An optimal solution procedure for the multiple tour maximum collection problem using column generation

The Multiple Tour Maximum Collection Problem (MTMCP) is closely related to the classical Traveling Salesman and Vehicle Routing Problems. One major difference with the MTMCP is that it is not possible to visit all of the nodes in the graph in the total time allocated on a given set of tours. However, with the MTMCP, a reward is collected from each node that is visited. The objective of the MTMCP is to determine which nodes to visit on m time-constrained tours for which the total reward collected is maximized. It is assumed that each tour begins and ends at a central depot and that each node can be visited no more than one time, on at most one tour. In this paper, an optimal solution procedure is presented for the MTMCP. This procedure is based on a set-partitioning formulation and makes efficient use of both column generation and constraint branching. Numerical results are presented which show that this optimal procedure can be used to solve problems of realistic size in a reasonable amount of time.