Liner alliance shipping network design model with shippers' choice inertia and empty container relocation

Liner companies have responded to escalating trade conflicts and the impact of the COVID-19 pandemic by forming alliances and implementing streamlined approaches to manage empty containers, which has strengthened the resilience of their supply chains. Meanwhile, shippers have grown more sensitive during these turbulent times. Motivated by the market situation, we investigate a liner alliance shipping network design problem considering the choice inertia of shippers and empty container relocation. To address this problem, we propose a bilevel programming model. The upper model aims to maximize the alliance's profit by optimizing the alliance's shipping network and fleet design scheme. The lower model focuses on optimizing the slot allocation scheme and the empty container relocation scheme. To ensure the sustainable operation of the alliance, we develop an inverse optimization model to allocate profits among alliance members. Furthermore, we design a differential evolution metaheuristic algorithm to solve the model. To validate the effectiveness of the proposed model and algorithm, numerical experiments are conducted using actual shipping data from the Asia-Western Europe shipping route. The results confirm the validity of the proposed model and algorithm, which can serve as a crucial decision-making reference for the daily operations of a liner shipping alliance.