Abstract
We study a basic scheduling problem with resource constraints: A number of jobs need to be scheduled on two parallel identical machines with the objective of minimizing the makespan, subject to the constraint that jobs may require a unit of one of the given renewable resources during their execution. For this NP-hard problem, we develop a fully polynomial-time approximation scheme (FPTAS). Our FPTAS makes a novel use of existing algorithms for the subset-sum problem and the open shop scheduling problem.
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