Cooperation mode for a liner company with heterogeneous ports: Business cooperation vs. port investment

•The port investment always make the port better but may harm the liner company.•The port investment can bring Pareto gains to the supply chain.•Which port can win liner lies on the handling capacity and the time value.•The triple-win realizes at the cost of extracting more surplus of the shippers.•The port investment does not necessarily bring a greater market share to port.