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

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).


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

Item Type: Article
Digital Object Identifier (DOI): doi:10.1023/A:1008608828763
ISSNs: 0926-6003 (print)
Related URLs:
Keywords: travelling salesman problem, inequalities, cutting planes, branch-and-bound
Subjects: Q Science > QA Mathematics
H Social Sciences > HD Industries. Land use. Labor
Divisions : University Structure - Pre August 2011 > School of Mathematics > Operational Research
ePrint ID: 29657
Accepted Date and Publication Date:
Date Deposited: 06 Feb 2007
Last Modified: 31 Mar 2016 11:55

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