A cooperative rich vehicle routing problem in the last-mile logistics industry in rural areas

•A cooperative rich VRP in the last-mile logistics industry in rural areas is proposed.•The problem is formulated under different information sharing modes among players.•A branch-price-and-cut algorithm is proposed to solve the problem.•The core and Shapley value are used to allocate the cost saving due to cooperation.•A horizontal and vertical value chain perspective of the cooperation is provided. This study proposes a cooperative rich vehicle routing problem (CoRVRP) among three typical logistics providers in the last-mile logistics industry in rural areas. The problem is formulated based on the information fusion system and the ordering interface system, and it is solved by a proposed branch-price-and-cut algorithm. Based on the optimized cooperation scheme, the core and Shapley value are used to fairly allocate the cost savings. The numerical results show that a long-term grand coalition will be beneficial to all the participators. The proposed information-merging-and-algorithm-driven cooperative optimization model will be practicable for intelligent logistics systems.