Stochastic Programming for Maritime Fleet Renewal Problems
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The scope of this thesis is to develop knowledge and methods, based on mathematical programming, for the Maritime Fleet Renewal Problem (MFRP). The MFRP consists of finding the best modification of the current fleet of ships by adding or removing ships. Ships can be added and removed in several ways (e.g. second-hand market, charter, new build, demolition). Modifications are done pursuing the shipping company’s objective while meeting the market requirements. This thesis consists of four research papers describing and improving the state-of-research relative to the MFRP. Given the high volatility in the shipping business, particular emphasis is put on handling uncertainty. For this reason, the new methods proposed are based on stochastic programming, which consists of mathematical programming when parameters are described by distributions. The first paper presents a survey of the scientific literature on the MFRP. The paper, in the first part, analyzes and categorized past research contributions to the problem. In the second part, based on the analysis of the gap between the available methods and the industrial needs, the paper proposes new research direction. The second paper presents a new stochastic programming model for the MFRP. The new model improves the available ones by considering more real-life elements of the problem, and uncertainty extended to several market parameters. Based on the case of Wallenius Wilhelmsen Logistics, a major liner shipping company, the paper shows the benefits of including uncertainty in the model, and suggests in which market conditions uncertainty is more important. The third paper presents a solution method for multistage stochastic programs with a special structure which is also present in the MFRP. The method is tested on the MFRP but can solve general multistage mixed-integer stochastic programs with the same structure. Tests show that the method outperforms commercial optimization software on medium and large instances. Finally, the fourth paper presents a method to numerically evaluate a model of the uncertainty affecting the problem. The method evaluates the importance of individual properties of the model of the uncertainty.