Cooperative Package Assignment for Heterogeneous Express Stations

The success of online shopping accelerates the development of express delivery business with economic and efficient service. Current express delivery systems usually deliver the packages in noncooperation mode and cannot jointly optimize the express fee and moving cost of users. This paper proposes the cooperative package assignment system by lumping packages at the same express station to share the express fee, and proposes a novel pricing structure to stimulate the express stations to join the system without revenue loss by introducing cooperation cost. We formulate the cooperative package assignment (CPA) problem with heterogeneous express stations for joint optimization of users' express fee and moving cost. Then, an approximate algorithm, CPAA, is proposed for the CPA problem based on the greedy approach using submodular function minimization. We show that the designed algorithm achieves computational efficiency and guaranteed approximation. Furthermore, we model the large-scale CPA problem as CPA-game and present a game theoretic algorithm, CPAGA. We show that CPA-game has at least one Nash Equilibrium, and CPAGA finally converges to a pure Nash Equilibrium. Through extensive simulations, we demonstrate that CPAA and CPAGA show great advantages in terms of comprehensive cost, which is 28.1% and 19.9% lower than that in noncooperation mode on average, respectively. Moreover, CPAGA shows great scalability and is more suitable for large-scale cooperative package assignment systems.