Abstract
This paper deals with the problem of processing a set of n jobs on two identical parallel machines. In order to reduce the probability of machine breakdown with minor sacrifices in production time, the machines cannot process the jobs consecutively, they need to be maintained regularly (here we assume that the largest consecutive working time for each machine cannot exceed an upper limit T). Two scheduling models are considered. In the first model, the maintenance activities are performed periodically and the objective is to schedule the jobs on two machines such that the makespan is minimized. In the second model, the maintenance activities are determined jointly with the scheduling of jobs, and the objective is to minimize the total completion time of jobs. For the first problem, we introduce an O ( n 2 ) time algorithm named MH FFD and show that the performance ratio of MH FFD is at most max { 1.6 + 1.2 σ , 2 } , where σ ≜ t / T , t is the amount of time to perform each maintenance activity. For the second problem, we apply the classical SPT algorithm to it and show that the worst-case bound of SPT algorithm is no more than 1 + 2 σ . We also point out that for the case of single machine, if the SPT schedule has three batches, then the upper bound of SPT algorithm can be reduced from the known result 21/17 to 11/9 under the assumption that t < T .
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.