Exact methods for the quay crane scheduling problem when tasks are modeled at the single container level

Mohamed Kais Msakni, Ali Diabat, Ghaith Rabadi, Mohamed Al-Salem, Mariam Kotachi

Research output: Contribution to journalArticlepeer-review


The scheduling of quay cranes (QCs) to minimize the handling time of a berthed vessel is one of the most important operations in container terminals as it impacts the terminal's overall productivity. In this paper, we propose two exact methods to solve the quay crane scheduling problem (QCSP) where a task is defined as handling a single container and subject to different technical constraints including QCs’ safety margin, non-crossing, initial position, and nonzero traveling time. The first method is based on two versions of a compact mixed-integer programming formulation that can solve large problem instances using a general purpose solver. The second is a combination of some constraints of the proposed mathematical model and the binary search algorithm to reduce the CPU time, and solve more efficiently large-sized problems. Unlike existing studies, the computational study demonstrates that both methods can reach optimal solutions for large-sized instances and validates their dominance compared to an exact model proposed in the literature which finds solutions only for small problems.

Original languageEnglish (US)
Pages (from-to)218-233
Number of pages16
JournalComputers and Operations Research
StatePublished - Nov 2018


  • Container terminals
  • Mixed-integer programming
  • Quay crane scheduling problem
  • Scheduling

ASJC Scopus subject areas

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research


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