Modeling and Optimization of the Inland Container Transportation Problem Considering Multi-Size Containers, Fuel Consumption, and Carbon Emissions

This paper investigates the inland container transportation problem with a focus on multi-size containers, fuel consumption, and carbon emissions. To reflect a more realistic situation, the depot’s initial inventory of empty containers is also taken into consideration. To linearly model the constraints imposed by the multiple container sizes and the limited number of empty containers, a novel graphical representation is presented for the problem. Based on the graphical representation, a mixed-integer programming model is presented to minimize the total transportation cost, which includes fixed, fuel, and carbon emission costs. To efficiently solve the model, a tailored branch-and-price algorithm is designed, which is enhanced by improvement schemes including a heuristic label-setting algorithm, decremental state-space relaxation, and the introduction of a high-quality upper bound. Results from a series of computational experiments on randomly generated instances demonstrate that (1) the proposed branch-and-price algorithm demonstrates a superior performance compared to the tabu search algorithm and the genetic algorithm; (2) each additional empty container in the depot reduces the total transportation cost by less than 1%, with a diminishing marginal effect; (3) the rational configuration of different types of trucks improves scheduling flexibility and reduces fuel and carbon emission costs as well as the overall transportation cost; and (4) extending customer time windows also contributes to lower the total transportation cost. These findings not only deepen the theoretical understanding of inland container transportation optimization but also provide valuable insights for logistics companies and policymakers to improve efficiency and implement more sustainable operational practices. Additionally, our research paves the way for future investigations into the integration of dynamic factors and emerging technologies in this field.