Multiship crane sequencing with yard congestion constraints

Shawn Choo*, Diego Klabjan, David Simchi-Levi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


Crane sequencing in container terminals determines the order of ship discharging and loading jobs that quay cranes (QCs) perform, so that the duration of a vessel's stay is minimized. The ship's load profile, berthing time, number of available bays, and QCs are considered. More important, clearance and yard congestion constraints need to be included, which, respectively, ensure that a minimum distance between adjacent QCs is observed and yard storage blocks are not overly accessed at any point in time. In sequencing for a single ship, a mixed-integer programming (MIP) model is proposed, and a heuristic approach based on the model is developed that produces good solutions. The model is then reformulated as a generalized set covering problem and solved exactly by branch and price (BandP). For multiship sequencing, the yard congestion constraints are relaxed in the spirit of Lagrangian relaxation, so that the problem decomposes by vessel into smaller subproblems solved by B&P. An efficient primal heuristic is also designed. Computational experiments reveal that large-scale problems can be solved in a reasonable computational time.

Original languageEnglish (US)
Pages (from-to)98-115
Number of pages18
JournalTransportation Science
Issue number1
StatePublished - Feb 2010


  • Branch and price
  • Optimization
  • Port operations

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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