Single machine flow-time scheduling with a single breakdown
Acta Informatica
Single machine flow-time scheduling with scheduled maintenance
Acta Informatica
Scheduling preemptable tasks on parallel processors with limited availability
Parallel Computing - Special issue on new trends on scheduling in parallel and distributed systems
Computers and Operations Research
Computers and Industrial Engineering
Approximation results for flow shop scheduling problems with machine availability constraints
Computers and Operations Research
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
Complexity and algorithms for two-stage flexible flowshop scheduling with availability constraints
Computers & Mathematics with Applications
Makespan Minimization with Machine Availability Constraints
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Approximation algorithms for scheduling with a variable machine maintenance
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Approximation schemes for scheduling with availability constraints
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Approximation schemes for parallel machine scheduling with availability constraints
Discrete Applied Mathematics
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We investigate the problems of scheduling n weighted jobs to one or more identical machines with the constraint that the machines may be unavailable in some specified time intervals. The objective is to find a schedule that minimizes the total weighted completion time. We consider both non-resumable and resumable schedules. Our first contributions concern approximability. For both resumable problem and non-resumable problem, we show that they cannot be approximated within an exponential factor by any polynomial time algorithm for multiple machines where each of them has an unavailable interval, even if the weight of each job equals to its processing time. Additionally, the non-resumable problem is also exponentially inapproximable for a single machine with two or more unavailable intervals. Then we develop the first FPTASs for the problems with a single unavailable interval among all machines. The running time is O(cnlog^dn(1@elogw)^d) for the non-resumable problem, and O(cnlog^dn(1@elogw)^d^+^1) for the resumable problem, where w is the product of the total weight and the total processing time of all jobs, c is the number of machines that are always available and d=6c+12. Thus our results give a clear boundary delineating the inapproximable cases and approximable cases. When there is a single machine and w=O(n^l^o^g^n^^^O^^^(^^^1^^^)), our algorithms greatly improve the current results. Note that instead of conventional ways of sequentially processing the jobs, our fast schemes process jobs in a divide-and-conquer fashion, which greatly reduces the running time. This may give some insight for some other related problems.