In 2018 the International Maritime Organization (IMO) agreed to cut the shipping sector's overall CO2 output by 50% by 2050. One of the key methods in reaching this goal is to improve operations to limit fuel consumption. However, it is difficult to optimize speed for a complete liner shipping network as routes interact with each other, and several business constraints must be respected. This paper presents a unified model for speed optimization of a liner shipping network, satisfying numerous real-life business constraints. The speed optimization is in this research achieved by rescheduling the port call times of a network, thus, the network is not changed. The business constraints are among others related to transit times, port work shifts and emission control areas. Other restrictions are fixed times for canal crossing, speed restrictions in the piracy areas and desire for robust solutions. Vessel sharing agreements and other collaboration between companies must also be included. The modeling of the different restrictions is described in detail and tested on real-life data. The scientific contribution of this paper is threefold: We present a unified model for speed optimization together with numerous business constraints. We present a general framework for handling routes with different frequencies. Moreover, we present a bi-objective model for balancing robustness of schedules against fuel consumption. The tests show that the real-life requirements can be handled by mixed integer programming and that the model finds significant reductions of bunker consumption and cost for large-scale real-life instances.
In this paper the Container Positioning Problem is revisited. This problem arises at busy container terminals and requires one to minimize the use of block cranes in handling the containers that must wait at the terminal until their next means of transportation. We propose a new Mixed Integer Programming model that not only improves on earlier attempts at this problem, but also better reflects reality. In particular, the proposed model adopts a preference to reshuffle containers in line with a just-in-time concept, as it is assumed that data is more accurate the closer to a container's scheduled departure the time is. Other important improvements include a reduction in the model size, and the ability of the model to consider containers initially at the terminal. In addition, we describe several classes of valid inequalities for this new formulation and present a rolling horizon based heuristic for solving larger instances of the problem. We show that this new formulation drastically outperforms previous attempts at the problem through a direct comparison on instances available in the literature. Furthermore, we also show that the rolling horizon based heuristic can further reduce the solution time on the larger of these instances as well as find acceptable solutions to much bigger, artificially generated, instances.
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