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

#### Mrad, Mehdi . 2014

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, solved directly using a

state-of-the-art LP solver. The second formulation is a 0-1 programming model, solved using a constraints generation technic. 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 bounds over the lower bound gives the so called relative gap. This relative gap measures the deviation from the optimal solution. Finally an extensive computational experiments are presented and provide evidence that the proposed procedures are very effective. Since, 90% of instances are solved optimally and for the unsolved ones the mean relative gap is 1.41%.

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