Modelling and Solving the Senior Transportation Problem

This paper defines a novel transportation problem, the Senior Transportation Problem (STP), which is inspired by the elderly door-to-door transportation services provided by non-profit organizations. Building on the vehicle routing literature, we develop solution approaches including mixed integer programming (MIP), constraint programming (CP), two logic-based Benders decompositions (LBBD), and a construction heuristic. Empirical analyses on both randomly generated datasets and large real-life datasets are performed. CP achieved the best results, solving to optimality 89% of our real-life instances of up to 270 vehicles with 385 requests in under 600 s. The best LBBD model can only solve 17% of those instances to optimality. Further investigation of this somewhat surprising result indicates that, compared to the LBBD approaches, the pure CP model is able to find better solutions faster and then is able to use the bounds from these sub-optimal solutions to reduce the search space slightly more effectively than the decomposition models.