The multiple traveling purchaser problem

The traveling purchaser problem (TPP) is a generalization of the well-known traveling salesman problem (TSP) and has many real-world applications, such as purchasing required raw materials for manufacturing factories, scheduling a set of jobs for certain machines, and many others. TPP also could be extended to the vehicle routing problem (VRP) by incorporating additional constraints, such as multi-purchaser, capacity, distance, and time restrictions. In the last decade, TPP has received the attention of some operational researchers. However, it has not received the same amount of interest as TSP and VRP. Therefore, there are no studies for the multiple TPP. The purpose of this paper is to introduce the ILP formulation for capacitated and uncapacitated multiple TPP.