New Valid Inequalities for the Two-Echelon Capacitated Vehicle Routing Problem

We introduce new valid inequalities for the two-echelon variant of the Capacitated Vehicle Routing Problem (CVRP)In particular, a first group of inequalities is obtained by extending to 2E-CVRP some of the most effective among the existing CVRP valid inequalities. A second group of inequalities is explicitly derived for the 2E-CVRP and concerns the flow feasibility at customer nodes and the satellitecustomer route connectivity. The inequalities are then introduced in a Branch & Cut algorithm. Computational results show that the proposed algorithm is able both to solve to optimality many open literature instances and significantly reduce the optimality gap for the remaining instances

The two-echelon capacitated vehicle routing problem: models and math-based heuristics

Multiechelon distribution systems are quite common in supply-chain and logistics. They are used by public administrations in their transportation and traffic planning strategies, as well as by companies, to model own distribution systems. In the literature, most of the studies address issues relating to the movement of flows throughout the system from their origins to their final destinations. Another recent trend is to focus on the management of the vehicle fleets required to provide transportation among different echelons. The aim of this paper is twofold. First, it introduces the family of two-echelon vehicle routing problems (VRPs), a term that broadly covers such settings, where the delivery from one or more depots to customers is managed by routing and consolidating freight through intermediate depots. Second, it considers in detail the basic version of two-echelon VRPs, the two-echelon capacitated VRP, which is an extension of the classical VRP in which the delivery is compulsorily delivered through intermediate depots, named satellites. A mathematical model for two-echelon capacitated VRP, some valid inequalities, and two math-heuristics based on the model are presented. Computational results of up to 50 customers and four satellites show the effectiveness of the methods developed

The Two-Echelon Capacitated Vehicle Routing Problem

Multi-echelon distribution systems are quite common in supply-chain and logistic systems. They are used by public administrations in their transportation and traffic planning strategies as well as by companies to model their distribution systems. Unfortunately, the literature on com- binatorial optimization methods for multi-echelon distribution systems is very poor. The aim of this paper is twofold. Firstly, it introduces the family of Multi-Echelon Vehicle Routing Problems. Second, the Two-Echelon Capacitated Vehicle Routing Problem, is presented. The Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) is an extension of the classical VRP where the delivery passes through intermediate depots (called satellites). As in the classical VRP, the goal is to deliver goods to customers with known demands, minimizing the total delivery cost while considering vehicle and satellites capacity constraints. A mathematical model for 2E-CVRP is presented and some valid in- equalities given, which are able to significantly improve the results on benchmark tests up to 50 customers and 5 satellites. Computational re- sults under different realistic scenarios are presented

Two-Echelon Vehicle and UAV Routing for Post-Disaster Humanitarian Operations with Uncertain Demand

Humanitarian logistics service providers have two major responsibilities immediately after a disaster: locating trapped people and routing aid to them. These difficult operations are further hindered by failures in the transportation and telecommunications networks, which are often rendered unusable by the disaster at hand. In this work, we propose two-echelon vehicle routing frameworks for performing these operations using aerial uncrewed autonomous vehicles (UAVs or drones) to address the issues associated with these failures. In our proposed frameworks, we assume that ground vehicles cannot reach the trapped population directly, but they can only transport drones from a depot to some intermediate locations. The drones launched from these locations serve to both identify demands for medical and other aids (e.g., epi-pens, medical supplies, dry food, water) and make deliveries to satisfy them. Specifically, we present two decision frameworks, in which the resulting optimization problem is formulated as a two-echelon vehicle routing problem. The first framework addresses the problem in two stages: providing telecommunications capabilities in the first stage and satisfying the resulting demands in the second. To that end, two types of drones are considered. Hotspot drones have the capability of providing cell phone and internet reception, and hence are used to capture demands. Delivery drones are subsequently employed to satisfy the observed demand. The second framework, on the other hand, addresses the problem as a stochastic emergency aid delivery problem, which uses a two-stage robust optimization model to handle demand uncertainty. To solve the resulting models, we propose efficient and novel solution approaches

Path Planning for Cooperative Routing of Air-Ground Vehicles

We consider a cooperative vehicle routing problem for surveillance and reconnaissance missions with communication constraints between the vehicles. We propose a framework which involves a ground vehicle and an aerial vehicle; the vehicles travel cooperatively satisfying the communication limits, and visit a set of targets. We present a mixed integer linear programming (MILP) formulation and develop a branch-and-cut algorithm to solve the path planning problem for the ground and air vehicles. The effectiveness of the proposed approach is corroborated through extensive computational experiments on several randomly generated instances

A large neighbourhood based heuristic for two-echelon routing problems

In this paper, we address two optimisation problems arising in the context of city logistics and two-level transportation systems. The two-echelon vehicle routing problem and the two-echelon location routing problem seek to produce vehicle itineraries to deliver goods to customers, with transits through intermediate facilities. To efficiently solve these problems, we propose a hybrid metaheuristic which combines enumerative local searches with destroy-and-repair principles, as well as some tailored operators to optimise the selections of intermediate facilities. We conduct extensive computational experiments to investigate the contribution of these operators to the search performance, and measure the performance of the method on both problem classes. The proposed algorithm finds the current best known solutions, or better ones, for 95% of the two-echelon vehicle routing problem benchmark instances. Overall, for both problems, it achieves high-quality solutions within short computing times. Finally, for future reference, we resolve inconsistencies between different versions of benchmark instances, document their differences, and provide them all online in a unified format