Periodic airline fleet assignment with time windows, spacing constraints, and time dependent revenues

Given the sets of flights and aircraft of an airline carrier, the fleet assignment problem consists of assigning the most profitable aircraft type to each flight. In this paper we propose a model for the periodic fleet assignment problem with time windows in which departure times are also determined. Anticipated profits depend on the schedule and the selection of aircraft types. In addition, short spacings between consecutive flights which serve the same origin–destination pair of airports are penalized. We propose a non-linear integer multi-commodity network flow formulation. We develop new branch-and-bound strategies which are embedded in our branch-and-price solution strategy. Finally, we present computational results for periodic daily schedules on three real-world data sets. 2005 Elsevier B.V. All rights reserved.

[1]  M. Desrochers,et al.  A Generalized Permanent Labelling Algorithm For The Shortest Path Problem With Time Windows , 1988 .

[2]  Amos Levin.  Scheduling and Fleet Routing Models for Transportation Systems , 1971 .

[3]  George L. Nemhauser,et al.  The fleet assignment problem: Solving a large-scale integer program , 1995, Math. Program..

[4]  C. Ribeiro,et al.  Essays and Surveys in Metaheuristics , 2002, Operations Research/Computer Science Interfaces Series.

[5]  J. Desrosiers,et al.  A dynamic programming algorithm for the shortest path problem with time windows and linear node costs , 1998 .

[6]  Jacques Desrosiers,et al.  Time Constrained Routing and Scheduling , 1992 .

[7]  François Soumis,et al.  An Optimization Model for the Simultaneous Operational Flight and Pilot Scheduling Problem , 2001, Manag. Sci..

[8]  Jacques Desrosiers,et al.  Weekly airline fleet assignment with homogeneity , 2002 .

[9]  Roy E. Marsten,et al.  COLDSTART -- FLEET ASSIGNMENT AT DELTA AIR LINES. , 1994 .

[10]  George B. Dantzig,et al.  Decomposition Principle for Linear Programs , 1960 .

[11]  George L. Nemhauser,et al.  Flight String Models for Aircraft Fleeting and Routing , 1998, Transp. Sci..

[12]  Jacques Desrosiers,et al.  Daily Aircraft Routing and Scheduling , 1994 .

[13]  Cynthia Barnhart,et al.  Itinerary-Based Airline Fleet Assignment , 2002, Transp. Sci..

[14]  Teodor Gabriel Crainic,et al.  Fleet management and logistics , 1998 .

[15]  Russell A. Rushmeier,et al.  Advances in the Optimization of Airline Fleet Assignment , 1997, Transp. Sci..

[16]  Jacques Desrosiers,et al.  Fleet assignment and routing with schedule synchronization constraints , 1994, Eur. J. Oper. Res..

[17]  Jephthah A. Abara,et al.  Applying Integer Linear Programming to the Fleet Assignment Problem , 1989 .

[18]  Jacques Desrosiers,et al.  Accelerating Strategies in Column Generation Methods for Vehicle Routing and Crew Scheduling Problems , 2002 .

[19]  George L. Nemhauser,et al.  Handbooks in operations research and management science , 1989 .

[20]  Cynthia Barnhart,et al.  Airline Fleet Assignment with Time Windows , 2000, Transp. Sci..

[21]  George L. Nemhauser,et al.  Maintenance and Crew Considerations in Fleet Assignment , 1996, Transp. Sci..