Traveling Salesman Problem with Hotel Selection: Comparative Study of the Alternative Mathematical Formulations

Abstract

Tour scheduling has a central importance in logistics in service-based industries. Many logistics and distribution planning problems can be modeled as a variant of the Traveling Salesman Problem (TSP). One such variation is the TSP with Hotel Selection (TSPHS) in which a salesman needs to visit a group of cities in a way that the cities are visited via a number of trips whose lengths cannot exceed the maximum length a salesman can cover in a day. Each of the trips starts and ends at a hotel. Moreover, the hotel location where the salesperson ends one day has to be the same as the starting hotel for the next day. The TSPHS is one of the node routing problems and has interesting practical applications in real-life. This study constitutes of the comparison of mathematical formulations which are already exist in the literature with the formulations which have new adaptations for sub-tour elimination constraints.