A node current-based 2-index formulation for the fixed-destination multi-depot travelling salesman problem

The travelling salesman problem forms a basis for many optimisation problems in logistics, finance, and engineering. Several variants exist to accommodate for different problem types. In this paper, we discuss the fixed-destination, multi-depot travelling salesman problem, where several salesmen will start from different depots, and they are required to return to the depot they originated from. We propose a novel formulation for this problem using 2-index binary variables and node currents, and compare it to other 2-index formulations from the literature. This novel formulation requires less binary variables and continuous variables to formulate a problem, resulting in lower computation times. Using a large benchmark the effectiveness of the new formulation is demonstrated.