Maximizing road carriers profit by combining trips and sizing the carrier coalition

In the present paper the issue of horizontal cooperation in a road transportation network is tackled. Different road trips belonging to a set of carriers that form a coalition are shared, with the final goal of maximizing the carriers' profit. The higher the number of carriers belonging to the coalition, the greater the possibility of obtaining profitable trip combinations; however, this makes also the cost sustained for managing the coalition increase. In this work, the proper size of the carrier coalition with the final goal of further improving the coalition profit is obtained by using an optimization based scheme. At first, a mathematical model is formulated with the goal of finding the best trip combinations to minimize the total costs for performing trips. Then, a second mathematical model is stated in order to assign both combined and single trips to carriers. This second optimization problem is solved several times for different number of carriers participating to the coalition in order to determine the best coalition size. An experimental campaign based on real data sets has been performed to validate the proposed approach. Various instances considering different number of trips and different values of the coalition management cost have been analyzed.