Integer and combinatorial optimization
Integer and combinatorial optimization
A new optimization algorithm for the vehicle routing problem with time windows
Operations Research
An additive bounding procedure for the asymmetric travelling salesman problem
Mathematical Programming: Series A and B
A parallel branch and bound algorithm for solving large asymmetric traveling salesman problems
Mathematical Programming: Series A and B
Exact solution of large-scale, asymmetric traveling salesman problems
ACM Transactions on Mathematical Software (TOMS)
A polyhedral approach to the asymmetric traveling salesman problem
Management Science
Computers and Operations Research - Special issue on the traveling salesman problem
Integer Programming Formulation of Traveling Salesman Problems
Journal of the ACM (JACM)
Flight String Models for Aircraft Fleeting and Routing
Transportation Science
2-Path Cuts for the Vehicle Routing Problem with Time Windows
Transportation Science
A Branch-and-Cut Procedure for the Vehicle Routing Problem with Time Windows
Transportation Science
Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints
Operations Research Letters
Discrete Applied Mathematics
Solving shortest path problems with a weight constraint and replenishment arcs
Computers and Operations Research
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The asymmetric travelling salesman problem with replenishment arcs (RATSP), arising from work related to aircraft routing, is a generalisation of the well-known ATSP. In this paper, we introduce a polynomial size mixed-integer linear programming (MILP) formulation for the RATSP, and improve an existing exponential size ILP formulation of Zhu [The aircraft rotation problem, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1994] by proposing two classes of stronger cuts. We present results that under certain conditions, these two classes of stronger cuts are facet-defining for the RATS polytope, and that ATSP facets can be lifted, to give RATSP facets. We implement our polyhedral findings and develop a Lagrangean relaxation (LR)-based branch-and-bound (BNB) algorithm for the RATSP, and compare this method with solving the polynomial size formulation using ILOG Cplex 9.0, using both randomly generated problems and aircraft routing problems. Finally we compare our methods with the existing method of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408-427]. It turns out that both of our methods are much faster than that of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408-427], and that the LR-based BNB method is more efficient for problems that resemble the aircraft rotation problems.