Speed optimization for a container shipping route in competitive environment

Considering the fact that different companies operate simultaneously in the same route, shipping companies should focus on the market segments in which they are expert to achieve the competitive advantages. Meanwhile, the increasing oil price urges them to reduce fuel costs by slow-steaming. A speed optimization model incorporating transit time and price is proposed to satisfy the demands of customers. A Lagrangian Relaxation Algorithm is applied to decompose the original problem into two kinds of sub problems, minimizing the oil cost and opportunity loss cost, which are coordinated by subgradient algorithm. Numerical studies show that the model can be considerably refined and solved very fast with the proposed algorithm, the results indicate that higher speed should be taken on segments full of cargoes, while fewer cargoes lead to lower speed, studies on three kinds of cargoes imply that decreasing price results in higher profit except for those who care little about price.