Abstract
In the double TSP with multiple stacks, a vehicle with several stacks performs a Hamiltonian circuit to pick up some items and stores them in its stacks. It then delivers every item by performing another Hamiltonian circuit while satisfying the last-in-first-out policy of its stacks. The consistency requirement ensuring that the pickup and delivery circuits can be performed by the vehicle is the major difficulty of the problem. This requirement corresponds, from a polyhedral standpoint, to a set covering polytope. When the vehicle has two stacks this polytope is obtained from the description of a vertex cover polytope. We use these results to develop a branch-and-cut algorithm with inequalities derived from the inequalities of the vertex cover polytope.
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- 1.
In the rest of the paper, the DTSPMS will refer to either the problem and the integer linear formulation depending on the context.
- 2.
We use the lifted version \(y_{ij}+y_{jk}+y_{ki}-x_{ji}\ge 1\), for all distinct \(i, j, k\in V\setminus \{0\}\).
- 3.
Note that the optimal values can differ when passing from the finite capacity case to the infinite capacity case.
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Barbato, M., Grappe, R., Lacroix, M., Wolfler Calvo, R. (2016). A Set Covering Approach for the Double Traveling Salesman Problem with Multiple Stacks. In: Cerulli, R., Fujishige, S., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2016. Lecture Notes in Computer Science(), vol 9849. Springer, Cham. https://doi.org/10.1007/978-3-319-45587-7_23
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