New decision models for travelling salesman problem with time windows

Travelling Salesman Problem (TSP) is baseline for transportation, routing and scheduling problems. Travelling Salesman Problem with Time Windows (TSPTW) is the extension of TSP which has a lot of special cases. TSPTW is formed by adding special constraints, time windows, which are determined by the cities previously and the salesman must visit the cities between these time windows. TSPTW is a NP-hard and the combinatorial optimization problem like TSP. In the literature, there exist some decision models which have binary variables polynomially with different structures and properties. In this note, we present forthcoming models in the literature, their drawbacks and propose two new formulations. Performances of the newly proposed and existing formulations in terms of CPU times and linear programming relaxations are analyzed by the aid of the software directly. In addition to property of user friendly, we show the new formulations are the base for Vehicle Routing Problems (VRP).