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New path elimination constraints for multi-depot routing problems

New path elimination constraints for multi-depot routing problems
New path elimination constraints for multi-depot routing problems
Multi-depot routing problems arise in distribution logistics where a set of vehicles based at several depots are used to serve a number of clients. Most variants of this problem have the basic requirement that the route of each vehicle starts and ends at the same depot. This article describes new inequalities, namely multi-cut constraints (MCC), which enforce this requirement in mathematical programming formulations of multi-depot routing problems. The MCCs are exponential in size, and are equivalent to a compact three-index formulation for the problem in terms of the associated linear programming relaxations. The article describes how a generalization of the MCCs can be obtained, in a similar manner, by using a stronger version of the three-index formulation. The connection between the compact and the exponential formulations implies a separation procedure based on max-flow/min-cut computations, which has reduced complexity in comparison with a previously known set of constraints described for the same purpose. The new inequalities are used in a branch-and-cut algorithm. Computational results are presented for instances with up to 300 clients and 60 depots.
1097-0037
246-261
Bektas, Tolga
0db10084-e51c-41e5-a3c6-417e0d08dac9
Gouveia, Luis
128ee1cb-d547-456b-bda3-74115e39a60f
Santos, Daniel
ae508dba-aae8-48b3-b9dc-67b6dac5d0ae
Bektas, Tolga
0db10084-e51c-41e5-a3c6-417e0d08dac9
Gouveia, Luis
128ee1cb-d547-456b-bda3-74115e39a60f
Santos, Daniel
ae508dba-aae8-48b3-b9dc-67b6dac5d0ae

Bektas, Tolga, Gouveia, Luis and Santos, Daniel (2017) New path elimination constraints for multi-depot routing problems. Networks, 70 (3), 246-261. (doi:10.1002/net.21760).

Record type: Article

Abstract

Multi-depot routing problems arise in distribution logistics where a set of vehicles based at several depots are used to serve a number of clients. Most variants of this problem have the basic requirement that the route of each vehicle starts and ends at the same depot. This article describes new inequalities, namely multi-cut constraints (MCC), which enforce this requirement in mathematical programming formulations of multi-depot routing problems. The MCCs are exponential in size, and are equivalent to a compact three-index formulation for the problem in terms of the associated linear programming relaxations. The article describes how a generalization of the MCCs can be obtained, in a similar manner, by using a stronger version of the three-index formulation. The connection between the compact and the exponential formulations implies a separation procedure based on max-flow/min-cut computations, which has reduced complexity in comparison with a previously known set of constraints described for the same purpose. The new inequalities are used in a branch-and-cut algorithm. Computational results are presented for instances with up to 300 clients and 60 depots.

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Accepted/In Press date: 6 July 2017
e-pub ahead of print date: 9 August 2017
Published date: October 2017

Identifiers

Local EPrints ID: 412993
URI: https://eprints.soton.ac.uk/id/eprint/412993
ISSN: 1097-0037
PURE UUID: 66044d48-a9be-448a-9c94-89fd7800bbd6
ORCID for Tolga Bektas: ORCID iD orcid.org/0000-0003-0634-144X

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Date deposited: 10 Aug 2017 16:30
Last modified: 08 Oct 2019 04:45

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