A Matheuristic Approach for the University Carpooling Problem

The carpooling problem consists of a shared use of private cars. Typically it is organized by a large company for encouraging its employees to pick up their colleagues minimizing the number of private cars travelling to/from the company site. The core of the efficient management of such a service is to find an optimal matching between the users and their preferred routing in such a way that spontaneous user matching is substituted by a solution found by means of an algorithmic approach. We consider the special case when users are the students of a university. This case differs from the carpooling problems considered in the literature mainly for the following characteristics: users (students) can have very different timetables (depending on the classes attended); users may indicate other users they would prefer to car-pool with (friends) or they don’t want to (enemies). The objectives are to maximize the number of served users, minimize the total route length, maximize the satisfied friendship preferences, respecting the user time windows, and car capacities. In this work we propose a Mixed Integer Linear Programming (MILP) formulation of the university carpooling problem in order to apply a matheuristic based on VNS, namely the Variable Neighborhood Branching (VNB).