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The two-period travelling salesman problem applied to milk collection in Ireland

The two-period travelling salesman problem applied to milk collection in Ireland
The two-period travelling salesman problem applied to milk collection in Ireland
We describe a new extension to the Symmetric Travelling Salesman Problem (STSP) in which some nodes are visited in both of 2 periods and the remaining nodes are visited in either 1 of the periods. A number of possible Integer Programming Formulations are given. Valid cutting plane inequalities are defined for this problem which result in an, otherwise prohibitively difficult, model of 42 nodes becoming easily solvable by a combination of cuts and Branch-and-Bound. Some of the cuts are entered in a pool and only used when it is automatically verified that they are violated. Other constraints which are generalisations of the subtour and combine qualities for the single period STSP, are identified manually when needed. Full computational details of solution process are given.
travelling salesman problem, inequalities, cutting planes, branch-and-bound
0926-6003
291-306
Butler, Martin
f81d324a-f4f5-4a41-85fc-9db1ff736d4b
Williams, H. Paul
6a5ec3bd-b447-4cbe-8509-6c3589525ebf
Yarrow, Leslie-Ann
9dc35a2e-87cb-4c14-9b40-ad86508c0247
Butler, Martin
f81d324a-f4f5-4a41-85fc-9db1ff736d4b
Williams, H. Paul
6a5ec3bd-b447-4cbe-8509-6c3589525ebf
Yarrow, Leslie-Ann
9dc35a2e-87cb-4c14-9b40-ad86508c0247

Butler, Martin, Williams, H. Paul and Yarrow, Leslie-Ann (1997) The two-period travelling salesman problem applied to milk collection in Ireland. Computational Optimization and Applications, 7 (3), 291-306. (doi:10.1023/A:1008608828763).

Record type: Article

Abstract

We describe a new extension to the Symmetric Travelling Salesman Problem (STSP) in which some nodes are visited in both of 2 periods and the remaining nodes are visited in either 1 of the periods. A number of possible Integer Programming Formulations are given. Valid cutting plane inequalities are defined for this problem which result in an, otherwise prohibitively difficult, model of 42 nodes becoming easily solvable by a combination of cuts and Branch-and-Bound. Some of the cuts are entered in a pool and only used when it is automatically verified that they are violated. Other constraints which are generalisations of the subtour and combine qualities for the single period STSP, are identified manually when needed. Full computational details of solution process are given.

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More information

Published date: 1997
Keywords: travelling salesman problem, inequalities, cutting planes, branch-and-bound
Organisations: Operational Research

Identifiers

Local EPrints ID: 29657
URI: https://eprints.soton.ac.uk/id/eprint/29657
ISSN: 0926-6003
PURE UUID: 5d9d3089-0bc6-4aba-9e8b-e4f4c20f910a

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Date deposited: 06 Feb 2007
Last modified: 15 Jul 2019 19:08

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Contributors

Author: Martin Butler
Author: H. Paul Williams
Author: Leslie-Ann Yarrow

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