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- W1567693392 abstract "We consider a scheduling problem where the processing time of any job is dependent on the usage of a discrete renewable resource, e.g. personnel. An amount of $k$ units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The objective is to find a resource allocation and a schedule that minimizes the makespan. We explicitly allow for succinctly encodable timeresource tradeoff functions, which calls for mathematical programming techniques other than those that have been used before. Utilizing a (nonlinear) integer mathematical program, we obtain the first polynomial time approximation algorithm for the scheduling problem, withperformance bound $(3 + varepsilon)$ for any $varepsilon > 0$. Our approach relies on a fully polynomial time approximation scheme to solve the mathematical programming relaxation. This result is interesting in itself, because we also show that the underlying mathematical program isNP-hard to solve. We also derive lower bounds for the approximation." @default.
- W1567693392 created "2016-06-24" @default.
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- W1567693392 date "2008-04-01" @default.
- W1567693392 modified "2023-09-26" @default.
- W1567693392 title "Scheduling Parallel Jobs with Time-Resource Tradeoff via Nonlinear Programming" @default.
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