A column generation algorithm for the team orienteering problem with time windows

The Team Orienteering Problem with Time Windows (TOPTW) is a well-known variant of the Vehicle Routing Problem (VRP) whose aim is to maximize the total amount of profit collected from the visited customers while taking into consideration some resource limitations. In this variant, customers must be served at most once in their time windows while respecting the predefined maximum travel time limit of each vehicle. In this paper we propose a column generation based algorithm to solve the linear relaxation of TOPTW. A dynamic programming algorithm is used to solve the subproblems in order to generate additional columns. Experiments conducted on the benchmark of TOPTW show the effectiveness of our algorithm and the strengthen of our formulation since we were able to prove the optimality of several instances by finding their integer solutions at the root node while solving the linear relaxation of the model.