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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 746781, 9 pages
Research Article

Multi Objective Optimization of Coordinated Scheduling of Cranes and Vehicles at Container Terminals

1Department of Industrial Engineering, Lenjan Branch, Islamic Azad University, Zarinshahr, Esfahan 84741, Iran
2Department of Mechanical and Manufacturing Engineering, Faculty of Engineering, Universiti Putra Malaysia, UPM Serdang, 43400 Selangor, Malaysia

Received 20 March 2013; Revised 28 May 2013; Accepted 1 June 2013

Academic Editor: Wen-Jer Chang

Copyright © 2013 Seyed Mahdi Homayouni and Sai Hong Tang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


According to previous researches, automated guided vehicles and quay cranes in container terminals have a high potential synergy. In this paper, a mixed integer programming model is formulated to optimize the coordinated scheduling of cranes and vehicles in container terminals. Objectives of the model are to minimize total traveling time of the vehicles and delays in tasks of cranes. A genetic algorithm is developed to solve the problem in reasonable computational time. The most appropriate control parameters for the proposed genetic algorithm are investigated in a medium size numerical test case. It is shown that balanced crossover and mutation rates have the best performance in finding a near optimal solution for the problem. Then, ten small size test cases are solved to evaluate the performance of the proposed optimization methods. The results show the applicability of the genetic algorithm since it can find near optimal solutions, precisely and accurately.