Optimal consumed electric energy while sequencing vehicle trips in a personal rapid transit transportation system

Abstract

In this paper, we address the problem of minimizing the consumed electric energy for a personal rapid transit transportation system, in order to fulfil a planned list of trips, performed by a set of powered-batteries vehicles. For that aim, the list of trips is represented by a network, where each trip is associated with a node and the consumed electric energy is assigned to the arcs. Based on this network representation, two mathematical formulations, minimizing the electric energy are established. The first one is a mixed integer programming formulation, which is solved directly with a state-of-the-art LP solver. The second formulation is a 0–1 programming model, which is solved with a constraints generation technique. In addition, if an optimal solution is not obtained within a fixed time limit, the first mathematical formulation provides an upper bound and the second formulation gives a lower bound for the optimal solution. For the unsolved instances, the difference of the upper and lower bound relative to the lower bound gives the so called relative gap. This relative gap measures the maximum deviation from the optimal solution. Finally, extensive computational experiments are presented. The results provide evidence that the proposed procedures are very effective, since, 90% of the instances are solved to optimality and the mean relative gap is 1.41% for the unsolved instances.