Integer linear programming model ha

Integer linear programming model has been built for solving it. Furthermore, our numerical analysis illustrates that our proposed optimization problem, with a realistic problem size, can be solved by commonly available optimization software with a very promising performance. However, notice that the VRP is itself an NP-hard problem, and our proposed model focuses on coordinating two VRP models and hence is much more complex in computation. Thus, when the scale of served suppliers and customers is increased or the number of nodes in routes is increased, it will be very difficult to obtain the optimal solution within a few seconds or minutes. Therefore, like many prior studies on VRP in the literature, heuristic based approaches will play an important role to tackle the problem under such situations. In addition, this study does