Planning school transport: design of routes with flexible school opening times

Abstract

This paper puts forward a methodology for designing a system for school transport which, apart from designing routes, specifies school opening times. Traditionally school opening times have always been identical in the same area meaning many buses have to be used at the same time. This paper suggests the staggering of school opening times in order to minimise the number of buses and thereby reduce the enormous costs involved in running them. The methodology is based on: a first phase which addresses the classic routing problem by using mixed integer lineal programming and a second phase which uses bi-level programming to find the vector for school opening times, which, when staying within the constraints of the problem, minimises the direct costs of the system. The upper level represents the evaluation of the system costs and the lower level finds the best combination of optimum routes for the same bus.