A branch-and-cut-and-price algorithm for shared mobility considering customer satisfaction

This study determines the exact optimal fleet size, ride-matching patterns, and vehicle routes for shared mobility services (SMS) that maximize the profit of service operators considering ride-pooling and customer satisfaction. We make the first attempt to consider a nonlinear multivariate customer satisfaction function with respect to the features of the riders and the system under a ‘two riders-single vehicle’ ride-pooling scenario in a special case of dial-a-ride problem (DARP). A set packing model and a tailored branch-and-cut-and-price (BCP) approach are proposed to find the exact optimal solution of the problem. Unlike existing exact solution methods for DARP, we exploit the characteristic of the ride-pooling scenario and decompose the ride matching and vehicle routing in an effective two-phase method to solve the pricing problem of the BCP approach. Particularly, in Phase 1, feasible matching patterns subject to practical constraints are identified. In Phase 2, a heuristic and an exact label-correcting method with a bounded bi-directional search are sequentially employed to solve a new variant of elementary shortest path problem with time window (ESPPTW) in a network constructed upon rides and feasible ride matching patterns identified in Phase 1. The labeling methods are further accelerated by a strengthened dominance test, the aggregate extension to other depots, and the decremental search space. Valid inequalities are also incorporated to further improve the upper bound. The proposed solution method is evaluated in randomly generated instances and the instances created from the real mobility data of Didi. Managerial insights are generated through impact analysis.