Integer and combinatorial optimization
Integer and combinatorial optimization
Solving binary cutting stock problems by column generation and branch-and-bound
Computational Optimization and Applications
Discrete Mathematics
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
A Column Generation Approach for Large-Scale Aircrew Rostering Problems
Operations Research
Simultaneous Vehicle and Crew Scheduling in Urban Mass Transit Systems
Transportation Science
Selected Topics in Column Generation
Operations Research
A new modeling and solution approach for the set-partitioning problem
Computers and Operations Research
Bi-dynamic constraint aggregation and subproblem reduction
Computers and Operations Research
A dynamic driver management scheme for less-than-truckload carriers
Computers and Operations Research
A new version of the Improved Primal Simplex for degenerate linear programs
Computers and Operations Research
Exact approaches for integrated aircraft fleeting and routing at TunisAir
Computational Optimization and Applications
An Improved Primal Simplex Algorithm for Degenerate Linear Programs
INFORMS Journal on Computing
Integrated Airline Crew Pairing and Crew Assignment by Dynamic Constraint Aggregation
Transportation Science
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Column generation is often used to solve problems involving set-partitioning constraints, such as vehicle-routing and crew-scheduling problems. When these constraints are in large numbers and the columns have on average more than 8-12 nonzero elements, column generation often becomes inefficient because solving the master problem requires very long solution times at each iteration due to high degeneracy. To overcome this difficulty, we introduce a dynamic constraint aggregation method that reduces the number of set-partitioning constraints in the master problem by aggregating some of them according to an equivalence relation. To guarantee optimality, this equivalence relation is updated dynamically throughout the solution process. Tests on the linear relaxation of the simultaneous vehicle and crew-scheduling problem in urban mass transit show that this method significantly reduces the size of the master problem, degeneracy, and solution times, especially for larger problems. In fact, for an instance involving 1,600 set-partitioning constraints, the master problem solution time is reduced by a factor of 8.