A Mathematical Model for the Coach Trip with Shuttle Service Problem

In this work we consider the Coach Trip with Shuttle Service Problem (CTSSP), which is a routing problem where passengers have to be transported from bus stops to a central hub with a fleet of coaches and shuttles. The capacity of each vehicle must not be exceeded and for each group of passengers waiting at a bus stop there is a maximal travel time that must not be exceeded while travelling to the hub. Shuttles can use bus stops as transfer points to drop their passengers from which they have to be picked up by a coach. Coaches must end their trip at the hub while shuttles can stop at any bus stop. The goal is to minimize costs. The costs consist of travelling costs of the used vehicles plus fixed costs for the usage of the shuttles. We prove the computational complexity of the problem and present a novel mathematical model for the CTSSP. This model is implemented in CPLEX and the optimal solution of the "example" instance of the VeRoLog Solver Challenge 2015 is shown.