MATH-HEURISTIC FOR THE CAPACITATED TWO-ECHELON VEHICLE ROUTING PROBLEM

Abstract

In this paper, we propose a math-heuristic that combines mathematical programming techniques with a heuristic approach based on the Simulated Annealing metaheuristic to solve the Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP). This problem arises in the context of a distribution network that is divided in two levels: satellite facilities that connect customers to fulfilment centers where freight originates. As it is an NP-hard problem, the proposed approach combines a cluster-first route-second math-heuristic in which approaches are more appropriate, particularly for problem sizes that are more commonly found in practice. The results of the experiments with benchmark instances show that such cluster-first route-second math-heuristic approach utilizing package solvers (CPLEX and TSP CONCORDE) can effectively help solving the CVRP for small instances when compared to an exact method. The experiments conducted on benchmark instances demonstrated the effectiveness of the proposed “cluster-first, route-second” math-heuristic approach, which utilizes package solvers such as CPLEX and TSP CON-CORDE, in solving the CVRP for small instances, outperforming exact methods. This research contributes to demonstrating the potential applications of package solvers on heuristic structures for solving the CVRP. Although the presented math-heuristic has limitations, mainly due to the extensive usage of mathematical programming and the chosen characteristics of the implemented local search operators, it can quickly generate high-quality initial solutions for medium and large instances. By showcasing the “cluster-first, route-second” approach, this paper provides a framework that can be further improved by local search or embedded in other metaheuristics, such as GRASP or tabu search, and has practical implications for various industries.