A Column-Generation Approach to Line Planning in Public Transport

• Published in: Transportation science Vol. 41; no. 1; pp. 123 - 132
• Main Authors: Borndorfer, Ralf, Grotschel, Martin, Pfetsch, Marc E
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.02.2007; Transportation Science & Logistic Society of the Institute for Operations Research and Management Sciences; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Analysis; Applied sciences; column generation; Computational methods; Exact sciences and technology; Fixed costs; Geometric lines; Germany; Ground, air and sea transportation, marine construction; line planning; Mathematical programming; Model testing; Network access lines; Operating costs; Operations research; Passengers; Planning; Planning systems; Public transportation; Rail lines; Railway transport; Railway transportation and traffic; Road transport; Routes; Studies; Total costs; Transport economics; Transportation; Transportation planning; Transportation planning, management and economics; Travel expenses; United States; Germany; Experimental result; line planning; Pricing; Strategic planning; Problem solving; column generation; Rail transportation; Modeling; Public transportation; Passenger transportation; Origin destination model
• ISSN: 0041-1655; 1526-5447
• DOI: 10.1287/trsc.1060.0161

The line-planning problem is one of the fundamental problems in strategic planning of public and rail transport. It involves finding lines and corresponding frequencies in a transport network such that a given travel demand can be satisfied. There are (at least) two objectives: the transport company wishes to minimize operating costs, and the passengers want to minimize traveling times. We propose a new multicommodity flow model for line planning. Its main features, in comparison to existing models, are that the passenger paths can be freely routed and lines are generated dynamically. We discuss properties of this model, investigate its complexity, and present a column-generation algorithm for its solution. Computational results with data for the city of Potsdam, Germany, are reported.