Combinatorial problems in an adaptive public transportation network

Abstract

The paper addresses the following combinatorial problems: What are the minimal number of buses and drivers needed to keep up an adaptive public transportation network with prescribed departure and travel times. The system is adaptive in the sense that buses as well as drivers are not restricted to travel only one given two way line, but may also traverse among lines. However, adaptation to passenger loading is not yet directly considered. The relaxation of the “two way lines” constraint should provide more flexibility in employing the resources required to maintain and operate the network. No assumptions are imposed upon either the departure or travel times.

The solution process is simple and intuitive and it seems that it can serve as a basic framework for accommodating some changes in the underlying structure of the system. The algorithm is an interim step in a mathematical program where the departure times are taken as control variables and are selected to minimize the average waiting time of passengers, or alternatively other performance indices of the network. The final buses' trips are not unique and their choice is subject to managerial considerations.