Bektas, T. (2012) Formulations and Benders decomposition algorithms for multidepot salesmen problems with load balancing. European Journal of Operational Research, 216 (1), 83-93. (doi:10.1016/j.ejor.2011.07.020).
Abstract
This paper describes new models and exact solution algorithms for the fixed destination
multidepot salesmen problem defined on a graph with n nodes where the number of nodes each
salesman is to visit is restricted to be in a predefined range. Such problems arise when the time to visit
a node takes considerably longer as compared to the time of travel between nodes, in which case the
number of nodes visited in a salesman's tour is the determinant of their `load'. The new models are
novel multicommodity flow formulations with O(n^2) binary variables, which is contrary to the
existing formulations for the same (and similar) problems that typically include O(n^3) binary
variables. The paper also describes Benders Decomposition algorithms based on the new formulations
for solving the problem exactly. Results of the computational experiments on instances derived from
TSPLIB show that some of the proposed algorithms perform remarkably well in cases where
formulations solved by a state-of-the-art optimization code fail to yield optimal solutions within
reasonable computation time.
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