THE 2-PERIOD TRAVELING SALESMAN PROBLEM APPLIED TO MILK COLLECTION INIRELAND

We describe a new extension to the Symmetric Travelling Salesman Probl em (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 p ossible Integer Programming Formulations are given. Valid cutting plan e inequalities are defined for this problem which result in an, otherw ise prohibitively difficult, model of 42 nodes becoming easily solvabl e 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 comb inequalities for the single period STSP, are ide ntified manually when needed. Full computational details of solution p rocess are given.