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Formulations and Benders decomposition algorithms for multidepot salesmen problems with load balancing

Formulations and Benders decomposition algorithms for multidepot salesmen problems with load balancing
Formulations and Benders decomposition algorithms for multidepot salesmen problems with load balancing
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.
0377-2217
83-93
Bektas, T.
0db10084-e51c-41e5-a3c6-417e0d08dac9
Bektas, T.
0db10084-e51c-41e5-a3c6-417e0d08dac9

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).

Record type: Article

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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More information

Published date: January 2012
Organisations: Management, Southampton Business School

Identifiers

Local EPrints ID: 71349
URI: https://eprints.soton.ac.uk/id/eprint/71349
ISSN: 0377-2217
PURE UUID: 1a6db9a1-af40-4665-bf86-ca14a4e33b0a
ORCID for T. Bektas: ORCID iD orcid.org/0000-0003-0634-144X

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Date deposited: 03 Feb 2010
Last modified: 06 Jun 2018 12:37

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Author: T. Bektas ORCID iD

University divisions

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