Variable Neighborhood Search for Multi-Port Berth Allocation with Vessel Speed Optimization

Abstract

This paper delves into the multi-port berth allocation problem (MBAP), enriching the traditional berth allocation problem (BAP) with vessel speed optimization (VSO). In the MBAP, it is assumed that there is cooperation between the port and the shipping companies, and the operation of the vessels and the ports is planned to maximize the overall benefits. Exploring this potential collaboration between ports and shipping entities has the potential to mitigate, or even resolve, the challenges plaguing maritime transportation, e.g., port congestion and suboptimal vessel schedules, to ultimately enhance the efficiency of maritime trade. In this paper, a new mixed-integer linear programming (MILP) model for the MBAP is formulated, which attempts to minimize the total cost incurred during operations, with various constraints such as vessel sailing, the vessel space–time relationship in ports, and the planning period. Meanwhile, an innovative variable neighborhood search (VNS) algorithm is presented, in which the initial solution generation method and neighborhood structures are proposed according to the MBAP characteristics. Furthermore, two sets of MBAP instances are generated to test the proposed MILP and VNS, of which the first set is based on real-world port data and the second on existing studies. The numerical experiments verify that the VNS can efficiently and reliably solve instances of all scales, with each neighborhood structure contributing uniquely to the iterative process. In addition, by analyzing the impact of varying oil prices on the MBAP, the study offers valuable management insights. Finally, a case study based on real data from a port group in the Yangtze River Basin is presented to further demonstrate the necessity of considering vessel service time window and planning period in the MBAP as well as the important role of the VSO in scheduling.