Positioning empty containers among multiple ports with leasing and purchasing considerations

With the recent development of container transportation, the imbalance of empty containers among ports has become more serious. We consider the problem of positioning empty containers. The goal of this study is to propose a plan for transporting empty containers between container ports (terminals) to reduce the imbalance. There is currently a demand at each port and any backlog of containers is not permitted. The objective is to minimize the total relevant costs such as transportation cost, handling cost, and holding cost, etc. In this study, we develop a model with respect to the leasing and purchasing of containers. Mixed integer programming and genetic algorithms are used to solve the model. A hybrid GA is also proposed to reduce the computation time while still obtaining an acceptable result.