TY - GEN A1 - Borndörfer, Ralf A1 - Schelten, Uwe A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - A Column Generation Approach to Airline Crew Scheduling N2 - The airline crew scheduling problem deals with the construction of crew rotations in order to cover the flights of a given schedule at minimum cost. The problem involves complex rules for the legality and costs of individual pairings and base constraints for the availability of crews at home bases. A typical instance considers a planning horizon of one month and several thousand flights. We propose a column generation approach for solving airline crew scheduling problems that is based on a set partitioning model. We discuss algorithmic aspects such as the use of bundle techniques for the fast, approximate solution of linear programs, a pairing generator that combines Lagrangean shortest path and callback techniques, and a novel rapid branching'' IP heuristic. Computational results for a number of industrial instances are reported. Our approach has been implemented within the commercial crew scheduling system NetLine/Crew of Lufthansa Systems Berlin GmbH. T3 - ZIB-Report - 05-37 KW - Integer Programming KW - Airline Crew Scheduling KW - Branch and Generate Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8713 ER - TY - THES A1 - Wenzel, Ron T1 - On the In-Flight Rest Assignment Problem N2 - The airplane has changed the world in a tremendous way. Efficient scheduling of airmen and aircrafts is of considerable importance for cost-effectiveness of compa- nies. Attentiveness of flight crew members is vital as fatigue can lead to severe accidents. Therefore, duty times of flight crews are strictly limited. Long distance flights may be difficult to schedule with only one set of crew members. Furthermore, pertu- bations of the schedules may entail exchanging the entire crew, which confounds multiday schedules. A new EU regulation introduced in-flight rest: a schedule may extend pilots’ duty times if they rest for a certain time in designated crew compart- ments provided aboard airplanes. Of course they have to be replaced in that period of time. This thesis examines the in-flight rest assignment problem, which is the decision problem whether a given schedule allows for all crew members to take their compul- sory rest. The problem can be seen as multimachine scheduling problem. Efficient algorithms for special cases were developed and an alternative approach for entire hard cases is discussed. Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-59328 ER - TY - THES A1 - Borndörfer, Ralf T1 - Mathematical Optimization and Public Transportation N2 - This cumulative thesis collects the following six papers for obtaining the habilitation at the Technische Universität Berlin, Fakultät II – Mathematik und Naturwissenschaften: (1) Set packing relaxations of some integer programs. (2) Combinatorial packing problems. (3) Decomposing matrices into blocks. (4) A bundle method for integrated multi-depot vehicle and duty scheduling in public transit. (5) Models for railway track allocation. (6) A column-generation approach to line planning in public transport. Some changes were made to the papers compared to the published versions. These pertain to layout unifications, i.e., common numbering, figure, table, and chapter head layout. There were no changes with respect to notation or symbols, but some typos have been eliminated, references updated, and some links and an index was added. The mathematical content is identical. The papers are about the optimization of public transportation systems, i.e., bus networks, railways, and airlines, and its mathematical foundations, i.e., the theory of packing problems. The papers discuss mathematical models, theoretical analyses, algorithmic approaches, and computational aspects of and to problems in this area. Papers 1, 2, and 3 are theoretical. They aim at establishing a theory of packing problems as a general framework that can be used to study traffic optimization problems. Indeed, traffic optimization problems can often be modelled as path packing, partitioning, or covering problems, which lead directly to set packing, partitioning, and covering models. Such models are used in papers 4, 5, and 6 to study a variety of problems concerning the planning of line systems, buses, trains, and crews. The common aim is always to exploit as many degrees of freedom as possible, both at the level of the individual problems by using large-scale integer programming techniques, as well as on a higher level by integrating hitherto separate steps in the planning process. KW - set packing KW - set partitioning KW - set covering KW - polyhedral combinatorics KW - public transport KW - railways Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13613 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Schulz, Christof A1 - Swarat, Elmar A1 - Weider, Steffen T1 - Duty Rostering in Public Transport - Facing Preferences, Fairness, and Fatigue N2 - Duty rostering problems occur in different application contexts and come in different flavors. They give rise to very large scale integer programs which ypically have lots of solutions and extremely fractional LP relaxations. In such a situation, heuristics can be a viable algorithmic choice. We propose an mprovement method of the Lin-Kernighan type for the solution of duty rostering problems. We illustrate its versatility and solution quality on three different applications in public transit, vehicle routing, and airline rostering with a focus on the management of preferences, fairness, and fatigue, respectively. T3 - ZIB-Report - 15-44 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-56070 SN - 1438-0064 ER -