Variable notations.

Logistics, as a tertiary industry, has developed rapidly and become an important part of the national economy. However, owing to the behindhand logistics pattern, the logistics vehicles drive empty-loaded on their return trip, resulting in wastage of half of the delivery resources. This paper proposes a logistics–client matching model under fourth-party logistics (4PL) to reduce the empty-loaded rate. First, a preference calculation model between logistics providers and clients was constructed. Next, for clients with small quantities of goods, a linear logistics−client one-to-one stable matching model was constructed based on the stable marriage matching model. Then, for clients with large quantities of goods, a linear logistics−client many-to-one stable matching model was constructed with a novel linear many-to-one stable matching constraint. Finally, the case study indicated that the linear model supports large-scale and global optimization. The real case study verified that the proposed stable matching model is effective in reducing the empty-loaded rate compared to the ordinary matching model, and the matching solution was fairer.