Optimizing driver menus under stochastic selection behavior for ridesharing and crowdsourced delivery

Peer-to-peer logistics platforms coordinate independent drivers to fulfill requests for last mile delivery and ridesharing. To balance demand-side performance with driver autonomy, a new stochastic methodology provides drivers with a small but personalized menu of requests to choose from. This creates a Stackelberg game, in which the platform leads by deciding what menu of requests to send to drivers, and the drivers follow by selecting which request(s) they are willing to fulfill from their received menus. Determining optimal menus, menu size, and request overlaps in menus is complex as the platform has limited knowledge of drivers’ request preferences. Exploiting the problem structure when drivers signal willingness to participate, we reformulate our problem as an equivalent single-level Mixed Integer Linear Program (MILP) and apply the Sample Average Approximation (SAA) method. Computational tests recommend a training sample size for inputted SAA scenarios and a test sample size for completing performance analysis. Our stochastic optimization approach performs better than current approaches, as well as deterministic optimization alternatives. A simplified formulation ignoring ‘unhappy drivers’ who accept requests but are not matched is shown to produce similar objective values with a fraction of the runtime. A ridesharing case study of the Chicago Regional transportation network provides insights for a platform wanting to provide driver autonomy via menu creation. The proposed methods achieved high demand performance as long as the drivers are well compensated (e.g., even when drivers are allowed to reject requests, on average over 90% of requests are fulfilled when 80% of the fare goes to drivers; this drops to below 60% when only 40% of the fare goes to drivers). Thus, neither the platform nor the drivers benefit from low driver compensation due to its resulting low driver participation and thus low request fulfillment. Finally, for the cases tested, a maximum menu size of 5 is recommended as it produces good quality platform solutions without requiring much driver selection time.