Abstract
The single machine scheduling with resource constraint is a nonlinear combinatorial optimization problem in cloud computing applications. Given a set of jobs and certain resource, the problem is to find a permutation of jobs and a distribution of resource to optimize certain objective function. The processing time of each job is a nonlinear function with respect to the resource assigned to it. In this paper, we propose a naive algorithm and study a subproblem in the algorithm that suppose the permutation of jobs is also given, how to find a resource distribution to minimize the total weighted flow time. We found a polynomial-time optimal solution for a special case and an approximation solution in general case.
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The author cordially thanks the anonymous referees for their valuable comments which lead to the improvement of this paper.
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Wu, L., Cheng, CD. On single machine scheduling with resource constraint. J Comb Optim 31, 491–505 (2016). https://doi.org/10.1007/s10878-014-9721-5
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DOI: https://doi.org/10.1007/s10878-014-9721-5