The vast majority of world trade is carried by the sea shipping industry and petroleum is still the major energy source. To reduce greenhouse gas emissions, it is an urgent need for both industry and government to promote green shipping. To move shipping towards a more environmentally and financially sustainable future, we consider to develop an integrated fleet deployment and bunker management model in this paper. The fleet deployment refers to the decisions on which ships to operate on which route, at what speed and what cargos to be transported. The bunker management refers to the decision on which ships to bunker on which port and at what volume. A more realistic fuel consumption function with considering not only cruise speed but also freight tonnage on board is adopted in the proposed optimization model, which can further improve its effectiveness in practice. An efficient algorithm termed "Most Promising Area Search" (MPAS) is developed afterwards to solve the corresponding mixed integer programming problem, which can guarantee to converge to a local optimal solution. The benefits of the integrated model and the computational performance of the MPAS are illustrated by numerical examples and a case study. learn more on arXiv