Application of a mixed fuzzy decision making and optimization programming model to the empty container allocation

Containerization transportation has been growing fast in the past few decades. International trades have been growing fast since the globalization of world economies intensified in the early 1990s. However, these international trades are typically imbalanced in terms of the numbers of import and export containers. As a result, the relocation of empty containers has become one of the important problems faced by liner shipping companies. In this paper, we consider the empty container allocation problem where we need to determine the optimal volume of empty containers at a port and to reposition empty containers between ports to meet exporters’ demand over time. We formulate this empty container allocation problem as a two-stage model: in stage one, we propose a fuzzy backorder quantity inventory decision making model for determining the optimal quantity of empty container at a port; whereas in stage two, an optimization mathematical programming network model is proposed for determining the optimal number of empty containers to be allocated between ports. The parameters such as the cost of loading container, cost of unloading container, leasing cost of empty container, cost of storing container, supplies, demands and ship capacities for empty containers are considered in this model. By taking advantages of the fuzzy decision making and the network structure, we show how a mixed fuzzy decision making and optimization programming model can be applied to solve the empty container allocation problem. The utilization of the proposed model is demonstrated with a case of trans-Pacific liner route in the real world. Six major container ports on the trans-Pacific route are considered in the case study, including the Port of Kaohsiung, the Port of Hong Kong, the Port of Keelung, the Port of Kobe, the Port of Yokohama and the Port of Los Angles. The results show that the proposed mixed fuzzy decision making and optimization programming model can be used to solve the empty container allocation problem well.