A New Approach for Sequencing Loading and Unloading Operations in the Seaside Area of a Container Terminal

Document Type: Research Paper


1 Ablmalek Essadi University, Tétouan, Morocco

2 College of Sciences, Abdelmallek Essaadi University, Tetuan, Morocco



Due to the considerable growth in the worldwide container transportation, optimization of container terminal operations is becoming highly needed to rationalize the use of logistics resources. For this reason, we focus our study on the Quay Crane Scheduling Problem (QCSP), which is a core task of managing maritime container terminals. From this planning problem arise two decisions to be made: The first one concerns tasks assignment to quay crane and the second one consists of finding the handling sequence of tasks such that the turnaround time of cargo vessels is minimized. In this paper, we provide a mixed-integer programming (MIP) model that takes into account non-crossing constraints, safety margin constraints and precedence constraints. The QCSP has been shown NP-complete, thus, we used the Ant Colony Optimization (ACO), a probabilistic technique inspired from ants’ behaviour, to find a feasible solution of such problem. The results obtained from the computational experiments indicate that the proposed method is able to produce good results while reducing the computational time.


Main Subjects

Bierwirth, C. & Meisel, F.(2010) A survey of berth allocation and quay crane scheduling problems in container terminals. European Journal of Operational Research, Vol. 202, pp. 615-627.

Chandra Mohan,B. & Baskaran,R. (2012) A survey: Ant Colony Optimization based recent research and implementation on several engineering domain. Expert Systems with Applications, Vol. 39, pp. 4618-4627.

Chen, J .H. Lee, D.-H. & Goh, M. (2014) An effective mathematical formulation for the unidirectional cluster-based quay crane scheduling problem. European Journal of Operational Research, Vol. 232, pp. 198-208.

Daganzo, C. F. (1989) The crane scheduling problem. Transportation Research Part B : Methodological, Vol. 23, pp. 159-175.

Diabat, A. & Theodorou, E. (2014) An Integrated Quay Crane Assignment and Scheduling Problem. Computers & Industrial Engineering. Vol. 73, pp. 115-123.

Dorigo, M.,Maniezzo, V. & Colorni, A. (1996) Ant system: optimization by a colony of cooperating agent. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, Vol. 26, pp. 29-41.

Exposito- Izuierdo, C., Gonzalez-Velarde, J.L., Melian-Batista, B. & MARCOS MORENO-VEGA, J. (2013) Hybrid Estimation of Distribution Algorithm for the Quay Crane Scheduling problem. Applied Soft Computing. Vol. 13, pp. 4063-4076.

Fu, Y.-M., Diabat, A. & Tsai, I. T. (2014) Amulti-vessel quay crane assignment and schedualing problem: Formulation and heuristic solution approach. Expert Systems with Applications, Vol. 41, pp. 6959-6965.

Kaveshgar, N. & Huynh, N. (2014) Integrated quay crane and yard truck scheduling for unloading inbound containers. International Journal of Production Economics.

Kaveshgar, N., Huynh, N. & Rahimian, S. K. (2012) An efficient genetic algorithm for solving the quay crane scheduling problem. Expert Systems with Applications, Vol. 39, pp. 13108-13117.

Keskinturk, T., Yildirim, M. B. & Barut, M. (2012) An ant colony optimization algorithm for load balancing in parallel machines with sequence-dependent setup times. Computers & Operations Research, Vol. 39, pp. 1225-1235.

Kim, K. H. & Park, Y.-M. (2004) A crane scheduling method for port container terminals. European Journal of Operational Research, Vol. 156, pp. 752-768.

Lajjam, A., El Merouani, M., Medouri, A. & Tabaa, Y. (2013) Mathematical model for Quay Crane Scheduling Problem with spatial constraints. International Journal of Innovation and Applied Studies, Vol. 4, pp. 547-551. 

Lajjam, A., El Merouani, M., Tabaa, Y. & Medouri, A. (2014a) An Efficient Algorithm for Solving Quay Crane Assignment Problem. pp. 13-18. 

Lajjam, A., El Merouani, M. & Medouri, A. (2014b) Ant colony system for solving quay crane scheduling problem in container terminal. In: 2nd IEEE Conf. on Logistics Operations Management (Ed. IEEE). Proc IEEE, Rabat, Morocco. 

Legato, P., Trunfio, R. & Meisel, F. (2012) Modeling and solving rich quay crane scheduling problems. Computers & Operations Research, Vol. 39, pp. 2063-2078. 

Meisel, F. & Bierwirth, C. (2011) A unified approach for the evaluation of quay crane scheduling models and algorithms. Computers & Operations Research,Vol. 38, pp. 683-693. 

Moccia, L., Cordeau, J.-F., Gaudioso, M. & Laporte, G. (2006) A branch-and-cut algorithm for the quay crane scheduling problem in a container terminal. Naval Research Logistics (NRL), Vol. 53, pp. 45-59. 

Peterkofsky, R. I. & Daganzo, C. F. (1990) A branch and bound solution method for the crane scheduling problem. Transportation Research Part B: Methodological, Vol. 24, pp. 159-172. 

Sammarra, M., Cordeau, J.-F., Laporte, G. & Monaco, M. F. (2007) A tabu search heuristic for the quay crane scheduling problem. Journal of Scheduling, Vol. 10, pp. 327-336. 

Tavakkoli-Moghaddam, R., Makui, A., Salahi, S., Bazzazi, M. & Taheri, F. (2009) An efficient algorithm for solving a new mathematical model for a quay crane scheduling problem in container ports. Computers & Industrial Engineering, Vol. 56, pp. 241-248. 

Tavares Neto, R. F. & Godinho Filho, M. (2013) Literature review regarding Ant Colony Optimization applied to scheduling problems: Guidelines for implementation and directions for future research. Engineering Applications of Artificial Intelligence, Vol. 26, pp. 150-161.

Unsal, O. & Oguz, C. (2013) Constraint programming approach to quay crane scheduling problem. Transportation Research Part E: Logistics and Transportation Review, Vol. 59, pp. 108-122.