International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2572

Full Length Research Paper

Using simulated annealing algorithm for optimization of quay cranes and automated guided vehicles scheduling

S. M. Homayouni1,2*, S. H. Tang2, N. Ismail2 and M. K. A. Ariffin2
  1Department of Industrial Engineering, Lenjan Branch, Islamic Azad University, Isfahan, Iran. 2Mechanical and Manufacturing Engineering Department, Engineering Faculty, Universiti Putra Malaysia, UPM Serdang, 43400, Malaysia.
Email: [email protected]

  •  Accepted: 24 August 2011
  •  Published: 02 November 2011



Sea port container terminals play an important role in the national and regional economy. The integrated scheduling of handling equipment has been recently investigated in literature to improve the performance of the container terminals. In this paper, an integrated scheduling of quay cranes and automated guided vehicles is formulated as a mixed integer linear programming model. This model minimizes the makespan of all the loading and unloading tasks for a set of cranes in a scheduling problem. Based on the simulated annealing (SA) algorithm, a scheduling method is proposed to solve the problem in a relatively short period of time. Comparison of the respective results of the mathematical model and the SA algorithm evidently shows acceptable performance of the proposed SA algorithm in finding good solutions for practical scheduling problems. Moreover, the effects of three cooling processes and two sets of control parameters on the best solution of the SA are investigated.


Key words: Quay cranes, automated guided vehicles, simulated annealing, integrated scheduling.


AGV, Automated guided vehicle; ALV: automated lifting vehicle; GA, genetic algorithm; SA, simulated annealing; CT, container terminal; YC, yard crane; QC, Quay crane; TEU, twenty equivalent units; UNCTAD, United Nations conference on trade and development; MIP, mixed integer programming; L/U, load/unload station; OQ, operational time for QCs; TQ, transferring time for QCs; PC, proposed cooling process; EC, exponential cooling process; LC, linear cooling process; M, the number of iterations in each temperature level; TI, initial Temperature; Tf, final temperature; Tr, Current temperature.