A mixed integer linear programming formulation is proposed for the simultaneous design of network and fleet deployment of a liner service providers for deep-sea shipping. The underlying network design problem is based on a 4-index (5-index by considering capacity type) formulation of the hub location problem which are known for their tightness. The demand is considered to be elastic in the sense that the service provider can accept any fraction of the origin-destination demand. We then propose a primal decomposition method to solve instances of the problem to optimality. Numerical results confirm superiority of our approach in comparison with a general-purpose mixed integer programming solver.