Andreas Löbel

A Bundle Method for Integrated Multi-Depot Vehicle and Duty Scheduling in Public Transit

This article proposes a Lagrangean relaxation approach to solve integrated duty and vehicle scheduling problems arising in public transport. The approach is based on a version of the proximal bundle method for the solution of concave decomposable functions that is adapted for the approximate evaluation of the vehicle and duty scheduling components. The primal and dual information generated by this bundle method is used to guide a branch-and-bound type algorithm.

Duty Scheduling in Public Transit

This article is about adaptive column generation techniques for the solution of duty scheduling problems in public transit. The current optimization status is exploited in an adaptive approach to guide the subroutines for duty generation, LP resolution, and schedule construction toward relevant parts of a large problem. Computational results for three European scenarios are reported.

Optimierung des Fahrzeugumlaufs im Öffentlichen Nahverkehr

This paper addresses the problem of scheduling vehicles in a public mass transportation system. We show how this problem can be modelled as a special multicommodity flow problem and outline the solution methodology we have developed. Based on polyhedral investigations, we have designed and implemented a branch&cut algorithm and various heuristics with which real vehicle scheduling problems of truely large scale can be solved to optimality. We describe some implementation issues and report computational results.

Duty scheduling templates

We propose duty templates as a novel concept to produce similar duty schedules for similar days of operation in public transit. Duty templates can conveniently handle various types of similarity requirements, and they can be implemented with ease using standard algorithmic techniques. They have produced good results in practice.

Der schnellste Weg zum Ziel

Das Thema „Wege“ weckt Assoziationen zu Strasen, Transport, Verkehr — und Mathematik. Hier sind vier Beispiele.