**7. Conclusions**

This work proves that realistic Fleet Management Problem is an NP-hard problem, Apart from suggesting that exact and optimal solutions may not be realizable, it paves way to the application of heuristic and metaheuristic algorithms. This work proposed a novel methodology in optimizing fleet placement in station-based round-trip carsharing and suggests how such problems can be modeled. It is among the first to model the problem of fleet placement in carsharing and to apply a state-of-the-art optimization algorithm in attempting to determine satisfactory solutions. A set of heuristic, metaheuristic (NSGA-II), and exact (multi-criteria solver) algorithms have been applied and their performance evaluated on three instances with two objectives, i.e.,maximizing the number of carsharing users and minimizing the maximum global walking-to-the-car distance, under consideration.

This work is also the first to use real and exact instances (instead of just an abstract) for the study. Three different instances have been used, and each has its own characteristics with different sizes and objectives to reflect real world demand. The proposed method demonstrates that NSGA-II is superior to the manual allocation by a significant margin in user coverage and in terms of approximated Pareto front, and presents a number of solutions for decision makers to choose from. Solutions from our proposed method are also more efficient in terms of both user coverage and walking distance. While a metaheuristic approach has received much attention lately, this works affirms its application in transportation and Fleet Management Problem, in particular. The model proposed ought to be a good starting point in solving similar problems for further research among transportation and logistic communities.

Future work could apply the proposed approach to other cities such as London, Athens, and Paris. Additional objectives such as car fleet utilization, car fleet size, and the number of stations may also be included, since these are also real concerns after the initial launch of the carsharing business. A tailor-made metaheuristic algorithm may also be invented with the Fleet Management problem in mind too.

**Author Contributions:** Conceptualization, B.C., D.K. and P.B.; methodology, B.C., Grégoire Danoy, M.B. and F.G.; software, B.C.; validation, B.C., J.M. and K.L.; formal analysis, B.C., F.G. and J.M.; investigation, B.C. and D.K.; resources, D.K. and P.B.; data curation, B.C.; writing—original draft preparation, B.C., G.D. and D.K.; writing—review and editing, B.C. and K.L.; visualization, B.C.; supervision, P.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
