Minimum Walking Static Repositioning in Free-Floating Electric Car-Sharing Systems

This article presents algorithms for operator-based static repositioning in free-floating car-sharing systems (FFCSs) which derive cost-effective relocation tours. The FFCS fleet may include both electric and conventional cars. Car repositioning takes place overnight and aims at complete rebalancing of the system i.e., at achieving an optimal, based on user demand, distribution of cars among non-overlapping cells of the FFCS operating area. It is also combined with battery recharging of electric cars i.e., the level of battery power is taken into account when deciding if and where each vehicle will be relocated. The Minimum Walking Car Repositioning Problem (MWCRP) is solved whose main objective is to minimize the walking distance in the relocation tours as the walking part of a relocation tour is the most laborious, time-consuming and therefore, the most expensive part compared to the driving one. The MWCRP is extended to the $k$-MWCRP to handle the case that a team of $k > 1$ drivers is required to undertake the entire set of car relocations e.g., in case of a large fleet of cars and/or operating area. To the best of our knowledge this is the first vehicle repositioning approach aiming at minimizing the relocation cost by primarily minimizing the walking cost. Simulation results based on an FFCS operating in the cities of Rome and Florence, demonstrate the efficiency and the effectiveness of our approach.