An improved approach for quay crane scheduling with non-crossing constraints

Der Horng Lee*, Jiang Hang Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)


Common deficiencies found in previous studies that modelled quay crane scheduling with non-crossing constraints (QCSNC) in port container terminals are identified. Remedies for the problems are proposed to prevent the occurrence of unrealistic optimal solutions for QCSNC. Additionally, two approximation schemes for QCSNC are studied. The first one is called the best partition (BP) method, which can be solved by dynamic programming (DP) with time complexity of O(mn2). A more efficient algorithm is designed to improve the original DP by adopting binary search. Next, based on BP and an exact algorithm for QCSNC (with pseudo-polynomial computational time), the second approximation scheme, called the enhanced best partition (EBP) method, is proposed to achieve a better estimation of the optimal makespan for QCSNC. The results of numerical experiments show that EBP is an effective approximation scheme for the problem of QCSNC.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalEngineering Optimization
Issue number1
Publication statusPublished - Jan 2010
Externally publishedYes


  • Approximation algorithms
  • Non-crossing constraints
  • Quay crane scheduling

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