Quasi-Optimal Sizing of a Vehicle Fleet Considering Environmental Impact, Maintenance, and Eventual Containment Measures

In this paper, $N$ types of vehicles having different environmental impacts and different failure rates are considered to perform a set of missions during a predefined period. The sizing problem of the fleet of vehicles is typically based on the literature for the environmental impact of each type of vehicle. This work intends to develop a model that allows considering not only the extent of recourse to non-polluting vehicles but also the preventive maintenance (PM) policy to be adopted for each of the N types of vehicles. More specifically, the objective of this work consists in determining simultaneously the quasi-optimal number of vehicles of each type to be used, the duration of their use, and their average usage rate as well as the period according to which each type of vehicle should be submitted to preventive maintenance. A mathematical model is developed to express and optimize the expected total cost, which includes the costs related to acquisition, operating, maintenance, and environmental impact in addition to considering the resale value. Then, the situation of using the acquired vehicle fleet in a context of a health crisis with containment measures is considered. The latter make it impossible to perform preventive maintenance actions during the containment period. For such situations, given the accumulated degradation in absence of preventive maintenance, the cost model is modified to generate a new preventive maintenance plan to be applied for each vehicle after the containment exit. Numerical results related to fuel and electric vehicles of two brands (Renault and Nissan) are presented and discussed.