Branch-cut-and-price algorithms for two routing problems with hotel selection

The Traveling Salesperson Problem with Hotel Selection (TSPHS) and the Orienteering Problem with Hotel Selection (OPHS) are combinatorial optimization problems that arise in various real-world applications, from logistics to tourism. Both problems consider a set of customers and hotels and aim to find a sequence of concatenated trips limited in time. A trip is defined as a sequence of visited customers, starting and ending at hotels, such that any other nodes are customers. The main differences between the problems are the following. The TSPHS assumes that all customers are visited and involves two hierarchical objectives: reducing the number of trips and minimizing the total travel time. On the other hand, in the OPHS, not all customers are required to be visited; rather, each customer is associated with a positive profit, and the objective is to maximize the total profit related to the visited ones. In this paper, we propose exact branch-cut-and-price algorithms for these problems that are coded within the VRPSolver framework. For TSPHS and OPHS, we show that the proposed methods outperform the best exact models from the literature and optimally solve most of the open benchmark instances.