Telebus Berlin: Vehicle Scheduling in a Dial-a-Ride System

Abstract

Telebus is Berlin’s dial-a-ride system for handicapped people who cannot use the public transportation system. The service is provided by a fleet of about 100 mini-buses and includes assistance in getting in and out of the vehicle. Telebus has between 1,000 and 1,500 transportation requests per day. The problem is to schedule these requests onto the vehicles such that punctual service is provided while operation costs are minimized. Additional constraints include pre-rented vehicles, fixed bus driver shift lengths, obligatory breaks, and different vehicle capacities.

We use a set partitioning approach for the solution of the bus scheduling problem that consists of two steps. The first clustering step identifies segments of possible bus tours (“orders”) such that more than one person is transported at a time; the aim in this step is to reduce the size of the problem and to make use of larger vehicle capacities. The problem of selecting a set of orders such that the traveling distance of the vehicles within the orders is minimal is a set partitioning problem that can be solved to optimality. In the second step the selected orders are chained to yield possible bus tours respecting all side constraints. The problem to select a set of bus tours such that each order is serviced once and such that the total traveling distance of the vehicles is minimum is again a set partitioning problem that is solved approximately.

We have developed a computer system for the solution of the bus scheduling problem that includes a branch-and-cut algorithm for the solution of the set partitioning problems. A version of this system has been in operation at Telebus since July 1995. Its use made it possible for Telebus to serve about 30% more requests per day with the same resources.