Minimizing the driving distance in ride sharing systems

Reducing the number of cars driving on roads is an important objective for smart sustainable cities, for reducing emissions and improving traffic flow. To assist with this aim, ride-sharing systems match intending drivers with prospective passengers. The matching problem becomes more complex when drivers can pick-up and drop-off several passengers, both drivers and passengers have to travel within a time-window and are willing to switch roles. We present a mixed integer programming model for this switching rider problem, with the objective of minimizing the total distance driven by the population. We exhibit how the potential saving in kilometres increases as the driver flexibility and the density of the distribution of participants increases. Further, we show how breaking symmetries among the switchers improves performance, gaining over an order of magnitude speed up in solving time, and allowing approximately 50% more participants to be handled in the same computation time