A mathematical model for a ride-pooling problem with price discount as an incentive

The advent of smartphones equipped with the internet and GPS has revolutionized the way people travel, leading to the emergence of ride-sourcing companies to cater to the increasing demand for transportation. However, this mode of transportation has had negative repercussions on traffic congestion and air pollution, as individual rides result in many empty seats. To address these issues, some ride-sourcing platforms have introduced ride-sharing services, allowing people to share their rides with others. In this paper, we present a mixed-integer nonlinear model that enables individuals to share their rides with passengers who have close itineraries, thereby reducing trip fares as an incentive. The primary objective of this model is to maximize social welfare. Passengers who are willing to share their rides submit their requests a day in advance via the platform. The platform then determines whether a person can have a shared ride based on their pickup and drop-off time windows and locations or if they should travel individually. Shared rides are established by matching the information of other requesters. Passengers who take the shared ride will be incentivized with a price discount to compensate for their inconvenience during the ride. We solved and validated this model using CPLEX software, and the results demonstrate that social welfare can be improved through ride-pooling.