Parallel machines scheduling with nonsimultaneous machine available time
Discrete Applied Mathematics
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Single-machine scheduling with periodic maintenance and nonresumable jobs
Computers and Operations Research
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
The effect of machine availability on the worst-case performance of LPT
Discrete Applied Mathematics
Scheduling a maintenance activity to minimize total weighted completion-time
Computers & Mathematics with Applications
Some scheduling problems with general position-dependent and time-dependent learning effects
Information Sciences: an International Journal
Scheduling jobs under increasing linear machine maintenance time
Journal of Scheduling
Minimizing total completion time on a single machine with a flexible maintenance activity
Computers and Operations Research
Information Sciences: an International Journal
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We introduce and study a parallel machine scheduling problem with almost periodic maintenance activities. We say that the maintenance of a machine is ε-almost periodic if the difference of the time between any two consecutive maintenance activities of the machine is within ε. The objective is to minimize the makespan Cmax, i.e., the completion time of the last finished maintenance. Suppose the minimum and maximum maintenance spacing are T and T'=T+ε, respectively, then our problem can be described as Pm,MS[T,T']||C max. We show that this problem is NP-hard, and unless P=NP, there is no polynomial time ρ-approximation algorithm for this problem for any ρ2T'/T-approximation algorithm named BFD-LPT to solve the problem. Thus, if T'=T, BFD-LPT algorithm is the best possible approximation algorithm. Furthermore, if the total processing time of the jobs is larger than 2m(T'+TM) and min{ρi}≥T, where T"M is the amount of time needed to perform one maintenance activity, then the makespan derived from BFD-LPT algorithm is no more than that of the optimal makespan. Finally, we show that the BFD-LPT algorithm has an asymptotic worst-case bound of 1+σ/(1+2σ) if min{ρi}≥T, where σ=TM/T'.