Optimization of Berth allocations in container terminals

Abstract

Efficient and effective berth allocation is essential to guarantee high container

throughput in a container terminal. Modern mega-terminals are usually comprised of

multiple disjointed berths. However, this type of Berth Allocation Problem (BAP) has

not attracted a lot of attention from the academic world due to its great complexity.

This research develops new methodologies for solving complex BAPs, in particular,

BAPs involving quay crane scheduling in a multiple-berth environment.

This research develops a mathematical model and a new Branch and Price

algorithm (B&P) which hybridizes the column generation approach and the Branch

and Bound method (B&B) to generate optimal multiple-berth plans (MBAP) within

acceptable time limits. A new exact algorithm based on the label-correcting concept is

designed to obtain all potential columns by defining a new label structure and

dominance rules. To accelerate the generation of columns, two heuristics are proposed

to distribute vessels among berths and to establish the handling sequence of the

vessels allocated to each berth. An early termination condition is also developed to

avoid the “tailing off effect” phenomenon during column generation process. The

effectiveness and robustness of the proposed methodology are demonstrated by

solving a set of randomly generated test problems.

Since the Berth Allocation Problem (BAP) and the Quay Crane Scheduling

Problem (QCSP) strongly interact, this research also studies the Simultaneous Berth Allocation and Quay Crane Scheduling Problem (BAQCSP). An advanced

mathematical model and a new hybrid meta-heuristic GA-TS algorithm which is

based on the concept of Genetic Algorithm (GA) are developed to solve the proposed

BAQCSP effectively and efficiently. A new crossover operation inspired by the

memory-based strategy of Tabu Search (TS) and the mutation operation are

implemented to avoid premature convergence of the optimization process. The local

search ability of TS is incorporated into the mutation operation to improve the

exploitation of the solution space. Comparative experiments are also conducted to

show the superiority of the performance of the proposed GA-TS Algorithm over the

B&B and the canonical GA.

Furthermore, this research extends the scope of BAQCSP to consider the

Simultaneous Multiple-berth Allocation and Quay Crane Scheduling Problem

(MBAQCSP). A MBAQCSP model is developed consisting of various operational

constraints arising from a wide range of practical applications. Since MBAQCSP

combines the structures of both MBAP and BAQCSP, the exact B&P proposed for

solving MBAP can be modified to optimally solve MBAQCSP. However, the

calculation time of B&P increases significantly as the V/B ratio (i.e., vessel number to

berth number) grows. In order to eliminate this shortcoming, this research develops a

GA-TS Aided Column Generation Algorithm which hybridizes the GA-TS Algorithm

proposed for solving BAQCSP with the Column Generation Algorithm to locate the

optimal or near optimal solutions of MBAQCSP. The computational results show that

the proposed hybrid algorithm locates excellent near optimal solutions to all test

problems within acceptable time limits, even problems with high V/B ratios. Finally,

this research also shows that the proposed GA-TS Aided Column Generation

Algorithm can be easily modified to solve MBAP efficiently.