The scheduling problem on a single batching machine with family jobs was proposed.The single batching machine can process a group of jobs simultaneously as a batch.Jobs in the same batch complete at the same time.The ...The scheduling problem on a single batching machine with family jobs was proposed.The single batching machine can process a group of jobs simultaneously as a batch.Jobs in the same batch complete at the same time.The batch size is assumed to be unbounded.Jobs that belong to different families can not be processed in the same batch.The objective function is minimizing maximum lateness.For the problem with fixed number of m families and n jobs,a polynomial time algorithm based on dynamic programming with time complexity of O(n(n/m+1)m)was presented.展开更多
We study a scheduling problem with incompatible job families and rejection on a parallel-batching machine,where the objective is to minimize the makespan of all accepted jobs plus the total penalty of all rejected job...We study a scheduling problem with incompatible job families and rejection on a parallel-batching machine,where the objective is to minimize the makespan of all accepted jobs plus the total penalty of all rejected jobs.We provide a polynomial-time algorithm for the case where all jobs have identical release dates and a pseudo-polynomial-time algorithm for the case where the number of distinct release dates is fixed.We also present a 2-approximation algorithm and a polynomial-time approximation scheme for the general problem.展开更多
基金National Natural Science Foundation of China(No.70832002)Graduate Student Innovation Fund of Fudan University,China
文摘The scheduling problem on a single batching machine with family jobs was proposed.The single batching machine can process a group of jobs simultaneously as a batch.Jobs in the same batch complete at the same time.The batch size is assumed to be unbounded.Jobs that belong to different families can not be processed in the same batch.The objective function is minimizing maximum lateness.For the problem with fixed number of m families and n jobs,a polynomial time algorithm based on dynamic programming with time complexity of O(n(n/m+1)m)was presented.
基金supported in part by National Natural Science Foundation of China(NSFC,Nos.11326191,11401604,11401605 and 11171313)NSF of Henan Province(No.132300410392)the Education Department of Henan Province Natural Science Research Program(No.14A110027)。
文摘We study a scheduling problem with incompatible job families and rejection on a parallel-batching machine,where the objective is to minimize the makespan of all accepted jobs plus the total penalty of all rejected jobs.We provide a polynomial-time algorithm for the case where all jobs have identical release dates and a pseudo-polynomial-time algorithm for the case where the number of distinct release dates is fixed.We also present a 2-approximation algorithm and a polynomial-time approximation scheme for the general problem.
