A mathematical model of demand management for carsharing
A significant increase of carsharing service in Russia and worldwide has led to need a formal description of the process orders fulfilling on the service. The paper presents a mathematical model for computation the distance between customers and free car, which is built on the basis of the "nearest neighbor"method. A model of demand generation is proposed. The demand depends on the potential number of customers and the probability of finding a car in the area of walking distance. The number of free cars is described as stochastic process, which is based on a birth and death process. The death intensity in the process depends on the probability of finding a car. The estimation of the average number of free cars, their average load and the probability of finding a free car in the walking distance are obtained. The combination of the presented models allows to assess the impact of the number of carsharing vehicles on demand. In particular, a numerical example shows that an increase in the carsheribg fleet can lead to increaseasing in the cars average load. Thus, we can conclude that a larger car-sharing project can be cost-effective only if the carsharing service consists of a large fleet of vehicles, i.e. the service contains a high density of free cars.