Integer and combinatorial optimization
Integer and combinatorial optimization
SIAM Journal on Discrete Mathematics
Facets of the asymmetric traveling salesman polytope
Mathematics of Operations Research
A lifting procedure for the asymmetric traveling salesman polytope and a large new class of facets
Mathematical Programming: Series A and B
Polyhedral study of the capacitated vehicle routing problem
Mathematical Programming: Series A and B
Clique tree inequalities define facets of the asymmetric traveling salesman polytope
Discrete Applied Mathematics
On the monotonization of polyhedra
Mathematical Programming: Series A and B
Lifted Cycle Inequalities for the Asymmetric Traveling Salesman Problem
Mathematics of Operations Research
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
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) is a new class of problems arising from work related to aircraft routing. Given a digraph with cost on the arcs, a solution of the RATSP, like that of the Asymmetric Travelling Salesman Problem, induces a directed tour in the graph which minimises total cost. However the tour must satisfy additional constraints: the arc set is partitioned into replenishment arcs and ordinary arcs, each node has a non-negative weight associated with it, and the tour cannot accumulate more than some weight limit before a replenishment arc must be used. To enforce this requirement, constraints are needed. We refer to these as replenishment constraints. In this paper, we review previous polyhedral results for the RATSP and related problems, then prove that two classes of constraints developed in V. Mak and N. Boland [Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs, Technical Report TR M05/03, School of Information Technology, Deakin University, 2005] are, under appropriate conditions, facet-defining for the RATS polytope.