Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Approximate algorithms scheduling parallelizable tasks
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Approximation Algorithms for the Discrete Time-Cost Tradeoff Problem
Mathematics of Operations Research
Efficient approximation algorithms for scheduling malleable tasks
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Scheduling problems for parallel dedicated machines under multiple resource constraints
Discrete Applied Mathematics - International symposium on combinatorial optimisation
Unrelated parallel machine scheduling with resource dependent processing times
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
LP rounding and an almost harmonic algorithm for scheduling with resource dependent processing times
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Parallel machine scheduling with flexible resources
Computers and Industrial Engineering
Scheduling jobs with time-resource tradeoff via nonlinear programming
Discrete Optimization
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We consider a scheduling problem where a set of jobs is a-priori distributed over parallel machines. The processing time of any job is dependent on the usage of a scarce 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 dependence of processing times on the amount of resources is linear for any job. The objective is to find a resource allocation and a schedule that minimizes the makespan. Utilizing an integer quadratic programming relaxation, we show how to obtain a (3 + ε) -approximation algorithm for that problem, for any ε 0. This generalizes and improves previous results, respectively. Our approach relies on a fully polynomial time approximation scheme to solve the quadratic programming relaxation. This result is interesting in itself, because the underlying quadratic program is NP-hard to solve. We also derive lower bounds, and discuss further generalizations of the results.