Scheduling Three Identical Parallel Machines with Capacity Constraints

  • Jian Sun
  • Dachuan Xu
  • Ran Ma
  • Xiaoyan ZhangEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)


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.


Approximation algorithm Parallel machine scheduling with capacity constraints Complex semidefinite programming 


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Authors and Affiliations

  1. 1.Department of Information and Operations ResearchCollege of Applied Mathematics, Beijing University of TechnologyBeijingPeople’s Republic of China
  2. 2.School of Mathematics and Information ScienceHenan Polytechnic UniversityJiaozuoPeople’s Republic of China
  3. 3.School of Mathematical Science & Institute of MathematicsNanjing Normal UniversityJiangsuPeople’s Republic of China

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