A continuous time model for multiple yard crane scheduling with last minute job arrivals

Wenkai Li*, Mark Goh, Yong Wu, M. E.H. Petering, R. De Souza, Y. C. Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)


Container terminal (CT) operations are often bottlenecked by slow YC (yard crane) movements. Efficient YC scheduling to reduce the PM waiting time is therefore critical in increasing a CTs throughput. This paper develops an efficient continuous time MILP model for YC scheduling. The model treats realistic operational constraints such as multiple inter-crane interference, fixed YC separation distances, simultaneous container storage/retrievals, realistic YC acceleration/deceleration stages and gantry time, and require far fewer integer variables than previous work. The model significantly improves the solution quality compared to the existing discrete time models and other heuristics found in the literature. Using heuristics and a rolling-horizon algorithm, our model can solve actual container yard (CY) problems quickly and robustly in polynomial time. Also, to cope with the last minute container arrivals which can disrupt routine CT operations, two methods for handling these last minute job insertions are discussed and compared.

Original languageEnglish
Pages (from-to)332-343
Number of pages12
JournalInternational Journal of Production Economics
Issue number2
Publication statusPublished - 2012 Apr
Externally publishedYes


  • Container yard operations
  • Continuous time
  • Last minute jobs
  • Rolling-horizon algorithm
  • Scheduling

ASJC Scopus subject areas

  • General Business,Management and Accounting
  • Economics and Econometrics
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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