Reprint of: The multi-depot vehicle routing problem with profit fairness

One of the main obstacles in horizontal collaborative transportation is the proper distribution of gains among partners. In practice, a posteriori gain sharing mechanisms rarely guarantee that all partners feel treated fairly. In this paper, we present the multi-depot vehicle routing problem with profit fairness (MDVRP-PF), a bi-objective optimization problem that adds a fairness objective function to the classical cost minimization function. By studying the MDVRP-PF, we explore the effects of integrating fairness in the optimization process. To that end, we approximate the Pareto front of any problem instance using an adaptive large neighbourhood search algorithm, embedded within an ε-constraint scheme. This problem is solved for different instance types and time horizons. All the obtained Pareto fronts are characterized by six measures. Results show that the economic cost of fairness remains below 5%, even though remarkable differences exist among different instance types. We also observe that such costs tend to decrease when fairness is considered for longer time horizons.