The Multiport Berth Allocation Problem with Speed Optimization: Exact Methods and a Cooperative Game Analysis

Abstract

We consider a variant of the berth allocation problem—that is, the multiport berth allocation problem—aimed at assigning berthing times and positions to vessels in container terminals. This variant involves optimizing vessel travel speeds between multiple ports, thereby exploiting the potentials of a collaboration between carriers (shipping lines) and terminal operators. Using a graph representation of the problem, we reformulate an existing mixed-integer problem into a generalized set partitioning problem, in which each variable refers to a sequence of feasible berths in the ports that the vessel visits. By integrating column generation and cut separation in a branch-and-cut-and-price procedure, our proposed method is able to outperform commercial solvers in a set of benchmark instances and adapt better to larger instances. In addition, we apply cooperative game theory methods to efficiently distribute the savings resulting from a potential collaboration and show that both carriers and terminal operators would benefit from collaborating.

An adaptive large neighborhood search heuristic for the multi-port continuous berth allocation problem

“…This could be due to a low-quality solution or a poor lower bound. Martin-Iradi et al (2022b) indicated that the relaxation of the MIP formulation for the MBAP with a discrete quay could be poor and showed that a network-flow reformulation could tighten the relaxation significantly. As indicated in Martin-Iradi et al (2022a), network-flow formulations for the MCBAP can suffer from scalability but show that the relaxation is stronger.…”

“…It solved a dynamic and discrete BAP in multiple ports while optimizing ships' sailing speed between ports. Martin-Iradi et al (2022b) presented a branch-and-price method for the same problem and conducted a study of the collaboration mechanism using cooperative game theory. Martin-Iradi et al (2022a) extended the branch-and-price method to the MBAP with a continuous quay, the same problem of this study, and showed that exact methods are competitive for small and medium size instances but struggle to scale for larger instances.…”

“…It is well known that the relation between sailing speed and fuel consumption is non-linear. In fact, this relation is often approximated with a cubic function as in Equation (1) (Venturini et al, 2017;Martin-Iradi et al, 2022b)…”

“…The problem involves the joint optimization of carrier and terminal operations and relies on the a priori agreement of the vessels and ports involved. Martin-Iradi et al (2022b) showed that this type of collaboration could generate cost savings for the players involved (i.e., shipping carriers and terminal operators) but also benefit the environment as fuel emissions can be reduced significantly.…”

Container Shipping Scheduling Method Based on the Evidence Reasoning Approach in Fluctuating CCFI and BDI Cycle

“…For decades, many scheduling methods have been developed, such as scheduling with Soft Time Window [1][2][3]; Maritime considering inventory, draft limits, and bunker cost [4][5][6]; routing problem with berthing time clash avoidance constraints [7][8][9][10]; green logistics, green ports [11,12], and Big Data in Maritime Logistics [13,14]. In these methods, scheduling problems are modelled using shipping matrices in which an attribute is assessed using a certain number of criteria.…”