Solving a selective dial-a-ride problem with logic-based Benders decomposition

Previous research on the dial-a-ride problem primarily focused on serving a given set of requests with a fixed-size vehicle fleet at minimal traveling costs. It is assumed that the request set is sufficiently small to be served by the available vehicles. We consider a different scenario in which a maximal number of requests shall be served under the given constraints, i.e., it is no longer guaranteed that all requests can be accepted. For this new problem variant we propose a compact mixed integer linear programming model as well as algorithms based on Benders decomposition. In particular, we employ logic-based Benders decomposition and branch-and-check using mixed integer linear programming and constraint programming algorithms. We consider different variants on how to generate Benders cuts as well as heuristic boosting techniques and different types of valid inequalities. Computational experiments illustrate the effectiveness of the suggested algorithms.