Notes on "some single-machine scheduling problems with general position-dependent and time-dependent learning effects"

  • Authors:

  • Yunqiang Yin;Dehua Xu;Xiaokun Huang

  • Affiliations:

  • School of Mathematics and Information Sciences, East China Institute of Technology, Fuzhou, Jiangxi 344000, China;School of Mathematics and Information Sciences, East China Institute of Technology, Fuzhou, Jiangxi 344000, China;Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

This paper provides a continuation of the idea presented by Yin et al. [Yin et al., Some scheduling problems with general position-dependent and time-dependent learning effects, Inform. Sci. 179 (2009) 2416-2425]. For each of the following three objectives, total weighted completion time, maximum lateness and discounted total weighted completion time, this paper presents an approximation algorithm which is based on the optimal algorithm for the corresponding single-machine scheduling problem and analyzes its worst-case bound. It shows that the single-machine scheduling problems under the proposed model can be solved in polynomial time if the objective is to minimize the total lateness or minimize the sum of earliness penalties. It also shows that the problems of minimizing the total tardiness, discounted total weighted completion time and total weighted earliness penalty are polynomially solvable under some agreeable conditions on the problem parameters.