The multi-depot family traveling salesman problem and clustered variants: Mathematical formulations and branch-&-cut based methods.

In this article, we study the multi-depot family traveling salesman problem (MDFTSP) and two clustered variants, the soft-clustered MDFTSP (SC-MDFTSP) and the hard-clustered MDFTSP. We emphasize the relevance of this study by relating the problems with warehouse activities supported by scattered storage systems and by pointing out that clustered variants of routing problems have been scarcely addressed in the literature. For these three problems, we present several mixed integer linear programming formulations and develop appropriate branch-&-cut based algorithms which are tested with a newly generated data set including instances with up to 200 nodes and 40 depots. The results from the computational experiments allow us to identify the main differences between the three problems concerning modeling approaches as well as solution methods and put in evidence that these problems are challenging problems, in particular the SC-MDFTSP.