# Generalized multiple depot traveling salesmen problem - polyhedral study and exact algorithm

arXiv: https://arxiv.org/abs/1508.01813 · HTML: https://mlsanity.com/paper/1508.01813/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2015.

## Built on by (most cited first, 1 of 1)

- [MS*: A New Exact Algorithm for Multi-agent Simultaneous Multi-goal Sequencing and Path Finding](https://mlsanity.com/paper/2103.09979/) (2021)

## Abstract (arXiv)

The generalized multiple depot traveling salesmen problem (GMDTSP) is a variant of the multiple depot traveling salesmen problem (MDTSP), where each salesman starts at a distinct depot, the targets are partitioned into clusters and at least one target in each cluster is visited by some salesman. The GMDTSP is an NP-hard problem as it generalizes the MDTSP and has practical applications in design of ring networks, vehicle routing, flexible manufacturing scheduling and postal routing. We present an integer programming formulation for the GMDTSP and valid inequalities to strengthen the linear programming relaxation. Furthermore, we present a polyhedral analysis of the convex hull of feasible solutions to the GMDTSP and derive facet-defining inequalities that strengthen the linear programming relaxation of the GMDTSP. All these results are then used to develop a branch-and-cut algorithm to obtain optimal solutions to the problem. The performance of the algorithm is evaluated through extensive computational experiments on several benchmark instances.