The objectives are to minimize the total completion time of a...We consider several uniform parallel-machine scheduling problems in which the processing time of a job is a linear increasing function of its starting time.The objectives are to minimize the total completion time of all jobs and the total load on all machines.We show that the problems are polynomially solvable when the increasing rates are identical for all jobs;we propose a fully polynomial-time approximation scheme for the standard linear deteriorating function,where the objective function is to minimize the total load on all machines.We also consider the problem in which the processing time of a job is a simple linear increasing function of its starting time and each job has a delivery time.The objective is to find a schedule which minimizes the time by which all jobs are delivered,and we propose a fully polynomial-time approximation scheme to solve this problem.展开更多
文摘The combination of online or semi-online with deterioration jobs has never been researched in scheduling problems. In this paper, two semi-online parallel machine scheduling problems with linear deterioration processing time are considered. In the first problem, it is assumed that the deterioration rates of jobs are known in an interval, that is, bj ∈[0, α], where 0 〈α≤ 1 and bj denotes the linear deterioration rate. In the second problem, it is assumed that the largest deterioration rate of jobs is known in advance, that is, b = max1≤j≤n {bj }. For each of the two problems, a heuristic MBLS algorithm is worked out and its worst-case ratio is analyzed. At the same time, the worst-case ratio of the list （LS） algorithm is investigated and it is proved that all the ratios are tight.
基金This work was supported by the National Natural Science Foundation of China(Nos.11071142,11201259)the Natural Science Foundation of Shan Dong Province(No.ZR2010AM034)+1 种基金the Doctoral Fund of the Ministry of Education(No.20123705120001)We thank the two anonymous reviewers for their helpful and detailed comments on an earlier version of our paper.
文摘We consider several uniform parallel-machine scheduling problems in which the processing time of a job is a linear increasing function of its starting time.The objectives are to minimize the total completion time of all jobs and the total load on all machines.We show that the problems are polynomially solvable when the increasing rates are identical for all jobs;we propose a fully polynomial-time approximation scheme for the standard linear deteriorating function,where the objective function is to minimize the total load on all machines.We also consider the problem in which the processing time of a job is a simple linear increasing function of its starting time and each job has a delivery time.The objective is to find a schedule which minimizes the time by which all jobs are delivered,and we propose a fully polynomial-time approximation scheme to solve this problem.
