A Branch-and-Cut algorithm for an urban dial-a-ride problem

The paper investigates a dial-a-ride problem focusing on the residents of large cities. These individuals have the opportunity to use a wide variety of transportation modes. Because of this, ridepooling providers have to solve the tradeoff between a high pooling rate and a small detour for customers to be competitive. We provide a Branch-and-Cut algorithm for this problem setting and introduce a new technique using information about already fixed paths to identify infeasible solutions ahead of time and to improve lower bounds on the arrival times at customer locations. By this, we are able to introduce additional valid inequalities to improve the search. We evaluate our procedure in an extensive computational study with up to 120 customers and ten vehicles. Our procedure finds significantly more optimal solutions and better lower and upper bounds in comparison with a mixed-integer programming formulation.