Abstract
In many flexible manufacturing systems, it is quite important to balance the number of jobs allocated to each single production facility. Yang, Ye and Zhang (2003) considered the problem that schedules n jobs on two identical parallel machines, with a capacity constraint on each machine, i.e. the number of jobs that each machine can process is bounded, so as to minimize the total weighted completion time of these jobs by semidefinite programming relaxation. In this paper, we further consider the problem of three identical parallel machines with capacity constraints and present a 1.4446-approximation algorithm based on complex semidefinite programming relaxation by extending the previous techniques.
Supported by Natural Science Foundation of China(Grant Nos. 11531014, 11871081, 11871280, 11471003, 11501171) and Qinglan Project.
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Sun, J., Xu, D., Ma, R., Zhang, X. (2020). Scheduling Three Identical Parallel Machines with Capacity Constraints. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_107
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DOI: https://doi.org/10.1007/978-3-030-21803-4_107
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