Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness

Tatsushi Nishi, Yuichiro Hiranaka, Masahiro Inuiguchi

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

In this paper, we address a new Lagrangian relaxation (LR) method for solving the hybrid flowshop scheduling problem to minimize the total weighted tardiness. For the conventional LR, the problem relaxing machine capacity constraints can be decomposed into individual job-level subproblems which can be solved by dynamic programming. The Lagrangian dual problem is solved by the subgradient method. In this paper, a Lagrangian relaxation with cut generation is proposed to improve the Lagrangian bounds for the conventional LR. The lower bound is strengthened by imposing additional constraints for the relaxed problem. The state space reductions for dynamic programming for subproblems are also incorporated. Computational results demonstrate that the proposed method outperforms the conventional LR method without significantly increasing the total computing time.

Original languageEnglish
Pages (from-to)189-198
Number of pages10
JournalComputers and Operations Research
Volume37
Issue number1
DOIs
Publication statusPublished - Jan 2010
Externally publishedYes

Keywords

  • Cut generation
  • Dynamic programming
  • Hybrid flowshop scheduling
  • Lagrangian relaxation

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research

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