Balancing empty containers at ports: A bi-level programming approach for sustainable maritime logistics

Abstract

The challenges posed by global trade imbalances, coupled with the inefficient distribution of empty containers at ports, have remarkable effects on the shipping industry's environmental and economic performance, primarily through increased costs and reduced profitability. This paper introduces a bi-level programming model designed to promote sustainable management of empty container distribution within ports. In this model, the shipping company operates as a leader, focusing on maximizing revenue while simultaneously reducing greenhouse gas emissions. The non-vessel operating common carrier (NVOCC) acts as a follower at the second level, with the aim of optimizing its revenue and addressing container imbalance at ports. The shipping company establishes pricing strategies first, which then inform the NVOCC's pricing decisions based on actual demand. The framework also differentiates between two types of customers: those handling hazardous cargo and those managing non-hazardous cargoes. A novel matheuristic solution, utilizing an evolutionary algorithm, is developed to address this problem. To evaluate the proposed model, it was applied to two datasets. The first dataset represents the Asia–Australia shipping route, serving as the real-world case study for this research. The second dataset, the LINER-LIB benchmark, was used to assess the algorithm's efficiency on larger problem instances. Findings document the efficacy of this bi-level programming approach, indicating that even under crisis conditions—such as flooding—the model retains its operational effectiveness, resulting in only a 4.87 % increase in container imbalance and a 3.2 % rise in greenhouse gas emissions.