A bilevel mathematical approach for the empty container repositioning problem with a sharing and exchanging strategy in liner shipping

In the maritime industry, the management of empty containers is a significant issue whose costs account for a large proportion of the total world fleet running costs. To reduce repositioning activities and increase cost effectiveness, this paper proposes a solution framework considering empty container sharing and exchanging strategies to coordinate the shipping lines in a maritime transportation network. The proposed solution framework considers an empty container matching platform company and a group of shipping lines in a given shipping network. Because of the interactive relationship between the two parties, the proposed problem is formulated as a bilevel programming problem, and the Karush-Kuhn-Tucker (KKT) is applied. To validate the proposed solution approach, a practical Asia-Europe-Oceania shipping network is used to conduct numerical experiments. The benefits of the proposed solution framework are shown in the results.