Order assignment in a ride-hailing platform with heterogeneous participants

We study an order assignment problem in a ride-hailing system with two classes of riders (i.e., single-choice riders and multi-choice riders) and n types of vehicles. We regard the system as an M/G/n queueing system and develop an order assignment strategy based on the service loads of the n servers. We construct a nonlinear programming model to solve the order assignment problem with the objective of minimizing the average waiting time for riders. Using Lagrange duality theory, we derive the closed form of the optimal solution with a Lagrangian multiplier. Using parameter optimization theory, we carry out optimality analyses and theoretically demonstrate the Lipschitz stability of the feasible region and optimal objective value, the $$H\ddot{o}lder$$ H o ¨ l d e r stability of the optimal solution, and the existence and differentiability of the optimal solution. To understand the theoretical results intuitively, we conduct two groups of numerical experiments. The first one is implemented in an M/G/2 queueing system to graph the effects of parameter variation on the optimal order assignment strategy. The second one is conducted in an M/G/n queueing system to show the applicability of this study in systems with multiple heterogeneous service options. The results demonstrate that the service load of each server is directly related to its service capacity and order arrival rate. And the service load is a main factor influencing the optimal order assignment strategy. Management insights for the optimal order assignment strategy can be generated to inform real ride-hailing platforms.