A branch-and-cut algorithm for the target visitation problem

In this paper, we consider the target visitation problem (TVP) which arises in the context of disaster treatment. Mathematically speaking, the problem is concerned with finding a route to visit a set of targets starting from and returning to some base. In addition to the distance travelled, a tour is evaluated by taking also preferences into account which address the sequence in which the targets are visited. The problem thus is a combination of two well-known combinatorial optimization problems: the traveling salesman and the linear ordering problem. In this paper, we point out some polyhedral properties, develop a branch-and-cut algorithm for solving the TVP to optimality and present some computational results.