Scheduling under Linear Constraints

Kameng Nip Tsinghua University Zhenbo Wang Tsinghua University Zizhuo Wang University of Minnesota

Optimization and Control mathscidoc:1611.27001

European Journal of Operational Research, 253, 290-297, 2016
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job completion time among all feasible choices. This novel problem is motivated by various real-world application scenarios. We discuss the computational complexity and algorithms for various settings of this problem. In particular, we show that if there is only one machine with an arbitrary number of linear constraints, or there is an arbitrary number of machines with no more than two linear constraints, or both the number of machines and the number of linear constraints are fixed constants, then the problem is polynomial-time solvable via solving a series of linear programming problems. If both the number of machines and the number of constraints are inputs of the problem instance, then the problem is NP-Hard. We further propose several approximation algorithms for the latter case.
parallel machine scheduling; linear programming; computational complexity; approximation algorithm
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  title={Scheduling under Linear Constraints},
  author={Kameng Nip, Zhenbo Wang, and Zizhuo Wang},
  booktitle={European Journal of Operational Research},
Kameng Nip, Zhenbo Wang, and Zizhuo Wang. Scheduling under Linear Constraints. 2016. Vol. 253. In European Journal of Operational Research. pp.290-297.
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