Calibration of car-following models plays an important role not only in traffic simulation but also in the estimation of traffic-related energy consumption. However, the majority of calibration studies only focus on errors on position or speed, whereas these models are used to evaluate environmental parameters associated with road traffic (e.g. pollutant emissions, energy consumption). Then, this study focuses on the ability of Gipps' car-following model calibrated on trajectory parameters to estimate properly the fuel consumption of a heavy vehicle. First, the shape of one of the most used Goodness-of-Fit function, Theil's inequality coefficient, is investigated. It will be demonstrated that optimal domains are flat and large, and so many combinations of parameters could accurately reproduce the vehicle trajectory. Then, the authors found that Gipps model, calibrated via a multi-objective particle swarm optimisation is relevant to simulate the trajectory of a heavy vehicle, but fuel consumption estimation resulting of these trajectories exhibits large discrepancies. To solve this issue, it is proposed to add the fuel consumption estimation directly in the calibration process as a further dimension. The results show an improvement in the value of energy consumption estimation without increasing too much the error on the trajectory.