Minimization of number of buses in the school bus routing problem

In this paper a formal presentation and description of a method of solving the problem of both determining the set of bus stops and assignment of students that are authorized to transport to these stops is investigated. This problem can be treated as a sub problem of the bus school routing problem (SBRP). Although the problems of the SBRP class are one of the earliest logistics problems solved using methods of operations research, they remain valid and are the subject of research, as evidenced by numerous contemporary publications. Unfortunately, in most of the problems of SBRP class described in the literature the problem of determining the bus stops network and allocation of students to the particular stops is very often ignored. Based on the assumption that a small number of bus stops, from which the students are taken or to which they are set down, makes carrying out of school transport process easier, a problem of minimizing the number of active bus stops was considered. The main result of this paper is proposition of a greedy algorithm to solving the problem of determining the minimum set of school bus stops. To illustrate functioning the proposed algorithm a simple numerical example has been presented.