Semi-online scheduling on two uniform processors
Theoretical Computer Science
Semi-online scheduling on two uniform machines with the known largest size
Journal of Combinatorial Optimization
Journal of Combinatorial Optimization
Online scheduling with rejection and withdrawal
Theoretical Computer Science
Optimal semi-online algorithm for scheduling with rejection on two uniform machines
Journal of Combinatorial Optimization
International Journal of Applied Evolutionary Computation
Semi-online scheduling on two identical machines with rejection
Journal of Combinatorial Optimization
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In this paper, we consider the problem of on-line scheduling a job sequence on two uniform machines. A job can be either rejected, in which case we pay its penalty, or scheduled on machines, in which case it contributes its processing time to the makspan of the constructed schedule. The objective is to minimize the sum of the makespan of the schedule for all accepted jobs and the penalties of all rejected jobs. Both preemptive and non-preemptive versions are considered. For the preemptive version, we present an optimal on-line algorithm with a competitive ratio ** for any s≥1, where s is the machine speed ratio. For the non-preemptive version, we present an improved lower bound. Moreover, as an optimal algorithm for s≥1.6180 is known, we present a modified version of the known algorithm, and show that it becomes optimal for any 1.3852≤ss