Modelling Approaches for Maritime Fleet Deployment with Speed Optimization and Voyage Separation Requirements
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This thesis studies the fleet deployment problem within the liner shipping segment of the shipping industry. A shipping company has a predefined set of intercontinental trade routes, and serves numerous voyages on each trade route within a given planning horizon. These voyages are operated by a heterogeneous fleet of ships where each ship has a predefined speed range within which it can sail. The fuel consumption, hence the fuel costs, is a function of speed. Thus, optimizing the sailing speed has a great impact of the sailing costs. The shipping companies enter Contracts of Affreightment with the cargo owners, regarding the handling of cargo. On of the things that these state is that voyages on a given trade route should be fairly even spread between them. These two factors lead to the maritime fleet deployment problem with speed optimization and voyage separation requirements. Two models are proposed to solve the problem at hand, an arc flow and a path flow formulation. The fuel consumption function is a non-linear function of speed and is linearized by choosing discrete speed points and linear combinations of these. The voyage separation requirements are formulated as hard constraints, setting a lower limit for the required spread between voyages. The path flow model is in itself one of the main contributions from this thesis, as it has, to the authors' knowledge, never before been combined with speed optimization and the voyage separation requirement as presented in this thesis. The path flow model is based on a decomposition approach. A subproblem for each ship handles the generation of all possible paths a priori to solving the model. The master problem selects one path per ship, as well as deciding the speed along each sailing leg, in order to maximize profit. Further, path reduction heuristics are introduced. This enables the path flow model to handle larger problem instances and obtain better solutions faster. Computational results show that the path flow model outperforms the arc flow model, both with regard to solution time and objective value. Thus, further analyses are conducted on the path flow model only. Results from analyzing the speed optimization part of the problem shows that implementing speed optimization provide higher profits, though uses longer time to find the solution. In total, the path flow model performs well, but it struggles to handle problem instances with too many paths, and the number of paths increase vastly when problem size increases. Path reduction heuristics are used to solve larger instances, that are not possible to solve within reasonable time. The path flow model with the heuristics provide a better solution quality in a much shorter amount of time. When utilizing these heuristics, problem instances with 18 ships and a planing horizon up to 150 days are solved. The effects of combining the voyage separation requirement and speed optimization are analyzed. It is discovered that including speed optimization, intensifies the need for the voyage separation requirement.