A hybrid constructive mat-heuristic algorithm for the heterogeneous vehicle routing problem with simultaneous pick-up and delivery

Abstract

In this paper, a variant of Vehicle Routing Problem, called Heterogeneous Vehicle Routing Problem with Simultaneous Pick-up and Delivery (HVRPSPD), is considered. The HVRPSPD can be defined as determining the routes and vehicle types on each route in such a way that the pickup and delivery demands of each customer must be performed with same vehicle, while minimizing the total cost. We propose a mathematical model for the problem and some valid inequalities for the model. Since the HVRPSPD is an NP-hard problem, the proposed mathematical model can be used to find the optimal solution for the small-size problems. Therefore we propose a hybrid mat-heuristic approach based on the formulation and Local Search to solve medium and large-size HVRPSPDs. A series of experiments is performed to evaluate the performance of proposed algorithm. Computational results show that hybrid mat-heuristic is computationally efficient to find good quality of initial solutions.