Optimal Allocation of Ships to Quay Length in Container Ports

Document Type : Research Paper


1 Dep. of Industrial Engineering, Islamic Azad University, South Tehran Branch, Iran

2 Dep. of Transportation Engineering, Islamic Azad University, Science and Research Branch, Iran


Due to the continuously increasing container trade, many terminals are presently operating at or close to capacity. An efficient terminal is one that facilitates the quick transshipment of containers to and from ships. In this sake, this paper addresses the ship assignments problem at a maritime container terminal, where ships are normally assigned to specific quay cranes until the work is finished. The paper’s target is to develop a new Continues Berth Allocation Problem (CBAP) in the form of a mixed integer nonlinear programming to achieve the best service time in a container terminal. For illustrating the accuracy of Proposed model (PM), Imai et. al. 's model (IM) (TRANSPORT RES B, 39 (2005) 199–221) was applied and a wide variety of computational test examples were conducted. The results of demonstrated that the presented BAPC reduces the number of nonlinear variables (constraints) and generates substantial savings in the CPU time.


Main Subjects

[1] Brown G.G., Lawphongpanich S., Thurman K.P. (1994), Optimizing ship berthing; Naval Research
Logistics 41; 1–15.
[2] Brown G.G., Cormican K.J., Lawphongpanich S., Widdis D.B. (1997), Optimizing submarine berthing
with a persistence incentive; Naval Research Logistics 44; 301–318.
[3] Guan Y., Xiao W.-Q., Chueng R.K., Li C.-L. (2002), A multiprocessor task scheduling model for berth
allocation: Heuristic and worst case analysis; Operations Research Letter 30; 343–350.
[4] Imai A., Nagaiwa K., Chan W.T. (1997), Efficient planning of berth allocation for container terminals
in Asia; Journal of Advanced Transportation 31; 75–94.
[5] Imai A., Nishimura E., Papadimitriou S. (2001), The dynamic berth allocation problem for a container
port; Transportation Research Part B 35; 401–417.
[6] Imai A., Nishimura E., Papadimitriou S. (2003), Berth allocation with service priority; Transportation
Research Part B 37; 437–457.
[7] Imai A., Nishimura E., Hattori M., Papadimitriou S. (2007), Berth allocation at indented berths for
mega-containerships; European Journal of Operational Research 179(2); 579-593.
[8] Imai A., Sun X., Nishimura E., Papadimitriou S. (2005), Berth allocation in a container port: Using a
continuous location space approach; Transportation Research Part B 39; 199–221.
[9] Kim K.H., Moon K.C. (2003), Berth scheduling by simulated annealing; Transportation Research Part
B 37; 541–560.
[10] Lai K.K., Shih K. (1992), A study of container berth allocation; Journal of Advanced Transportation
26; 45–60.
[11] Li C.-L., Cai X., Lee C.-Y. (1998), Scheduling with multiple-job-on-one-processor pattern; IIE
Transactions 30; 433–445.
[12] Lim A. (1998), The berth planning problem; Operations Research Letters 22; 105–110.
[13] Nishimura E., Imai A., Papadimitriou S. (2001), Berth allocation planning in the public berth system
by genetic algorithms; European Journal of Operational Research 131; 282–292.
[14] Park K.T., Kim K.H. (2002), Berth scheduling for container terminals by using a sub-gradient
optimization technique; Journal of the Operational Research Society 53; 1054–1062.
[15] Park Y.-M., Kim K.H. (2003), A scheduling method for berth and quay cranes; OR Spectrum 25; 1–23.
[16] Seyedalizadeh-Ganji S.R., Javanshir H., Vaseghi F. (2009), Nonlinear Mathematical Programming for
Optimal Management of Container Terminals; International Journal of Modern Physics B 23(27);
[17] Javanshir H., Seyedalizadeh-Ganji S.R. (2010), Yard crane scheduling in port container terminals
using genetic algorithm; Journal of Industrial Engineering International; In Press.
[18] 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 and Industrial Engineering 56(1); 241–248.
[19] Zhang C., Liu J., Wan Y.-W., Murty K.G., Linn R. (2003), Storage Space Allocation in Container
Terminals; Transportation Research Part B: Methodology 37B(10); 883–903.
[20] Vis I.F.A., Koster R.D. (2003), Transshipment of containers at a container terminal: An overview;
European Journal of Operational Research 147; 1–16.
[21] Bierwirth C., Meisel F. (2010), A survey of berth allocation and quay crane scheduling problems in
container terminals; European Journal of Operational Research 202; 615-627.