A Bundle Algorithm Approach for the Aircraft Schedule Recovery Problem During Hub Closures

Benjamin G. Thengvall (), Jonathan F. Bard () and Gang Yu ()
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Benjamin G. Thengvall: Graduate Program in Operations Research, Department of Mechanical Engineering, University of Texas, Austin, Texas 78712-1063
Jonathan F. Bard: Graduate Program in Operations Research, Department of Mechanical Engineering, University of Texas, Austin, Texas 78712-1063
Gang Yu: Department of Management Science and Information Systems, Graduate School of Business, University of Texas, Austin, Texas 78712-1175

Transportation Science, 2003, vol. 37, issue 4, 392-407

Abstract: A bundle algorithm is presented to solve a multicommodity network model for determining a recovery plan for a single carrier with multiple fleets following a hub closure. The algorithm is shown to provide feasible near-optimal solutions much more quickly than can be obtained using a standard commercial mixed-integer programming code (CPLEX). In this application, a bundle method is used to solve a Lagrangian relaxation of the integer programming formulation. The full algorithm includes heuristic techniques for finding feasible solutions from the solutions to the relaxed problems. Extensive computations were performed using data from Continental Airlines. The results show that the proposed approach provides faster times to optimality in some cases and always obtains feasible, near-optimal solutions for larger problems much more quickly than can be found using CPLEX. In addition, while a standard commercial code will provide only one solution, this approach provides multiple high-quality solutions.

Date: 2003
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