MATHEMATICAL MODELS OF PROBLEMS OF OPTIMAL PLACEMENT OF ELECTRIC CAR CHARGING STATIONS AND DETERMINATION OF THEIR SERVICE AREAS

Modern requirements of transport communication require the use of more environmentally friendly transport, and electric transport requires a more thorough analysis of the locations of its service points, including charging stations for electric vehicles. In this paper, it is proposed to use the theory and methods of multiple coverage of sets for modeling and solving problems of optimal placement of charging stations of electric vehicles with simultaneous determination of their service areas, taking into account the possibility of overlap.

Coverage Reduction: A Mathematical Model

This paper deals with a mathematical model for reduction of the lack of coverage (LC) involving multiple coverage in presence of partial covering. The model proposes a new structure of assignment of facilities in a facility location system to cover in greater proportion of the demand territory, avoiding assignment of several facilities in the same space of the territory. A comparison between the engendered solution and its representation is carried out through known indicators to measure the improvement of the solution. The results of our proposed model are contrast and better compared to defined referred models in order to evaluate the reduction of LC.

Judgement Theorems and an Approach for Solving the Constellation-to-Ground Coverage Problem

The satellite constellation-to-ground coverage problem is a basic and important problem in satellite applications. A group of judgement theorems is given, and a novel approach based on these judgement theorems for judging whether a constellation can offer complete single or multiple coverage of a ground region is proposed. From the point view of mathematics, the constellation-to-ground coverage problem can be regarded as a problem entailing the intersection of spherical regions. Four judgement theorems that can translate the coverage problem into a judgement about the state of a group of ground points are proposed, thus allowing the problem to be efficiently solved. Single- and multiple-coverage problems are simulated, and the results show that this approach is correct and effective.