Lagrangian relaxation and cut generation for sequence-dependent setup time flowshop scheduling problems to minimise the total weighted tardiness

Tatsushi Nishi, Yuichiro Hiranaka

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

The Lagrangian relaxation and cut generation technique is applied to solve sequence-dependent setup time flowshop scheduling problems to minimise the total weighted tardiness. The original problem is decomposed into individual job-level subproblems that can be effectively solved by dynamic programming. Two types of additional constraints for the violation of sequence-dependent setup time constraints are imposed on the decomposed subproblems in order to improve the lower bound. The decomposed subproblem with the additional setup time constraints on any subset of jobs is also effectively solved by a novel dynamic programming. Computational results show that the lower bound derived by the proposed method is much better than those of CPLEX and branch and bound for problem instances with 50 jobs and five stages with less computational effort.

Original languageEnglish
Pages (from-to)4778-4796
Number of pages19
JournalInternational Journal of Production Research
Volume51
Issue number16
DOIs
Publication statusPublished - Aug 1 2013
Externally publishedYes

Keywords

  • Lagrangian relaxation
  • decomposition
  • flow shop scheduling
  • mathematical programming
  • mixed integer linear programming
  • operational research
  • optimisation
  • scheduling
  • sequence dependent setup time flowshop

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering

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