Transport typically represents 10-20% of the final cost of goods. Transport has serious environmental impacts. CO2 emission from seaborne transport is estimated at 1 billion tons annually. Use of discrete optimization in logistics has been a huge success. Studies refer to potential savings of 5-20% in costs and 14% in fuel consumption. The eVITA project DOMinant has led to improved models and optimization algorithms for important transport problems. As one of the results, SINTEF's inventory routing solver INVENT has already demonstrated large savings in the LNG business. There is still a gap between the research frontier and industrial needs. In DOMinant II, we will significantly reduce this gap by developing models and efficient solution algorithms for computationally hard discrete optimization problems (DOPs) in transport. NTNU, Molde University College (MUC), and SINTEF Applied Mathematics (SAM) shall work closely together. We shall develop formulations of critical DOPs. We will extend the inventory routing problem and the fleet composition problem to satisfy industrial needs that have not been studied yet. NTNU will focus on exact solution methods, relaxations, and bounds. Metaheuristics and hybrid methods for industrial sized problems will be developed in collaboration. Parallel and collaborative methods will be designed by MUC and SAM. Extensive computational experiments are integral to the project. To speed up development, we shall utilize supercomputers including the NOTUR infrastructure. Through DOMinant II, we shall further strengthen and integrate the work of the groups. 2 PhDs and 2 postdocs will be recruited. The groups have wide international networks that will be strengthened through workshops, visiting researchers, and joint publication. We have close cooperation with CIRRELT and GERAD, Canada (routing problems); INRIA, France (parallel and heterogeneous optimization); CIDMA, Portugal (stochastic optimization and exact methods).