A reduction approach to the Two-Campus transport problem

The two-campus transport problem (TCTP) is a dial-a-ride problem with only two destinations. The problem is motivated by a transport problem between two campuses of an academic college. The two campuses are located in two different cities. Lecturers living in one city are sometimes asked to teach at the other city’s campus. The problem is that of transporting the lecturers from one campus to the other, using a known set of vehicles, so as to minimize the time the lecturers wait for their transport. We mathematically model the general TCTP, and provide an algorithm that solves it, which is polynomial in the number of lecturers. The algorithm is based on a reduction to a shortest path problem.