An integrated modeling framework for a hybrid delivery service system considering endogenous traffic congestion at the urban level

The rapid development of urban logistics creates a strong demand for high-quality delivery services. To meet this demand, crowdsourced and dedicated delivery services are often integrated into a hybrid system, which enhances efficiency and reduces costs. In order to investigate the emerging system with endogenous traffic congestion determined by the traffic flows, we construct an integrated modeling framework consisting of two sub-models for the crowdsourced and the dedicated delivery service sub-system respectively, to describe the delivery service system launched by an integrated orders-delivery platform. For the crowdsourced delivery service sub-system, we propose a convex programming problem to demonstrate travelers’ choices between solo driving and crowdsourced delivery driving, along with their route selection behavior based on the user equilibrium (UE) principle. Furthermore, we find the conditions for the existence and uniqueness of the solution to this problem. For the dedicated delivery service sub-system, we develop a mathematical model in which the platform allocates the tasks and routes for dedicated deliveries. In addition, a Cobb-Douglas function is adopted to calculate the total delivery demand from the orders of the platform. Then we propose heuristic solution algorithm for solving the integrated modeling framework to capture the travel demand and flow patterns. The algorithm incorporates a dual subgradient algorithm with averaging for the crowdsourced delivery service sub-system and a genetic algorithm for the dedicated delivery service sub-system. The numerical studies show that comparing to traditional system only with dedicated drivers, crowdsourced delivery is positive for the total profit of the integrated system. The employment is relatively insensitive to the inconvenience cost of the crowdsourcing and ad hoc vehicles. Moreover, the commission rate of dedicated drivers affects the total profit and the employment simultaneously, which means it is supposed to be optimized for balance between the economic and the social benefits. Applications of the proposed approach in the Sioux Falls network demonstrate the feasibility and effectiveness of the framework in realistic cases.